MODELS OF NON-WORK ACTIVITY DURATION
by
JESSE JACOBSON
Inge'nieur Diplom6 de l'Ecole Polytechnique F6drale Lausanne
(1975)
S.M., Massachusetts Institute of Technology
(1977)
Submitted in partial fulfillment
of the requirement for the degree of
Doctor of Philosophy
at the
Massachusetts Institute of Technology
February 1979
Signature of Author...................y.-....-..............................-.
Department of Civil Engineering, September 22, 1978
Certified by..................r..rr.- ...r7K.'a s..o.'..***....s-.----
ThpzSupersor
Accepted by.....................---y -'-LV160 .a ---..- 6r-a---t...------------
Chairman, Departmental Commitee on Graduate Students of the
Department of Civil Engineering
Archives
(N4:~I
ABSTRACT
MODELS OF NON-WORK ACTIVITY DURATION
by
JESSE JACOBSON
Submitted to the Department of Civil Engineering on September 22, 1978
in partial fulfillment of the requirements for the degree of Doctor
of Philosophy.
This study describes both theoretical and empirical models of non-
work activity patterns (duration and participation). Most current research
has neglected to regard travel demand as demand derived from more basic
needs such as non-work activity patterns. By better understanding the
decision process that leads to non-work activity participation, however, it
is possible to obtain more realistic predictions of travel behavior. In
particular, this study considers that activity patterns, and not travel, are
the "commodities" that are subject to two types of constraints, monetary and
temporal. Thus, it is assumed that decision makers act as utility maximizers,
subject to the two types of constraints.
Empirical models of individual activity participation are estimated
for three types of non-work activities: shopping, social/recreation, and
remaining activities. The sample used for estimation is obtained from a home
interview survey collected in the Minneapolis-St. Paul area in 1970.
Socioeconomic, land-use, and transportation level-of-service data are used.
Two model types are developed. The first model assumes that individuals act
independently of other members of their household. The second model relaxes
the independence assumption. and assumes that household members decide
jointly on activity patterns.
The analysis of the policy predictions suggests that transportation
level-of-service changes impact significantly on activity patterns, primarily
for travel time policies (in- and out-of-vehicle times). In particular, a
decrease in the speed of travel decreases activity duration for all the
activities modelled, and decreases the total time individuals spend travelling.
The importance of socioeconomic characteristics is also significant. Speci-
fically, the possession of a driver's license, which represents the desire
for vehicular mobility, has a large impact on activity patterns. The estimati-
on of models for the joint activity patterns within the household has not
been entirely satisfactory, and further research on this topic is suggested.
2
The feasibility of modelling activity pattern and the importance of
such models in predicting travel impacts indicate the direction for future
development. In particular it is suggested to investigate further the
complex nature of the travel-related choice structure, both theoretically
and empirically.
Thesis Supervisor:
Title:
Moshe E. Ben-Akiva
Associate Professor of Civil Engineering
3
ACKNOWLEDGEMENT
Financial support for this research was provided in part through the
Program of University Research Contract No. DOT-OS-70054. Data for the
empirical study were obtained through the cooperation of the staff of the
Metropolitan Council of the Twin Cities in Minneapolis-St. Paul, Minnesota.
The help of my thesis advisor, Professor Moshe Ben-Akiva, was parti-
cularly appreciated. Professor Steven Lerman has been my principal advisor
for some sections of the research, in particular for the development of
the econometric models. Professors Marvin Manheim has been of guidance
in setting the conceptual framework in the earlier stages of the research,
and has reviewed and commented on the final draft. Professor Joel Horowitz
has kindly reviewed and commented on the final draft. David Damm, Harro
Volkmar, and my other friends at M.I.T. have been both a source of inspi-
ration and encouragement. Thanks to all. Earlier drafts and the final
document were typed by Caterina Gentile.
4
TABLE OF CONTENTS
Page
TITLE PAGE ................................. 1
ABSTRACT-.......................................................--2
ACKNOWLEDGEMENTS.................................................4
TABLE OF CONTENTS.............................. ................ 5
LIST OF TABLES................................................... 8
LIST OF FIGURES................................................10
CHAPTER 1: INTRODUCTION........................................11
1.1 Background...............................................11
1.2 Behavioral Issues......................-----.-----.12
1.3 Definition of Terms Used in this Research...............13
1.4 Research Objective.......................................14
1.5 The Approach............................................ 14
1.6 Summary of Major Findings................................15
1.7 Outline of the Remaining Chapters........................17
CHAPTER 2: LITERATURE REVIEW.................................18
2.1 Introduction............................................ 18
2.2 Economic Theory of Time Allocation,......................18
2.3 Descriptive Studies of Activity Duration................20
2.4 Constraints on Activity Duration........................23
2.5 Parametric Models of Activity Duration-..................26
2.6 Conclusions............. .........-....... 27
5
Page
CHAPTER 3: DATA ANALYSIS......................................29
3.1 Introduction........................................... . 29
3.2 The Data Base.......................................... . 29
3.3 Assumptions in Data Processing..........................33
3.4 Conclusions.............................................38
CHAPTER 4: THE THEORETICAL MODEL OF NON-WORK ACTIVITY
DURATION......................................... 39
4.1 Introduction........................................... . 39
4.2 Theory of Time Allocation Revisited....................39
CHAPTER 5: ECONOMETRIC MODELS.................................45
5.1 Introduction........................................... . 45
5.2 Single Equation Limited Dependent Variable Model. --.. 46
5.3 Extension of the Single Equation Limited Dependent
Variable Model..........................................48
5.4 Simultaneous Equations Limited Dependent Variable
Model................................................. 50
CHAPTER 6: EMPIRICAL MODELS................,55
6.1 Introduction.......................................... 55
6.2 Specification of the Models............................ 56
6.3 Estimation Results......................................63
CHAPTER 7: IMPLICATIONS OF THE ESTIMATED MODELS...............87
7.1 Introduction............................................87
7.2 Activity Patterns for Transportation Level-of-Service
Changes................................................87
7.3 Future Changes in Activity Patterns................... 92
6
CHAPTER 8: SUMMARY AND CONCLUSIONS...--......---.--..------ 106
8.1 Summary......................................--------.106
8.2 Recommendations and Directions for Further Research.... 109
APPENDIX I: THEORY OF ACCESSIBILITY.......................... 114
REFERENCES............................................--.......124
7
LIST OF TABLES
Table No.
6-1
6-2
6-3
6-4
6-5
6-6
6-7
6-8
6-9
6-10
7-1
7-2
7-3
7-4
7-5
Title Page
Average Total Activity Duration for Persons
Participating in the Specific Activity........65
Statistics for Accessibility Measures.........66
Individual Shopping Duration Model............68
Individual Social/Recreation Duration
Model........................................ 70
Individual Remaining Activities Duration
Model........................................ 72
Model of Shopping Activity Time for Male Head
of Household.................................. 77
Model of Shopping Activity Time for Female
Head of Household.............................78
Model of Travel Time to Shopping
Destinations................................. 81
Model of Travel Time to Social/Recreation
Destinations................................. 83
Model of Travel Time to the Remaining Activity
Destinations................................ 85
Base Values for the Exogenous Variables of
the Activity Duration Models for Use in
Level-of-Service Policy Predictions...........89
Measures of Activity Duration and Travel for
Level-of-Service Policies.....................91
Definition and Frequency of the Market
Segments in the Population....................94
Base Measures of Shopping Duration............95
Base Measures of Social/Recreation
Duration.................................... 96
8
Table No.
7-6
7-7
7-8
7-9
I-1
1-2
Title
Base Measures of Remaining Activity
Duration...............................
Effect of Socioeconomic Characteristics
on Activity Duration......................
Activity Program Changes for Increased
Female Labor Force Participation.........
Activity Program Changes for Increased
Possession of Driver's Licenses...........
Shopping Destination Mode Choice Model....
Social/Recreation Destination Mode Chocie
Model.....................................
9
Page
97
99
102
104
121
122
LIST OF FIGURES
Figure No.
3-1
3-2
6-1
6-2
I-1
1-2
Title
Items of Information Gathered in the
Home Interview Survey...................
Example of Allocation of Travel Time
to Activity...........................--
Variables for the Shopping Person
Model...................-..........--..-.
Variables of the Social/Recreation Person
Model...................................
Basic Choice Hierarchy.................
Non-Work Choice Hierarchy...............
10
Page
31
37
61
62
117
119
CHAPTER I
INTRODUCTION
1.1 Background
Extensive effort has been devoted in the past to the understanding of
non-work travel patterns. It has, in fact, been shown in several instances
(Adler and Ben-Akiva, 1976; Adler, 1976; Ben-Akiva, et.al. 1977; Oster, 1978)
that in many transportation planning contexts one cannot ignore the impact
of policy changes on non-work travel patterns. Specifically, the low
transaction costs involved in even the most radical changes in non-work
activity patterns suggest a sensitivity to changes in transportation
service which is different in magnitude than the response of travel to
work. Moreover, the daily volume of non-work travel is significant, and
ignoring it would bias considerably the forecasts of impacts of specific
policies. An analysis of survey data collected in the Washington, D.C.
metropolitan area in 1968 revealed that home based work trips account for
less than forty percent of the daily automobile vehicle-miles travelled
and less than forty percent of the daily emissions due to auto travel
(Horowitz, 1974). Also, analysis of these data show that, in Washington,
D.C., only fifty-three percent of the morning peak hour traffic are home
based work trips (Jacobson, 1977).
It is commonly recognized that non-work travel is more flexible than
work travel since, as mentioned above, it involves lower transaction costs.
As an example, an individual's response to a gasoline price increase might
be to participate less often in social/recreation or shopping activities.
11
This is in constrast with the expected response of the same individual to
the same pricing policy when considering alternative modes or routes for
the trip to work. The individual is, in the latter case, willing to "absorb"
a much higher gasoline price increase (for example by shifting to the more
inconvenient public transportation) before deciding to change job or
residential location.
1.2 Behavioral Issues
Models currently available for predicting consumers' responses to
transportation policy have been limited in a number of ways. First,
although it has been recognized for some time that travel demand is derived
from demand for more basic activities, current models have not incorporated
this notion explicitly.
Second, most available models do not explicitly incorporate time
constraints as determinants of the daily activity patterns. In order to
test the impact of temporal policies such as flexible work schedules
(flexi-time), four-day work week, stores' opening hours, etc., it is just
as important to determine which destinations are within reach of the
consumers as it is to determine by which mode they will go.
The purpose of this study is to start the development of a methodology
that explicitly addresses the above issues. The major aim of the past
research on non-work activity patterns has been to understand and develop
a theory of short-run behavioral response to changes in the socioeconomic
and demographic characteristics of the population. However, few of the
studies have developed econometric models; most of the empirical research
has been limited to data analysis with categorization of the population
12
into subgroups having similar behavior. Moreover, little inquiring has
been made into the linkage of travel-related activity patterns and
transportation level-of-service. It is the purpose of this research to
develop both a behavioral theory and parametric models that allow better
understanding of the most important factors that influence activity
duration, with specific emphasis on transportation level-of-service.
1.3 Definitions of Terms Used in This Research
Activity patterns is the all-inclusive term defining the components
of the travel-related activity decisions. The two major dimensions of
activity patterns are activity duration and travel patterns. Activity
duration is the time allocated to the activity under consideration.
Total activity duration includes both the time actually spent performing
the activity, and the travel time to and from the activity; net activity
duration excludes travel time. The travel 2attern includes all the
components of travel such as travel time, origin, destination, mode of
travel, routing, time of day, etc. A non-work activity program is the
set of durations for all non-work activities summed over the day, by
purpose. Other general terms such as sojourns, tours, home based tours
and home-work based tours, are used and, because they have a specific
meaning in this research, their definition is included. A sojourn is a
stop at a destination other than home, work or school. Work and school
travel are choices made within a longer time frame than travel for
purposes such as shopping, social/hecreation, etc. When non-work/non-
school travel is analyzed, choices related to the work or school travel
are considered exogenous. A tour is a trip that starts and ends at the
13
same place. A tour can include soujourns. For illustrative purposes, assume
the following travel diary: home-shopping-work-social/recreation-personal
business-work-home. This diary is composed of a home based tour and a
work based tour; one sojourn for the home based tour, the shopping destination,
and two sojourns for the work based tour, the social/recreation and
personal business destination. For convenience another type of tour is
defined: the home-work based tour. Home-work based tours are a subset
of the home based tours, and include trip sequences that start at home and
end at work, with or without sojourns.
1.4 Research Objective
The scope of this research is somewhat limited by the complexity that
the development of a comprehensive activity pattern theory would involve.
A more limited set of objectives was selected as follows:
1) To better understand decision maker behavior in
allocating time to non-work activities,
2) To investigate the feasibility of modelling directly
the participation in those activities for which
motorized travel is only the means of access,
3) To analyze the sensitivity of activity duration and
travel time to different transportation scenarios
(pricing policies, auto restraint policies, etc), and
4) To analyze the impact of demographic and socioeconomic
trends on activity patterns.
1.5 The Approach
The approach taken was to develop a general theory of behavior with
respect to activity patterns and to estimate models using a currently
available data base. Transportation level-of-service, one of the deter-
minants of activity patterns, is specifically included in the models that
14
predict the duration of different non-work activities (such as shopping,
social/recreation and remaining activities) on an average weekday.
The activity duration models are statistically estimated using a
limited dependent variable model. This model is written as a regression
equation with the addition of a restriction on the range of values that
the dependent variable can take. This type of estimator, first proposed
by Tobin (1958), is well adapted to activity duration modelling since
activity duration cannot take values lower than zero or higher than the
total amount of time allocated to non-work activities. The empirical
models are estimated using a data base collected in 1970 in the Minneapolis-
St. Paul metropolitan area. The usefulness of the data base for modelling
activity patterns is somewhat limited since it was primarily collected for
conventional travel demand modelling. However, this data base was selected
for this research because of its immediate availability and because the
recording of travel information is complete. The data base includes a
home interview survey of a 1% random sample of households, transportation
level-of-service attributes for each zonal pair in the metropolitan
area, and zonal-level land-use information. The home interview survey
includes a diary-type survey with travel information for each individual
reported only for one day.
1.6 Summary of Major Findings
This research includes theoretical and empirical results which are of
particular interest in the analysis of current issues in transportation
planning. The theoretical section presents the utility maximization
framework developed for activity duration modelling and discusses the
importance of accessibility as a determinant of activity patterns.
15
The models developed in the empirical section are sensitive to
transportation level-of-service and to socioeconomic and demographic
characteristics of the individuals. In general the results suggest that
shifts in level-of-service (cost and time) cause significant changes in
activity programs and in travel times. The elasticity of activity
duration with respect to in-vehicle and out-of-vehicle time is very
significant. The elasticity with respect to out-of-pocket cost is,
however, much smaller.
The changes in activity programs due to shifts in population charac-
teristics are also quite significant. Specifically, the most important
characteristic is whether the individual has a driver's license, which
can be interpreted as an indicator of the desire and capability for
mobility. The activity duration elasticity with respect to the work
status is small. This suggests that, if in the future the duration of
the work day were to decrease, individuals would allocate a large pro-
portion of their new "leisure" time to in-home activities.
The predicted effect of the increased participation of women i:
the labor force on non-work activity duration is small. Much more
significant is the effect of an increased number of individuals with
driver's licenses. In fact, for all activity types, the possession of
a driver's license yields longer and more frequent participation in all
activities.
Overall, the results of this research suggest that the analysis of
activities has great potential for understanding travel related choices.
This is all the more relevant in travel demand analysis if the importance
of travel characteristics is appropriately considered.
16
1.7 Outline of the Remaining Chapters
Chapter II reviews current literature in the field of activity
duration. Both theoretical and statistical contributions are analyzed
in this chapter. Chapter III presents the data base used in this
research, and some of the aggregate characteristics of the population
such as average activity duration by activity type, activity participation
rates, etc. Chapter IV develops a theoretical framework for activity
duration based on the economic theory of utility maximization. Chapter
V discusses the statistical issues involved in estimation of activity
duration models. Chapter VI presents the empirical results of model
estimation. Prototypical predictions using the estimated models are
presented in Chapter VII. Finally, in Chapter VIII, the results of this
research are summarized and recommendations are given for further research.
17
CHAPTER II
LITERATURE REVIEW
2.1 Introduction
This chapter reviews the literature on activity patterns which is
the most relevant to this research, placing particular emphasis on
activity duration.
The chapter is divided into five sections. The first section pre-
sents studies in micro-economic theory of time allocation, based on the
general framework of the theory of choice and utility maximization. The
second section presents studies which have tried to identify the exogenous
determinants of activity patterns through descriptive data analysis.
The third section presents another significant body of literature which
develops the theoretical concepts of physical reach and constrained time
budgets. The fourth section presents the results of parametric models
of activity patterns. The fifth section, the summary, reviews the
state of the art and discusses the relevance of existing studies to the
objectives of this research.
2.2 Economic Theory of Time Allocation
The most general and most innovative theoretical formulation of time
allocation can be found in Becker (1965). He suggests that households
act both as producers and as utility maximizers. As producers, households
combine basic commodities such as time and market goods to produce
activities. As utility maximizers, they purchase the commodities in the
optimal mix. The fundamental result of Becker's theory is that the
18
marginal utility of activity is directly porportional to the shadow price
of money and to the full price of a unit of activity. The full price of
an activity is the sum of the prices of the goods and time used per unit
of activity. If the full price of activity i increases, i.e. if either
the price of goods or time used to produce one unit of activity i goes up,
then, at the optimum, the marginal utility of activity i increases. As
an example, if the price of movies were to increase, the optimal marginal
utility of movies at optimality would increase. Since it is reasonable
to assume that the movie-going activity has positive and diminishing
marginal utility, an increase in marginal utility implies a decrease in
the optimal "quantity" of movie-going.
A review of more recent economic work on the value of time is found
in Watson (1974). Watson presents all the work done since Becker's
innovative paper as an extension of the original theory of time allocation.
Specifically, variables such as work duration, and wage rate were included
as decision variables of the time allocation process.
More recently, Gronau (1977) has presented theoretical findings
showing that "the average wage rate can be used as, at best, a very crude
approximation of the value of time". He demonstrates that there is no
unique value of time, and that it is important to recognize its variation
across individuals (because of socioeconomic and demographic characteristics)
and most significantly across activities.
The theoretical approach proposed in this research will combine Becker's
theory of time allocation, with Gronau's findings on cross-sectional
variability of consumer behavior.
19
2.3 Descriptive Studies of Activity Duration
While a number of studies have reported results of descriptive
analysis on activity duration, Chapin (1974) is the most complete study.
Chapin develops a classification method based on both theoretical and
empirical results. His method combines a-priori knowledge of the factors
influencing the activity program with analysis of empirical observations.
The results of Chapin's study suggest that the "preconditioning and pre-
disposing factors" of activity patterns behavior are the decision-making
role in the household and the mix of sex, breadwinning and child care
roles. Chapin also suggest that some personal characteristics are people's
age, stage in life-cycle, and general level of health. Needs are also
included as determinants of activity patterns and two main categories
can be identified: subsistence needs and culturally, socially and
individually-defined needs. Similar conclusions were derived by Kutter
(1973), who proposes a classification of individuals along the dimensions
of age, sex, stage in family life cycle, and females' work status.
Based on this classification, Kutter assumes that, in the aggregate,
the activity patterns for specified groups are, within the period of one
day, similar to the activity patterns of a single person during a longer
period (e.g. one month). Empirical tests which Kutter performed on a
sample of observations confirm, at least in the aggregate, this theory.
A study by Bullock et.al. (1974) analyzes data collected at two
different colleges and finds that the significantly different time
allocation in the two groups was due primarily to different class
schedules in the two schools. One of the schools left plenty of time
20
for lunch, and the other little or no time, Yeung and Yeh (1975) find that
inhabitants of two distinct settlements (one a squatter and one a public
housing project) allocate similarly their "obligatory" activity pattern,
but show significant differences in their leisure time activity pattern.
They concluded that both social and locational dimensions, such as
employment and housing type (apartment, squatter settlement, etc.) influence
time allocation.
A theoretical study by Doob (1971) emphasizes the importance of
activity duration as a determinant of activity patterns by suggesting
that the value of an activity is positively correlated with the frequency
of participation and its duration. Chapin gives an additional justi-
fication of the study of activity duration. He proposed to use it as
a description (or common measuring unit) of the "intensity" of parti-
cipation in different activities in the urban system. Nevertheless, he
warns that time allocation alone cannot fully describe the activities
and that, in particular cases, additional measures need to be specified.
Chapin's study also looks at the dynamic process by which the
individual's actions are motivated, produce a choice and finally yield
an outcome. The most important element in this process is the initial
motivational drive whose characteristics can vary across individuals
(or groups of individuals). Recognizing this variability, Brail and
Chapin (1973) state that individuals don't all have equal access to
opportunities, and that their status is an essential determinant of
their motivation. This is why it is very important, in human activity
pattern studies, to segment (or group) the population into categories
21
according to income, work status, sex role and family responsibility. Doob
(1971) discusses what he believes is the ability to formulate good pre-
dictions of behavior of a group member. In order to do this he classifies
the population along characteristics which include age, sex, occupation,
social status, beauty and strength.
Chapin points out that the essential purpose of activity pattern
studies is to detect "a tendency for a population to behave similarly".
This leads to the necessary simplification of grouping acts into activity
classes. It is thus possible to "define behavior patterns that are
common to whole groups of people". But grouping of acts is not done
solely for the purpose of finding commonalities, but also to facilitate
analysis. As an example, if our concern is with the shopping activity,
a very detailed definition of the in-home activities might not be
necessary.
A discussion of limitations of previous activity program studies is
presented by Szalai (1972). First of all, noting that "individuals often
perform several activities at the same time", he warns of the importance,
when trying to describe individuals' motivations and behavioral drives,
of identifying whether individuals perform joint activites (such as
listening to music while reading, taking a walk while window shopping, etc.)
or independent activities. Michelson and Reed (1975) note that, in
questionnaires, usually only one activity is reported for a specific
time period, thus rendering impossible the analysis of simultaneously-
executed activities.
22
Another issue that Szalai discusses is that very few studies have
"added an analysis of the timing of daily activities to the analysis of
their duration", although "some highly characteristic features of social
life in the industrial age are connected with timing: office hours,
rush hours, shifts, timetables...". Moreover few time-budget studies
have looked into a theoretical model of the sequential structure of
people's daily agenda. This issue has, however, been investigated in
some detail by Stone (1972). After briefly presenting Markov models of
time-budget, Stone suggest that they don't address the complexities of
the observed data. Stone's personal contribution is the theoretical
development of "path analysis models of causality" and of a "process
model". The main purpose of the models of causality is to trace and
quantify the dependency of one variable (or event) of the model on
another. Although the "causal analysis" process is self-explanatory,
Stone does not suggest what type of procedure should be used to quantify
the dependencies. The "process model", on the other hand, "attempts to
represent the decision making that goes into determining time allocation."
Stone suggest that this model should be used to find decisions which
are common to a certain class of individuals, in order to simulate
behavior of population groups.
2.4 Constraints on Activity Duration
Another area of research has been the study of individual's activity
patterns under spatial and temporal constraints. This area has been
pioneered by Hagerstrand (1970) whose theoretical framework presents the
concept of physical reach. The space of reach is the dimensional volume
23
(two geographical coordinates and one temporal coordinate) that an individual
can visit given his schedule and travel speed constraints. Hagerstrand
shows that the space defined by the individuals' constraint is a prism.
It is useful here to discuss in more detail some of H'agerstrand's ideas
which will be the base of the theoretical development presented in
Chapter IV.
Assume a city with no barriers and constant airline speed of travel.
An individual travelling in the city is limited in the locations he can
reach, given his origin, and given he has to reach a destination at a
particular time. In the simplified case where the origin and the final
destination of a tour are the same (a simple example of this could be a
home-shop-home tour), and the individual has m minutes available for the
activity, different scenarios can occur:
- The individual remains at the origin (no-travel option)
- The individual travels for t minutes (0Om<T) and spends
T-m time at the destination(s) of his choice
The physical reach for the first scenario is straightforward; the
individual has only his origin as space to perform his activities. For
the second scenario, the individual can reach all destinations that are
within m/2 min. travel time from his origin. The maximum surface that
encloses this activity pattern is a circle of radius (sem/2) where s
is the speed of travel. At the upper bound of m=T the individual can
reach destinations at a distance of (s'T/2), but cannot perform any
activity at the destination(s).
24
Assume now that the individual's origin is not the same as his final
destination. Given that the individual decides to travel for m minutes
(not including direct travel from the origin to the destination of the
tour), the maximum surface of intermediate destinations available to
him is enclosed within an ellipse with distance from any point of the
ellipse to the foci of (sem).
Lenntorp (1976) has formalized this concept of reachable domains.
Lenntorp's contribution is a more rigorous framework of analysis and
an empirical application to a model of simulation of urban travel.
An additional contribution to the study of time budgets can be
found in recent work by Zahavi (1977), Zahavi's primary assumption is
that a travel pattern can be predicted through constraints on travel
time and money expenditures that restrict the consumer's set of possible
choices.
Somewhat different from previous studies is the approach to the
understanding of activity patterns adopted by Jones (1976). Jones is
more interested in the "physical representation of the human activity
approach to studying travel behavior". The emphasis of his study is
on the scheduling of activities and the process by which individuals
satisfy their needs without violating the constraints. Jones assumes
that the household acts as a single decision-making entity, and his
research methodology tries to describe the complex process of intra-
household duty-sharing. Unfortunately this approach, although very
attractive from a theoretical perspective, does not, at this stage of
its development, lend itself to simplification for use in mathematical
modelling.
25
2.5 Parametric Models of Activity Duration
Bain (1976), in an empirical application of a model for activity
time allocation, used a limited dependent variable model of the type
proposed by Tobin (1958) and Amemiya (1973). Bain proposed four
categories of explanatory variables: activity characteristics, travel
mode and trip characteristics, socioeconomic characteristics of the
individual and of his or her family, and the distribution of locations
where the activity can be performed9 However, due primarily to limitations
in the data base, only total activity time (total travel time and destination
time) and socioeconomic information were specified for the actual model
estimation.
Four activity duration models were estimated for combinations of
two groups of activities, shopping-personal business and social/recreation,
and for two time periods, weekdays and weekend. The results show the
significant differences in the prediction of activity duration between
the weekday and the weekend model. The estimated models were used in
forecasting the impact of a four-day week on non-work activity duration,
and showed that on the free weekday both shopping-personal business
and social/recreation activity increase by approximately 20%, in part
offsetting the reduction in travel due to the elimination of the trip
to work. Oster (1978) investigated non-work trips in close relation to
work trips. Using alternative assumptions on consumer's behavior, Oster
estimated a model for the prediction of the use of work trips to visit
non-work destinations. The exogenous variables in this model are house-
hold income, the number of household members over 15 years of age, the
26
number of household members ages-5 to 15, the number of household members
age less than 5, accessibility indices for the residence, workplace of
the head and workplace of the second worker, and dummy variables for the
availability of a second (and third) automobile, and for the second
worker in the household. Osterls results suggest that, among these
variables, the primary determinants of the use of the work-related trip
to visit non-work destinations are household income, the household size
and number of children under 16 years of age, and the presence of a
second worker in the household.
2.6 Conclusions
It appears, from the review of the literature, that most of the work
in activity patterns has been devoted to descriptive analysis of observed
behavior. Very little work has been done in integrating the theoretical
framework of activity patterns with empirical observations. In particular,
the work by Becker, Doob, Hagerstrand, Gronau and Szalai presents a
discussion of theoretical models but derive only qualitative conclusions
on activity patterns. Work by Bain, Chapin, and Kutter, on the other
hand, is more empirical in nature, and presents a theory of activity patterns
which relies heavily on observations rather than on a more structured
model of behavior. Only the models of constrained behavior (Lenntorp
and Zahavi) have been somewhat able to integrate theoretical and empirical
findings into an analytical framework. Nevertheless, present theory of
constrained behavior is incomplete. In fact, the assumptions that
individuals behave solely according to constraints does not explain the
evident trade-offs that individuals face when making decisions. If an
27
individual goes from his home in the suburbs to a downtown shopping center,
this implies not only, as constrained behavior modelling suggests, that
he has time and money available; it also implies that downtown shopping
is more desirable than, say, shopping at the nearby mall.
It is the purpose of this research to bridge the gap still existing
between theoretical and empirical studies. Based on the previous studies,
this research develops a theory that considers activity patterns to be
derived from a utility maximization process subject to physical constraints
(such as time and cost). The major factors that cause people to choose
among alternative activity patterns include socioeconomic, demographic
characteristics, and transportation level-of-service, The remaining
chapters present the theory and the model estimation results.
28
CHAPTER III
DATA ANALYSIS
3.1 Introduction
The purpose of this chapter is to discuss the data base used in this
research and the data processing required for estimation of the models of
activity duration. The data base was originally collected in Minneapolis-
St. Paul, Minnesota, for use in a conventional urban transportation study.
It contains a one day diary-type home interview survey, transportation
level-of-service derived from networks and land-use information. The
main reason for choosing this data base were the easy access to it and
the fact that the survey was conducted in 1970, a census year.
3.2 The Data Base
The data was collected as part of the Travel Behavior Inventory (TBI)
conducted by the Metropolitan Council of the Twin Cities Area, between
April and July 1970 in the Minneapolis-St. Paul metropolitan area. The
home interview survey, the transportation level-of-service, and land-use
information which were used in this research are part of the TBI study.
The Home Interview Survey(*
The home interview survey is a 1% random sample of households in the
Minneapolis-St. Paul metropolitan area drawn from electric utility records
and consisting of 5,700 interviews. The usable portion of the survey
The home interview survey is described in detail in Metropolitan Council
of the Twin Cities Area (1974) and Mid-continent Surveys, Inc. (1970a,1970b).
(**)The original survey data contained severe coding errors. Observations
which contained such coding errors were excluded from the estimation sample.
29
includes 5,009 households and a total sample of 15,416 individuals.
Information is collected at the household level (mainly for socioeconomic
data), at the person level (mainly socioeconomic data), and at the trip
level (mainly data on reported level-of-service, timing and purpose of
the trip). The list of the principal items included in the survey is
presented in Figure 3.1. The trip-level diary covers a 24-hour time
period going from 4:00 AM of the day preceding the interview to 3:59 AM
of the interview day. The travel information recorded in the survey
is fairly complete; specifically, information is available on the number
of public transportation transfers (if transit was used), on the auto-
mobile parking cost (if auto used) and the purpose of the activity at
the destination. Nine different types of activities are recorded on the
survey: in-home activities, work, school, shopping, outdoor recreation,
other social or recreational activities, medical (doctor, dentist, etc.),
personal business (bank, barber, lawyer, etc.), and picking up or dropping
off a passenger. No additional information is available and heterogeneous
activities such as shopping (i.e. shopping for food, for clothing, for
furniture) are coded in one category. Morever only one activity can be
recorded for a given sojourn, typically the primary activity for that
sojourn. A change of activity during the same sojourn is not recorded;
if an individual goes to a mall and has lunch before the shopping visit, the
purpose of the sojourn will be recorded as a shopping, with an evident
over-reporting of shopping duration and under-reporting of social/recreation
duration.
(***)While the day for which travel is to be reported is fixed for each house-
hold, call-backs were made up to three days after that day.
30
Figure 3.1
ita: of Information Gathered in the Home Interview Survey (*)
For Each Household Fer Each Person
Type of dwelling(owner/renter, single
family/two family/(multi-familY)
Household type (families with/without
children marital status, age groups)
lncont classification
Car ownership and car availability
(includes company-owned cars and
friends' cars available for use)
Tenure at address
Previous residence (location)
Hlousehold relationship
Sex
Ae
Work Status
E:ployment
Work Place
Driver's license
Nimbar air trips in past
12 months
Reason for changing residence
Usual shopping place (except
for food and drugs)
Reason for shopping there
1oW long shopped there
Previous shopping place
Reason for changing shopping place
Weekend recreatinrl trip=
Travel date
Place of origin/
destination
Purpose
Land activity types
at trip end
Mode of travel
Time/duration of
trip
Blocks walked to or
from auto or bus
Time waited for bus
Number transfers
Fare
Auto availability (if
trip made by bus)
Auto parking type/
cost(for driver only)
Persons in car
Carpasi
Bridge crossings
Freeway usage
Bus availability (if.
person made trip by
auto)
Comparative bus data
(*)Source: Metropolitan Council of the Twin Cities Area(1974)
31
For Each Tr1r
Another problem encountered in the survey data is that activity
duration is not reported explicitly in the travel diary. Activity duration
has to be determined by computing the reported time elapsed between arrival
at the sojourn and the departure from sojourn. This measure of activity
duration, although the best available from the survey, is not, however,
completely accurate,primarily because of reporting errors. The errors
are all the more important considering that individuals are not required,
in the survey, to retrospectively time their activities, but only to time
their travel.
Note that, as in most major U.S. transportation surveys, no information
is available on trips made using the walk or the bicycle modes. In addition
to the complete loss of information on tours made exclusively by these two
modes (for example to go to the nearby grocery store), there are vehicular
tours which appear, from the recorded data, to be incomplete. However,
in most cases, it is possible to determine, by inspection, whether this
is due to miscoding or to missing walk links.
Land Use Data
The land use data is compiled for the 1,058 zones within the metro-
politan area. All data items are zone-specific and include employment
data by type of business (manufacturing, wholesale, transportation,
retail, service, financial, etc.), acreage by land use (recreational,
vacant, comnercial, etc.) and zonal distribution of household income,
automobile ownership and household size.
32
Transportation Level-of-Service
The transportation level-of-service is recorded as a matrix of skim
trees -- origin-destination minimum path times, travel costs and number
of transfers measured from coded networks. The level-of-service information
is mode-specific (highway and transit) and includes in-vehicle and out-of-
vehicle times, and number of transfers and fare for the transit mode. A
vector of parking costs is also available. It is very important to point
out that the level-of-service data is averaged over the whole day. That
is, no distinction is made to account for the difference in peak and off-
peak speeds, transit schedules, and parking costs. This averaging of
level-of-service information across the day causes under-estimation of
peak period travel times and over-estimation of off-peak travel times.
This has an impact on activity duration models. In fact, tabulations of
average network times (Metropolitan Council of the Twin Cities Area, 1974)
show significant differences in travel times for different times of the
day. In particular, travel time during the morning peak is 21.5% higher
than travel time during the off-peak period. Moreover, since most home-
to-work or work-to-home tours are made during the peak traffic period,
using average level-of-service under-estimates the travel time and cost
required for a non-work deviation during such tours.
3.3 Assumptions in Data Processing
The original data base, which includes the home interview survey,
land-use and transportation level-of-service, had to be reformatted and
processed for estimation of models of activity duration and travel time.
This was required because the original storage and coding did not permit
33
efficient accessing of the information needed for this research. It should
be pointed out that the transportation level-of-service variables which
have been appended to the socioeconomic and demographic characteristics
of the individuals and the households, are skim-tree values, i.e. estimated
and not reported values. This is done for two primary reasons. First,
it permits the evaluation of level-of-service of non-chosen alternatives
for which no recorded data is available in the home interview survey.
Second, the use of skim-tree values avoids the bias that exists in travel
characteristics which are reported by individuals in the household survey.
In particular, cognitive dissonance causes consistent under-reporting of
the time and cost of the chosen travel alternatives (and consistent over-
reporting of the time and cost of the non-chosen alternative.)
The following paragraphs present the major steps of the data pro-
cessing, which include the reduction of the size of the estimation sample
and the evaluation of the variables used for estimation of the models of
activity duration.
Sample Size Reduction
The first major step in the data processing was the reduction of the
number of observations in the home interview survey file by random sampling
(one in nine) of households from the original file. This permitted a
reduction in the cost of subsequent data processing steps. While
computation costs were reduced, the reliability of parameter estimates
was, however, also reduced. The loss of reliability is best quantified
by the variance of the parameter estimates. The variance of the parameter
estimates is proportional to the inverse of the size of the estimation
34
sample. Thus a doubling of the sample size is expected to reduce the
variance by half.
Evaluation of Accessibility
While socioeconomic variables such as work status, sex, age, are
easily obtained from the recorded data, it is somewhat more complicated
to evaluate a measure of accessibility to destinations where a given
activity could be performed. As discussed in more detail later,
accessibility is one of the key explanatory variables of activity pattern.
The evaluation of accessibility, which is specific to each decision
maker, requires extensive data processing.
Evaluation of Total Activity Duration
The dependent variable of the models, total activity duration, in-
cludes both actual time spent performing the activity (net activity
duration) and travel time to the activity. As discussed earlier, net
activity duration for each activity is computed as the time elapsed between
the arrival at the sojourn where the activity is performed, and the
departure from the sojourn. If an individual performs the same activity
at two sojourns, the two net activity durations are added. However, in
a multiple sojourn tour, when several activities are performed, it is not
straightforward to allocate travel time to each activity and a more complex
algorithm is necessary to evaluate travel time to each activity type. In
fact, if the origin and destination of the tour are different, then the
travel time .allocated to the activity is equal only to the travel time
incurred in excess of the direct travel time from the origin to the
destination of the -tour.
35
For multiple sojourn tours, it is necessary to develop a procedure
to allocate travel time to the different activities performed at the
different sojourns. Instead of allocating the tour travel time equally
among sojourns, it was considered more appropriate to allocate it
differently depending on the importance of the sojourn. It was hypo-
thesized that the sojourns are ranked on the basis of activity duration,
i.e. the longer the time spent at the sojourn performing the activity,
the higher the rank of the sojourn. Clearly, many other assumptions
could have been made for ranking of sojourns, but the one proposed here
seemed to be, among the ones considered, the most appropriate in many
instances. The procedure for allocating travel times assumes that travel
time to the primary sojourn is equal to the time incurred in excess of
the direct travel from the origin to the destination of the tour. If
the origin and the destination of the tour coincide, then travel time to
the primary sojourn is equal to the round-trip time from the origin to
that sojourn. Travel time allocated to the secondary sojourn is equal
to the travel time incurred in excess of the travel time of the tout
that includes only the origin of the tour, the primary sojourn, and the
destination of the tour. Travel time to lower ranking sojourns is only
the marginal (or excess) travel time to those sojourns, and it is shared
among them as a proportion of the time spent at the sojourn performing
the activity. A simplified example of the allocation algorithm is
presented in Figure 3.2. Summarizing, travel time to the primary sojourn
is equal to the total travel time to that sojourn, while travel time to
the remaining sojourns in the same tour is equal only to the marginal
travel time.
36
Social/Recreation (45 min)
H
i Q Shopping (30 min)
Work
Travel time allocated to social/recreation is travel time 0(2)* minus
travel time ® . Travel time allocated to shopping is travel time
®eQw) minus travel time O-®
Figure 3.2
Example of Allocation of Travel Time to Activities
37
3.4 Conclusions
This chapter has described the data used in this research and the
data processing required for estimation of the econometric models. A
major portion of the data processing costs was related to the evaluation
of accessibilities. An alternative, less expensive measure, which does
not involve enumeration of alternatives, has been considered. This
measure, however, is derived from highly simplifying assumptions on the
distribution of alternatives available to individuals, and has not been
sufficiently tested to be used in this research. The measure of
accessibility which involves enumeration of alternatives was used.
Nevertheless, the differnnce in computational costs between the two
measures is large enough to justify additional tests of the validity of
the simplified measure of accessibility.
38
CHAPTER IV
THE THEORETICAL MODEL OF NON-WORK ACTIVITY DURATION
4.1 Introduction
This chapter presents a theory of non-work activity duration. Only
travel related activities, that is, activities that have to be performed
away from home or work, and reached by a motorized vehicle are analyzed.
Primarily because of data limitations, it was not possible to model neither
in-home activities, nor activities which can be reached by a short walk.
Nevertheless, it should be noted that the. largest proportion of partici-
pation in out-of-home non-work activities requires motorized travel.
For the purpose of modelling non-work activity duration, it is
assumed that work or school duration, the mode to work or school,
residential location, and automobile ownership are exogeneous variables.
This implies that the choice of activity duration is made conditional on
these variables. While the scope of this research is limited to the
modelling of activity duration, related research currently in progress
(Damm, 1978) is investigating the issues involved in the scheduling of
activities and travel.
4.2 Theory of Time Allocation Revisited
This section presents a theory of time allocation which includes
explicitly transportation level-of-service. The theory of time
allocation presented in this section is a reformulation of Becker's
(1965) theory, with explicit inclusion of transportation level-of-service.
It is hypothesized that consumers behave rationally and have perfect
39
information and that the consumerst preferences are represented by a
utility function. The utility of an activity program is written as
follows:
U = U(Z1 ,...,Zi,..,Zy) (4.1)
where Z is the "quantity" of activity 1, with I non-work/non-school
activities. The "quantity" of activity i is assumed to be a function
of the inputs required. The inputs can be divided into three components:
goods (Xi), durational component (a1), and locational component (Ai).
The "quantity" of activity is dependent on the type and quantity of
goods purchased (or enjoyed) during the activity. The durational com-
ponent of the activity is the time input, i.e. the actual time spent
performing the activity, net of travel time. The locational component
is the travel input. The travel input is represented by the travel
pattern of individuals.. Note, however, that consumers decide on activity
duration prior to their decision on the travel pattern. Thus, the input
to models of activity duration is only a measure of an indeterminate
travel pattern. Appendix' I discusses such a measure, which is called
accessibility.
In order to simplify the discussion, assume that the Zr's are the
final activities, and that there is no joint production (i.e. producing
one activity does not produce any other activity). The "quantity" of
activity i can thus be written as:
Z,= f1(a1,A1,X1 ) (4.2)
40
where f is the "production function" via which a1, Ai, and K1 are
transformed into the activity. Assume that the production function
is continuous in the N-dimensional vector of goods X and in the
total activity duration T1, and that the utility function U is
continuous in the Z 's. Consumers are faced with time and budget
constraints:
E2 T = T (4.3)
E (tci + Pip = R (4.4)
where T is the time available for non-work/non-school activities, tc
is the travel cost to activity i, P is the vector of unit costs of
market goods used as input in activities, R is the sum of earned and
non earned income. Note that T and R are considered exogeneous
attributes of the behavioral process modelled here.
Activity time a is by definition:
a, =T - tt (4.5)
where tt is travel time to activity i.
For a given activity program, i.e. the set of activity durations
(Tl,...,Ti,..,T ),the travel pattern is described by A 's, tt 's, and
tc 's. A is the utility of the destinations for the optimal travel
pattern; tt and te are, respectively, the travel time and the travel
costs of the trips in the optimal travel pattern. The three measures
41
above are a function of activity durations (Ti), and of land use (LUi ) and
level-of-service characteristics (LOSi). This implies the following
relationship:
Ai=Ai(TLUiLOSi) (4.6)
tc, = tc (T ,LU ,LOSi) (4,7)
tt, = tti(Ti,LUi,LOSi) (4.8)
Defining the shadow price of time as p and the shadow price of money as
X, the Lagrangian of the constrained maximization is written as:
L = U - w(ETi-T) - A[E(tc+P'X) - R] (4.9)
The first order conditions with respect to the decision variables Ti
and X are:
AP
BUaP =n(4.10)
in aaz i
au- atc -p=0 (4.11)
Equations (4.10) and (4.11) can be transformed as:
az XPn (4.12)
ax in au/az i
atc
3 Z 3T (4.13)
3Z
42
Deriving from (4.12) and (4.13) the margilnal rate of substitution:
aZ 
_z+3T
i./ i. (4.14)
3 T 3 X n
Note that 3T /3Z and AX /az are, respectively, the marginal input of
time and goods in the production of the "quantity" of activity Z . The
left hand side of equation (4.14) is thus the marginal rate of substi-
tution of time for market goods in the production of activity i. The
second term in the right hand side numerator of (4.14) is the marginal
travel cost to activity i. Thus the "price" of activity duration for
activity i is the "value of time" as a resource (p/) plus the marginal
travel cost.
Similarly, at the optimum, the ratio of the marginal utilities with
respect to total activity time is written as:
3tc
ll i
.aUX .Ui(4.15)
3T T. 3tc.
i1!j
Equation (4.15) also implies that, if the marginal travel costs to all
activities were identical, then the ratio of marginal utilities of time
would be constant. Note however that the hypothesis of identical marginal
travel costs is not very realistic since trips to destinations where
different activities are performed involve different congestion levels,
43
roadway design, average speed and, in general, varying ease of access, all
elements which may increase the cpst of travel.
The implicit solution to the maximization problem in equation (4.1),
(4. 3), and (4. 4) will be
T. = T(T, R, , LOS, LU) Vi (4.16)i i
It is necessary now to provide a stochastic structure to the model to
account for taste variations in the population. It is assumed that total
activity times Tt for different individuals t differ only through ani
observable vector St of socioeconomic and demographic characteristics,
t
plus an additive term -E representing idiosyncratic preferences for
various activities. Equation (4.16) is thus generalized to:
T = T (Tt, Rt, LOSt, LUtt,P)+C Vi (4.17)
Typically Tt and Rt will vary across individuals depending on the work
duration, the duration of in-home activities, and the individual's income-
and wealth. L&St, LU will vary across the individual's residential
location, auto ownership, and work place. Note that the observed value
of Tt can never be negative or larger than T,. since no activity can have
negative duration (physical constraint) or have a duration exceeding the
duration allocated to all activities (time budget constraint).
44
CHAPTER V
ECONOMETRIC MODELS
5.1 Introduction
This chapter presents the econometric models of travel-related activity
duration. Daily duration of an activity, i.e. the time spent performing
the activity (including travel time to that activity), has a lower limit
at zero and an upper limit at 24 hours. For at least some of the non-work,
out-of-home activities many individuals will report null activity duration
during a given day because they did not participate in the given activity.
However, nobody will report a 24-hour activity duration. The form of the
model porposed for estimation of activity duration takes into account the
concentration of observations at the boundaries of activity duration.
Observations for the individuals that did not participate in the activity
modelled are concentrated at the lower limit. However, no individual will
be observed at the higher limit. The proposed model form also assumes,
because of model estimation requirements, that the explanatory variables
influence both the probability of participation and the duration of the
activity given participation. If only the probability of participation,
without regard to the value of duration given participation, were to be
predicted, a probit or other model of discrete choice would be suitable.
The required estimator; however, would predict, in addition to the
probability of participation, also the duration of the activity given
participation. If no individual had zro activity duration, estimation
of the model by ordinary least squares would be acceptable. However, for
45
the problem at hand, ordinary least squares is not an acceptable estimator,
because of the heavy concentration of observations at the lower limit;
a hybrid of probit analysis and multiple regression is thus required.
5.2 Single Equation Limited Dependent Variable Model
The hybrid probit and multiple regression model mentioned in the
previous paragraph was first developed by Tobin (1958). The model, called
the limited dependent variable model, includes the following relationships
for an individual t:
*
yt ="SX + Ettt t
Yt ( f Y*>0(5.1)
0 otherwise
Yt is a latent (not directly observable) random variable, Yt is the
observed dependent variable, Xt is a column vector of constants for the
observed exogeneous variables, et is the error term which is assumed
homoskedastic, serially uncorrelated and independent of X with distri-
2t
bution N (0,2), and S is a column vector of constants to be estimated.
The log likelihood of the model for M observations is written as:
S'xt (Y-1X )2
L* = E ln [1 - ( ) -#log 2  Y t t2 (5.2)
ts i 2a2 t.-Y2
46
where 0 Q-) and (-) are the unit normal density and cumulative functions
respectively, TV is the set of observations for which Yt = 0,T2 is the set
for which Yt> 0, and M2 is the number of individuals that did participate.
The estimation of $ and a requires the maximization of the likelihood
function. This maximization is performed by an iterative algorithm, and
requires the repeated evaluation of the cumulative normal density function.
Different types of iterative algorithms for estimation of the O's and .a
can be used: optimal gradient search algorithms (such as the well known
Newton-Raphson), and non-optimal search algorithms. Olsen (1976) has
demonstrated that the likelihood function in equation (5.2) has a single
maximum, and that any values of S and a which do not cause the matrix of
the second derivatives of the likelihood function (i.e. the hessian) to
be singular, would be acceptable as initial values for an algorithm.
Olsen's findings permitted the development of a search algorithm which
differs from the Newton-Raphson procedure. This procedure (Fair, 1977)
is shown to be considerable faster, for many problems, than the Newton-
Raphson procedure. For this research, however, the Newton-Raphson
procedure was available (National Bureau of Economic Research, Inc., 1975;
Nelson, 1974).
The expected mean and variance of the dependent variable are computed
somewhat differently than for the multiple regression model. Specifically,
the unconditional expected value of Yt given the estimated constants 0t 0
and a0 and given the lower limit of Yt at zero, is written as:
A program to run Fair's procedure on IBM 370 systems has been developed
and is available from the author.
47
E(YtIxt.) = o)t $ t) + acp(SO t (5.3)
The expected value of Yt given participation, and given 0,, a and the
lower limit at zero, is written:
s 'x
Et 0 t+ t 0'Xt 0 5'X(.40 t(D(a
0
The conditional variance of Y given 5 'X 46 >0 and the limit is written as:t ot t
E(Yt Ixtt tE>090) = IxtE(Y )+a02 (5.5)
Note, in particular, that the conditional expected value of equation (5.4)
is equal to the linear combination term o t'X plus a correction term
which becomes small when S'X Ia becomes large. P(YtfaoX t+St>0,0) tends.
to o'Xt the "regression's" expected value. The probability of participation
in the activity (a binary probit) is written as:
P (5'X If4 >0) = c (0 t) (5.6)
t t a
0
5.3 Extension of the Single Equation Limited Dependent Variable Model
The limited dependent variable model presented in the previous
paragraph assumes that the probability of participation and the time
duration are influenced by the same explanatory variables. A more general
48
model, proposed by Westin (1975), relaxes this assumption and allows the
probability of participation and the time duration to have different
explanatory variables. The two states are: participation (i.e. positive
duration) and non-participation (i.e. null, duration). The probability
density function of vector Yt (with elements Ytj and Yt2 the durations
for the two states) is written:
Y
tI) ' N[(w , o) (0 02)] (5.7)
t2 t
where the two states subscripts .on 3 and a are supressed. The probability
of choosing either state is defined by a probit model of choice:
P (Yt,W)= G(2Y +y'W) (5.8)
tZ t t t2 t
and
P tI (Yt,'Wt I t2 (Yt3, Wt) (5.9)
whera W is a vector of explanatory variables, y a vector of constants,
and a a scalar constant. The log likelihood function for the model is
written as:
L* = -22 ln a - Z- F (Yt-'X S In$D(aY +Y'W )+
T2 t t tET2  t2 t
+ 'ES ln 1-4[(Xa'X +Y'W ) /Y,-12421] (5.10)
tE T, t t
49
where M2 is the number of individuals who participated in the activity.
Note that even in the case where a is constrained to one and y is constrained
to zero, the log likelihood of Westin's model is not equal to the log like-
lihood of the limited dependent variable. In fact, the log likelihood in
(5.10) has an extra term, Z in $(czY +Y'W ), which is equal to the
t 6 22 t
component of the likelihood function for the probit analysis for the
individuals who participated in the activity, if duration is included as
an explanatory variable. Moreover the denominator of the fourth term in
equation (5.10) has a correction (1 + a& 1,, instead of a. Westin's
estimator is clearly more desirable than Tobin's estimator since it imposes
fewer restrictions on the model's specification. Nevertheless, the five
stage estimation procedure of the model as proposed by Westin and Gillen
(1977) produces estimates with very high variance when few individuals
participated in the given activity, because (a'Xt+y'Wt/ /1 + atca) cannot
be reliably evaluated. Thus, although Westin's theoretical model is
attractive, the empirical application is, in this case, unfeasible. The
models of activity duration presented in Chapter VI will thus be estimated
using Tobin's estimator.
5.4 Simultaneous Equations Limited Dependent Variable Model
Although single-equation limited dependent variable models have been
studied in detail, few econometricians have developed an estimator for
simultaneous equation systems. The basic problem is that the full information
maximum likelihood (FIML) estimator requires the evaluation of a multi-
50
variate normal cumulative distribution function, which is very tediuos
to compute. The two basic references for simultaneous models of the
type discussed here are Amemiya (1974) and Nelson and Olson (1977). The
model specification presented here is Nelson and Olson's, since it is
the better adapted for the estimation of activity duration models.
Amemiya's specification, in fact, breaks down when the proportion of
observations at the limit is large, as is the case for the data used in
this research.
For ease of exposition, a two equation model is presented. Both
dependent variables are limited:
(a) Y.O = a Y * + $ 'X +E'
t i jt i t it
(itifit*> i=l,2
(b) Yt = Y, theise j=1,2,jti (5.11)
it 0, otherwise =9ji
The reduced form is written as:
(a) Yit = r t 'I%+SCit
(b) Yi = ttotherYit* >0 i=1,2 (5.12)
it 0, otherwise
(*)Several references proposed simplified procedures for the approximate
evaluation of the multivariate normal cumulative function. Among them Clark
(1961), Dutt (1976), Hausman and Wise (1976), Manski et al. (1977). It was
however not feasible, within this research to develop the FIML estimator
using any of the proposed procedures.
51
The estimation of the model of equation (5,11) by FIML estimation requires
the maximization of the following likelihood function:
L = Tf P (1 - ,ICt2a) f (Yt-(ciy-Si'Xt, y-aaYgxt- 2'Xt) dy
IT f (1 - aia2) f (y -c1iY2t-I'X ,Ya 2t-a2y-S2'Xt) dy
f "f(O (1 - ct1ai) f (y-a 1 z-gI'Xt, Z-a2 y-f2'Xt) dydz
T3 -00 -wt
11 (1 -acc 2 ) f (Y1 COL1Y2 t-31t, 9Y2cta2Y 1t-f2'Xt) (5.13)
where Wi is the set of observations for which Y2t is at the limit, '2
is the set for which Y t is at the limit, T 3 is the set for which Yit
Y2 t are at the limit, and T4 is the set that has neither Yit nor Y2t
at the limit; f(-,-) is the bi-variate joint normal density function of
E and E j. Although the maximization of (5.13) is mathematically
it 2
feasible, in order to implement this estimator, a new computer program
would have to be written. This, however, was deemed outside of the scope
of this research. It was decided, instead, to follow the procedure
proposed by Nelson and Olson.
Nelson and Olson developed an estimator equivalent to the two stage
least square for estimation of simultaneous limited dependent variable
(*)John (1959) has derived a simple reduction expression for the evaluation
of the cumulative of a multivariate normal distribution.
52*
models (2SLDV). For a proof of consistency, and for the derivation of the
covariance matrix, the reader is referred to the original paper by Nelson
and Olson (1977) and to Amemiya (1977). The computational procedure for
the 2SLDV model is repeated here, for the special case of equation (5.11).
(a) Estimate irk, =1,2 in (5.12(a)) by maximum likelihood
applied to the 2 equations separately.
(b) Form the instruments Y ' t
(c) Replace the Y* 's on the right hand side of equation
it
(5.11(a)) by the corresponding Y* 's and, treating
these instruments as fixed regressors and the resulting
equations as single equation 'models, estimate the
structural parameters in (5.11) by maximum likelihood
applied to the two equations separately.
The covariance matrix of the estimated coefficients can be computed using
the equations proposed by Amemiya (1977). However, for simplicity, the
simultaneous models presented in the next chapter report only the approxi-
mated standard error computed by the second stage maximum likelihood.
Further investigation should be devoted to the measurement of the error
introduced by this approximation.
One major problem arises in the case of estimation of activity
duration models using the 2SLDV procedure. As Nelson and Olson suggest,
the 2SLDV procedure is well adapted when the limit on the dependent
variable arises because of incomplete data reporting. When this is the
case, Y1t*, the underlying value of the dependent variable, is a good
substitute for Yit. However, in the case of accivity duration the
equations in model (5.11) should be written as:
53
(a) Yit*= iYjt +iX +tE:it
Yt * if Y >0
(b) Y1 t = i> i=l,2 (5.14)
0, otherwise j=1,2 jit
The simplicity of the procedure proposed by Nelson and Olson however cannot
be duplicated with model (5.14). Since the development of a new estimation
specification was outside of the scope of this research, it was decided to
use as an approximation the 2SLDV procedure.
54
CHAPTER VI
EMPIRICAL MODELS
6.1 Introduction
This chapter describes the empirical results of the estimation of
models for out-of-home non-work activity duration and travel time. Two
types of models are estimated. The first type, the individual model,
assumes that the basic decision unit is the individual, arid that each
individual makes activity duration decisions independent of the actual
duration decisions made by other members of the household. The second
type, the joint model, assumes, like the individual model, that the
basic decision unit is the individual, but, contrary to the individual
model, it assumes that activity duration for the male head of household
is a function.of the activity duration for the female head of household.
The theoretical background for the individual activity duration
model is presented in Chapter IV. Because of the high non-linearity of
the process modelled, an algebraic expression for the optimal activity
duration cannot be found even when simplifying assumptions are made on
some of the underlying relationships of the process. Thus, it was chosen
to simplify the problem by assuming that the function relating the
exogeneous variables (total time allocated to non-work activities,
remaining income, land-use, level-of-service and the price of goods
purchased) to activity duration is accessibility to the given activity.
The other variables that enter the model include the socioeconomic and
demographic characteristics of the individual which were found in the
literature review (Chapter II) to be most relevant to activity duration.
55
The purpose of the first model type is to test empirically the validity
of the activity duration theory presented in Chapter IV and the relative
importance of the independent variables of the model. The second model
type explicitly tests whether the husband's activity duration is dependent
on the wife's activity duration and vice-versa.
The models of activity duration are calibrated using the limited
dependent variable model presented in Chapter V; the models of travel
time are estimated using ordinary least squares.
6.2 Specification of the Models
6.2.1 Models of Total Activity Duration
The purpose of this section is to formulate estimable models of total
activity duration. In order to do this, it is necessary to assume specific
functional forms for the theoretical relationships presented in Chapter IV
and to select the set of independent variables that should enter the model
specification.
Simplified Model of Activity Duration
The theoretical construct of the model of total activity duration
presented in Chapter IV has not defined the functional form that relates
variables such as utility, accessibility, travel time, etc. to the
endogeneous variables. In order to obtain an estimable model, the functions
have to be explicitly defined. However, even in the simplified case of
the featureless plane presented in Appendix I, accessibility A1 ,travel time
tt,, and travel cost tc1 are highly non-linear functions of T., the
total activity duration, and the solution of the constrained utility
56
maximization cannot be derived for the decision variables T . On a-priori
grounds, nevertheless, it was hypothesized that the activity duration would
be influenced by the ease of access to opportunities. Also individuals
who participate more than average in a particular activity would reside
closer to locations where the activity could be performed. The measure that
was considered best adapted to represent the ease of access and the distri-
bution of locations where activities can be performed, was accessibility.
Accessibility, which is presented in detail in Appendix I, is sensitive to
both changes in transportation level-of-service and to the changes in the
availability of alternatives to perform a given activity. The proposed
simplification is to use,as an explanatory variable, the expected accessi-
bility given Ti=4. In theory, accessibilities to all activities should
enter as explanatory variables to a given activity. Nevertheless,
estimation of a model of activity duration with those explanatory variables
did not yield reliable results, primarily because of the strong correlation
between accessibilities for different activities. Thus it was decided to
use, in the model for a given activity, only the accessibility to that
activity, instead of all the accessibilities. Note that, because the
accessibility measure developed in Appendix I is individual specific
(it includes location and socioeconomic variables), the expected accessi-
bility given T =o is labeled A 10 , ,where the superscript p refers to an
individual.
It is necessary, at this point, to provide a stochastic structure to
account for taste variation across the population. In fact, it should be
recognized that different individuals decide differently on activity
57
participation. It is assumed here that the difference in the outcome of the
decision can be attributed to two factors, socioeconomic and demographic
characteristics, (SP) and idiosyncratic preferences, (s ). While accessi-
bility varies for different individuals, thus explaining part of the taste
variation, it is hypothesized here that activity duration is a direct
function of SP, and additive in e * The general form of the model becomes:
T = (A PS) +r_ (6.1)
It is assumed that the vector of variables Sp and the variable A enter
the function g in a linear fashion, so that the model can be written as:
T = = 1+62A ,+(S )' p+E (6.2)
where 61, 62 are scalar constants, T is a column vector of constants, and
p
(SP )is the transpose of vector S
The Exogeneous Variables in the Models of Total Activity Duration
Models for three types of non-work activities were estimated. The
activity types are:
- Shopping
- Social/recreation
- Remaining Activities: Medical, Outdoor
Recreation, Personal Business, and Serve
Passenger
The model for shopping activity duration includes two measures of shopping
accessibility. The first one is the home based accessibility, the second
is the home-work based accessibility. The socioeconomic variables included
58
in the shopping model are dummy variables for sex, driver's license,
household size, age, work or (educational status), and the combined
characteristics of work status, number of children in the household
and age which describe the child rearing responsibilities.
The model for social/recreation activity duration includes social/
recreation accessibilit and socioeconomic characteristics. The socio-
economic characteristics include automobile ownership divided by household
size, natural logarithm of household income and dummy variables for sex,
Age, driver's license and child rearing responsibilities of the individual.
Note that the variable for child rearing responsabilities (role) is
different for.the shopping and the two other models. The role variable
in the shopping model, contrary to the definition of the same variable
in the two other models, changes value depending on whether the individual
went to work (or school). The justification for the above difference
is primarily due to the temporal characteristics of the activities.
Typically, in fact, shopping and work (or school), occur during the same
time period (the day), while social/recreation and activities such as
outdoor recreation, personal business, occur on days or hours of the day
during which work or school participation is not common.
The model of duration for the remaining activities includes the sum
of the accessibilities for shopping and social/recreation. This variable
is used as a proxy for locational attributes of the individual. The
socioeconomic variables include all those appearing in the social/recreation
model with the exclusion of the household income.
59
The exact definition of the variables for the three models described
above is presented in Figures 6.1 and 6.2. The joint model of intra-
household shopping activity duration has been estimated only for the
shopping activity. It is composed of two equations, one for the male
head of the household (the husband) and one for the female head of
household (the wife). Both equations included the duration of shopping
for the head of household of the opposite sex. The other variables
included in the equations of the joint model were the same as those for
the individual's shopping model with the exclusion of the dummy variables
for sex and age, which are the dimensions of stratification of the models.
6.2.2 Models of Travel Time
The general form for the evaluation of the expected travel time to
specific activities is written as:
E(tti) = foT tt P(Ti) dT (6.3)
where E(tt) is the expected travel time to activity i, tt. is the travel
time conditional on T, and P(T ) is the probability of activity duration.
The prediction of travel time by this functional form requires the integra-
tion of the function in equation (6.3). This approach, although theoretically
attractive, was not feasible within this research because of computer
budget constraints. It was decided, instead, to implement a simpler approach
and only the expected value of T (instead of its distribution) was used in
computing E(tti). In order to do this, models for prediction of the share
of total activity duration spent travelling were estimated. Three linear
regression models were estimated for the three activity types (shopping,
60
Figure 6.1
Variables for the Shopping Person Model
if male
if female
Driver's License
Went to work
or to school
Household size
1 10
no driver's license
has driver's license
1 yes
1 0 no
1
0
household size larger than two
(excluding children under 5)
otherwise
1 if age over 17, did not go to work
Role and household has children
.0 otherwise
1 if age under 17
Child 
-0 otherwise
Shopping accessibility for home based trips
Shopping accessibility for trips based on the home to
work trip
61
Sex
I l
l.o
Figure 6.2
Variables of the Social/Recreation Person Model
Autos owned/household size
Natural logarithm of household income
Jl if male
0 if female
'1 if age under 17
i 0 otherwise
1 if age over 17 and female or male
head of household and household
has children
o otherwise
Driver's License
Went to work
or school
1 no driver's license
0 has driver's license
1 yes
t0 no
Social/recreation accessibility
62
Sex
Child
Role
social/recreation and all remaining activities). The dependent variable of
the models, the travel share, is the ratio of total travel time to reach
the activity and the total activity duration. Total travel time includes
in- and out-of-vehicle time; total activity duration is the sum of total
travel time and net time spent performing the activity. Note that ttp T ;
therefore the ratio ttI/T. has to be always smaller than 1. Satisfying
this condition can be guaranteed for any value of the independent variables
by either simple truncation of the dependent variable (tti/T ) between zero
and one, or by predicting the value of the dependent variable assuming the
underlying model is a limited dependent variable model with a lower limit
at zero and an upper limit at one.The three regressionmodels have T linear
in tt because it was assumed that the ratio tt I/T is constant for all Ti.
The observations used for estimation of the models for each activity, include
only individuals participating in that activity, since the travel share is
undefined otherwise.
The variables included in the shopping travel share model are house-
hold income and accessibility for shopping trips. The social/recreation
model similarly includes household income and accessibility for social/
recreation trips. The model for the remaining activities includes a
dummy variable for driver's license and the sum of shopping and social/
recreation accessibilities.
6.3 Estimation Results
6.3.1 Models of Total Activity Duration
A) The Individual Activity Models
The individual models of total activity duration are estimated on a
63
sample of 1431 individuals. The sample includes all individuals over five
years of age in the 517 households which were randomly selected from the
home interview survey.
The dependent variable, activity duration for each activity type, is
always non-negative and, since the estimation sample is from a one day diary,
it cannot be higher than 24 hours. These restrictions on the observed
dependent variable are incorporated in the limited dependent variable
estimation described in Chapter V. Summary measures of duration (travel
and activity) for persons participating in activities are presented in
Table 6.1, and statistics for accessibility measures are presented in
Table 6.2.
Shopping Activity Duration
Several specifications were tried for the model of individual shopping
duration. The final model specification is partly obtained from prior
knowledge of the variables that should appear in the model, and partly from
empirical considerations derived from estimation of preliminary models. In
particular, the set of socioeconomic and demographic variables which appear
in the model specification is obtained from current literature on activity
pattern research. Included are variables such as sex, age, work or school
status, household size, child rearing responsibilities, and driver's license
status. Among the variables that were considered for inclusion in the model,
but were excluded because of statistical problems, are income and autos
owned. In particular, these two variables were found not to add any
explanatory power to the model. The coefficient of income was statistically
insignificant and correlated with the driver's license dummy variable when
64
TABLE 6.1
AverageTotalActivity Duration For Persons Participating
in the Specific Activity
Percent Participants Activity Duration
(*)
Travel Time to
Activity(*)
Shopping .194 61.2708 23.7331
(101.03) (18.6)
Social/Recreation .175 143.856 32.0843
(144.02) (24.5)
Medical .020 57.931 24.8276
(35.65) (23.7)
Outdoor Recreation .055 125.772 27.2569
(104.13) (25.4)
Personal Business .137 85.8367 26.8955
(112.18) (24.8)
Serve Passenger .052 40.48 29.9244
(50.26) (23.0)
Sample Size: 1431
(*) In parenthesis is the standard deviation.
65
Activity
Statistics for
Mean z
Std. dev. =
Median =
Statistics for
Mean =
Std. dev. =
Median m
TABLE 6.2
Statistics for Accessibility Measures
Home Based Shopping Accessibility
-22.8138
3.28772
-22.6
Home Based Social/Recreation Accessibility
-4.52342
1.21579
-4.26
66
the latter was included. Similarly, the coefficient of driver's license
was significant and correlated with autos owned by the household and autos
owned per household member when the latter was included. Moreover, when
the driver's license variable was left out of the specification of the
model, the coefficient of the automobiles owned variable (either the "by
household" or the "per household member" measure) had low statistical
significance, and was affecting the values of coefficients of other variables
in the model.
All the coefficients that were included in the final model specification
have the expected sign (Table 6.3). Specifically, the coefficient of the
dummy variable for participation in non-discretionary activities (work and
school) has a negative sign, suggesting that, as expected, workers (or
students) allocate less time to shopping than non-workers (or non-students).
A zero-one variable for participation was used instead of the duration of
participation for non-discretionary activities. It was in fact found that
the likelihood of the model was higher with the zero-one variable, than
with the duration variable. A preliminary model was estimated with both
variables (duration and dummy variable), but the duration coefficient was
highly correlated with the coefficient of the dummy variable and had a
positive sign, which is inconsistent with expected behavior. The role
variable, which represents the child rearing and household care responsi-
bilities, has a positive sign. This suggests that adults who don't go to
work in a family with children tend to spend more time shopping than other
individuals. Typically this market segment includes housewives who don't do
any work outside the home (14.9% of the population), and fathers on their
weekday off (4.9% of the population).
67
Unrestricted RestrictedVariable Model Model
-40.6864 -155.884Constant (.83943) (13.9372)
fl male -22.2465Sex 10 female (1.63719)
Driver's License nes (3.709
Went to work 1 yes -11.789
or school 10 no (.63419)
HH size over 2 1yes -41.0053
10 no(2.55676)
1 if age over 17, did not go to 32.2118
Role work and HH with children (1.6272)10 otherwise
l [ if age under 17 -14.3746
Child 0otherwise (.50474)
Home based shopping accessibility 2.01161
Home-work based shopping accessibility 1.02554
[for individuals that went to work] (.77098)
Standard Deviation2170.164 176.619Stadar Deiaton(20.715) (20.5422)
- Log Likelihood 2227.7 2268.33
Likelihood ratio test 81.3
p2  -. 018
(In parenthesis is the ratio of coefficient over its asymptotic standard
error).
Dependent Variable: Total Shopping Duration
Sample Size: 1431
No. of participants in shopping activity: 281
68
TABLE 6.3
Individual Shopping Duration Model
The coefficient for the household size dummy variable is negative.
The negative sign indicates that within larger families the task of shopping
is shared by the members of the household, with corresponding time savings
for each individual. Both the home based and the home-work based accessi-
bilities have positive coefficients. This implies that higher accessibility
leads to both more frequent and longer shopping durations. Note that the
home-work based accessibility is defined only for individuals that went to
work. This implies that, for workers, the value of the dependent variable
of the model is affected both by an intercept effect (the dummy variable
for participation in non-discretionary activities) and by a slope effect
(the home based accessibility). For school children, only the intercept
effect appears.
Social/Recreation Activity Duration
The specification of the model of social/recreation duration is similar
to the specification of the model of shopping duration. The coefficients
for the final specification of the social/recreation activity duration model
all have the expected signs (Table 6.4). The variable which impacts the
most on activity duration is the dummy variable for driver's license status.
Specifically, a change in driver's license status shifts activity duration
more than a change in work status or role in the household. The lack of a
driver's license has, as expected, a larger negative effect on social/
recreation duration than on shopping or the remaining activities. Also
negative is the effect of the participation in the work or school activity
and the child rearing and household care responsabilities. The coefficient
of the natural logarithm of income is positive and indicates that individuals
69
TABLE 6.4
Individual Social/Recreation Duration Model
Unrestricted Restricted
Variable Model Model
-420.924 -289.633
Constant (2.15143) (13.2984)
8.03613
Autos owned/H! size (.165453)
ln(HH income) 39.9866(2.1076)
Sex 1 male -39.96320 female (1.62808)
( 1 if age under 17 49.5106Child 0 otherwise (.994965)
1 if age over 17, and female or 
-34.3341
Role male hd of hh, and hh w/child. (1.23797)0 otherwise o 
-185.281
Driver's License t yes (3.95456)
Went to work 1 yes -56.8308
or school 0 no (2.16153)
Accessibility social/recreation (2.4425)
307.587 318.25
Standard Deviation (19.2883) (19.1810)
- Log likelihood 2254.4 2279.97
Likelihood ratio test 51.1
p2  .011
(In parenthesis is the ratio of coefficient over its asymptotic standard
error).
Dependent Variable: Total Social/Recreation Duration
Sample size: 1431
No. of participants in social/recreation activity: 261
70
in wealthier households tend to allocate more time to social/recreation.
The logarithmic transformation of income was chosen because it is assumed
that there is a decreasing marginal effect of income on activity duration.
The coefficient of accessibility has a large positive effect on activity
duration. A small change in level-of-service to social/recreation desti-
nations, for example, causes significant changes in the predicted time
allocation. The variable of automobile ownership per household member (a
measure of car availability) has a positive coefficient. The coefficient's
low statistical significance is due primarily to the correlation of this
with the coefficient of the driver's license status. Although the stati-
stical significance of the coefficient is low, it was decided to include
the car availability variable in the model because this variable is, on a
priori grounds, believed to be a significant determinant of activity
participation, particularly in the case of the most discretionary of the
non-work activities, (social/recreation, personal business, outdoor
recreation, etc.). Note that the car availability variable already appears
in the measure of social/recreation accessibility.
Activity Duration for the Remaining Activities
The coefficients of the model for the remaining non-work activities all
have the expected sign (Table 6.5). The role dummy variable, which represents
the child rearing and household responsibilities, has a positive coefficient,
suggesting that individuals in families with children allocate more time
to non-work activities such as outdoor recreation, medical visits, etc. Note
that the coefficient of automobiles owned per household member is larger than
71
TABLE 6.5
Individual Remaining Activities Duration Model
Variable Unrestricted RestrictedModel Model
Constant -138.637 -159.245(2.34924) (13.2520)
Driver's License 11 no -93.0428Drve'sLiene 0. yes (4.51015)
Went to work 1 yes -28.9148
or school t0 no (1.71031)
x l male 25.5746
Sex 0 female (1.59557)
69.7321
Autos owned/RH size (2.22319)
1 if age > 17 and female or male 47.4211
Role head of HH and family w/ child. (2.72956)0 otherwise
Accessibility shopping + 1.39524
Accessibility social/recreation (.729734)
StndrdDvitin219.301 226.312Standard Deviation (23.1776) (23.0666)
- Log likelihood 2845.87 2880.19
Likelihood ratio test 68.6
P2 .012
(In parenthesis is the ratio of the coefficient over its asymptotic standard
error).
Dependett Variable: Total Activity Duration for Medical, Outdoor
Recreation, Personal Business and Serve
Pansenger Activities
Sample Size: 1431
Nc. of participants in other activities: 354
72
the coefficient for the same variable in the social/recreation model,
suggesting the added importance of car availability for the most dis-
cretionary activities such as personal business, serve passenger (activities
which clearly cannot be performed without having an automobile available),
and outdoor recreation.
Summary of the Estimation of the Individual Activity Models
The three models presented above all have the expected sign for the
different variables. However, for some coefficients, the asymptotic
standard error is relatively high. It is hypothesized that the above is
due mainly to the nature of the process modelled., the type of observational
data, and the small size of the data.
Specifically, the choice of activity duration is a process whose day
by day outcome has very high variability, although over a longer time period
it might be fairly stable. Typically, if an individual engages in a given
activity every other day, on a given day there is a 50% probability of
observing his participation. This probability distribution however, might
be totally irrelevant over longer time periods (say a week), when the
individual might be observed devoting a constant number of hours to the
given activity.
The data used in the estimation of the models discussed here is composed
of a day's diary. This implies that the activity durations show high
variability both in the observed values and in the model predictions. As
discussed above, this is not necessarily due to the model's misspecification,
but in large part to the sampling procedure.
73
Note, however, that averaging activity participation of individuals
over a longer period of time is not desirable. Although using averages
improves the statistical fit of the model, the inherent variability of
the process is lost. Moreover, with the "averages" it would be impossible
to estimate a frequency (or generation) model.
Overall, it should be pointed out that in the estimated models, most
of the variation in the activity duration is explained by the choice of
whether to participate in a given activity or not. Probability of parti-
cipation and how long to participate, are decisions which are assumed to
be made jointly and should thus be estimated as a joint model. The hypo-
thesis of jointness of the two decisions (participation/duration) was
further validated by limited tests on the estimation of sequential models
of probability of participation and duration given participation.
Specifically, ordinary least squares estimation of activity duration given
participation, using only observations on individuals who participated in
the given activity, yielded wrong signs for the coefficients of some of
the independent variables of the model. The joint model (the limited
dependent variable estimator), with the same set of independent variables,
however, yielded correct signs.
A different joint model was tried for the models of activity duration.
This model (Westin, 1975), discussed in detail in Chapter V, is a
generalization of the limited dependent variable estimator proposed by
Tobin (1958). It assumes that the decisions of participation and duration
given participation are made jointly, but can be a function of a different
set of independent variables. Westin'f model was, however, unacceptable
because the actual model calibration yielded statistically unreliable
estimates.
74
Although the models presented are statistically valid, it is suggested,
for future work, to use a larger sample, A larger sample was available for
this research, but it was reduced to limit the computational expense of the
estimation. A larger sample would yield lower variance of the coefficients
and would probably yield acceptable estimates for the general model of choice
proposed by Westin. The transportation policy and socioeconomic implications
of the individual activity duration models is presented in Chapter VII.
B) The Joint Activity M odel
The hypothesis of intrahousehold task sharing is explicitly tested by
the estimation of a joint limited dependent variable model forthe total
shopping activity duration of male and female heads of households. The
individual activity duration models include some measure of intrahousehold
jointness of decision, particularly through the dummy variable for house-
hold size. The joint activity model explicitly tests the jointness by
estimating simultaneous equations. The estimator adopted is the two stage
least squares equivalent proposed by Nelson and Olson (1977) and presented
in detail in Chapter V. Coefficients obtained using this estimator are
compared to the coefficients obtained by estimating two single equation
limited dependent variable models for the two household heads. The two
equations for the male and for the female head of household include, as
one of the explanatory variables, the shopping activity duration of the
spouse. In the case of the simultaneous estimation, the shopping activity
duration of the spouse is assumed to be an endogenous variable; in the
case of the single equation estimation, it is assumed exogenous. By
analogy to the simultaneous regression model, it is hypothesized that the
75
coefficients of the limited dependent variable single equation estimation
are inconsistent. The comparison of the coefficients of the simultaneous
and the single equation joint models can thus provide insight on the
existance of "strong" or "weak" simultaneity. For comparative purposes,
coefficients are estimated also for an additional reduced form specification
which does not include the companion's shopping activity duration. The
joint and reduced form model estimated with data from 342 male heads of
household and as many females belonging to the same households. The sample
of 342 households is a subset of the of the original 517 households; house-
holds which did not have both male and female heads were excluded. The
variables of the model include the spouse's shopping activity duration, and
the variables of the individual shopping duration model with the exclusion
of sex, age and school participation.
For reasons discussed in Chapter V, the two-stage limited dependent
variable (2SLDV), procedure proposed by Nelson and Olson (1977) was used
for estimating the coefficients of the joint equation model. The results
of the estimation are presented in Tables 6.6 and 6.7.
Model for the Male Heads of Household
The statistical significance of the model coefficients if low for all
the coefficients except home-work based shopping accessibility. It is
hypothesized that the low statistical significance of the estimated co-
efficients is due to two primary reasons. First, the estimator of the
model, as discussed above and in Chapter V, is not entirely appropriate
for the problem at hand. Second, the sample size of 342 observations is
probably small for modelling activity duration, given that less than 20%
of the individuals participate in shopping the day recorded in the interview.
76
TABLE 6.6
Hodel of Shopping Activity Timefor
Male Head of Household
Reduced Form
Model
JOINT MODEL
Simultaneous
Estimation
Single Equat.
Estimation
Constant -213.482 -178.185 -195.264
(1.57787) (1.21611) (1.46773)
Driver's) 1 no -64.7825 -53.0577 -48.2226
License 0 yes (.606463) (.488703) (.447938)
Went to work 1 yes 3.5062 -1.79656 1.6287
tO11 (.06372) (.031917) (.029473)
Ilyes
HH size over 2 -36.6386 -30.294 -15.7426
0 no (1.07048) (.848836) (.462064)
1 if -4.55442 -7.75775 -7.63769
Role household with (.074681) (.126738) (.125932)
children
10 otherwise
Home Based Shopping -2.84731 -1.87322 -.20311
Accessibility (.54008) (.340974) (.038713)
Home-Work Based 4.83937 4.72401 4.67524
'hopping Accessibility (1.6573) (1.61924) (1.6226)[if went to work]
Shopping Activity - .217736 1.14978
Time Female Head (.603286) (3.75125)
Sigma 231.286 230.955 225.392
(11.5492) (11.5515) (11.6307)
-Log Likelihood 661.887 661.703 654.627
(In parenthesis is the asymptotic t-statistic)
Dependent variable:
Sample size:
Total Shopping Activity Duration
342
77
Variable
TABLE 6.7
Model of Shopping Activity Time for
Female Head of Household
Reduced Form
Model
JOINT MODEL
Simultaneous
Estimation
Single Equat.
Estimation
Constant -110.038 -185.445 -117.285
(1.88485) (2.33412) (2.02164)
Driver's fl no -105.923 -115.061 -104.445
License 0 yes (4.40125) (4.58934) (4.37311)
Went to work U1 yes -63.3797 -65.4912 -62.9707
10 no (2.07929) (2.16486) (2.08265)
(1 yes
HH size over 2 -36.4711 -48.1024 -34.6973
.0 no (2.6244) .(2.59257) (2.19567)
1 if household 7.49386 3.4992 5.95977
with (.3693442) (.17238) (.296225)
Role children
t0 otherwise
Home Based Shopping -4.28355 -5.2572 -4.45562
Accessibility (1.79037) (2.1229) (1.87856)
Home-Work Based -2.42379 -2.12696 
-2.48061
Accessibility (1.24295) (1.09414) (1.283)[if went to work]
Shopping Activity - -.371556 .17922
Time Male Head (1.4247) (2.59333)
Sigma 113.182 112.07 111.793
(12.6938) (12.6911) (12.7181)
-Log likelihood 766.7 765.695 763.305
(In parenthesis is the asymptotic t-statistic)
Dependent variable:
Sample size:
Total Shopping Activity Duration
342
78
Variable
Despite the poor statistical properties of the model, it is possible
to derive some useful insight from the estimation. In particular, it
should be noted that the simultaneous and the single equation estimation
of the joint model yield somewhat different coefficient estimates. This
would suggest the existance of at least a "weak" simultaneity in the
process. Also note that the coefficient of the shopping time of the wife
has a positive coefficient, indicating that husbands tend to shop more when
their wives shop more. This phenomenon is probably due to the face that
typically Saturday shopping is done by all the members of the household
together.
Model of the Female Heads of Household
The same statistical caveats apply for the model of female head of
household as for the model of male head of household. However in this
model all the coefficients of the socioeconomic variables
have the expected sign and, except for the role variable, are significant
at the 95% confidence level. Note that the coefficient estimates for the
two accessibilities are negative and fairly stable for the reduced form
and joint models. It is interesting to note also that the coefficient for
the shopping activity time of the husband is negative for the simultaneous
equation and positive for the independent estimation. Since, as suggested
earlier, it is hypothesized that single equation estimation of one equation
in a simultaneous equation system yields inconsistent results, the simulta-
neous estimation is a priori deemed more reliable. The negative coefficient
of male shopping activity time indicates that the husband's shopping has a
negative effect on shopping activity duration of the wife. This suggests
79
that wives substitute their own shopping time for their husbands shopping
time;that is, wives do not have a strong preference to going themselves
or to sending their husbands. On the other hand, as shown by the male
head of household model, husbands prefer to shop with their wives and thus
shop more if their wives shop more.
Summary
The joint model discussed in this section is a first attempt to
explicitly explain simultaneity in intrahousehold task sharing. Additional
research should be devoted to the development of a behavioral theory of the
joint process which recognizes the substitutability and ccmplementarity
of the household heads' activity time. Ih addition to the theoretical
issue, it is also suggested 1) to develop an improved estimator for
simultaneous limited dependent variables models, possibly using FIML (full
information maximum likelihood), and 2) to use larger samples.
6.3.2 Models of Travel Time
Three models of travel time were estimated for the three activity
types: shopping, social/recreation and remaining activities. The models
predict the share of total activity duration devoted to travel. The
models were estimated using ordinary least squares on observations with
non-zero travel times.
Model of Travel Time to Shopping Destinations
The coefficients of travel time to shopping destinations have the
excpected signs (Table 6.8). A decrease in accessibility implies an
increase in the share of total activity duration devoted to travel.
80
Dependent variable:
Sample size
R 2.02847
Share of total shopping activity duration spent
travellins
Mean - .34571
:281
= .02148
c = .1771
Constant
.n (household income)
Accessibility shopping
Coefficient
-. 18529
.04653
-. 00412
t-statistics
.99379
2.59488
1.30157
TABLE 6.8
Model of Travel Time to Shopping Destinations
81
Specifically, if the cost of travel increases individuals will travel a
longer amount of time to destinations which have lower travel costs
associated with them. If in- or out-of-vehicle time increases, individuals
will have to travel a longer amount of time to get to activities and the
share of total activity duration they will devote to travel will increase.
Income is also positively related to the share of travel since wealthier
people can allocate a larger monetary budget to travel.
Model of Travel Time to Social/Recreation Destination
Because of problems with the software used for estimation of the
travel time models, it was not possible to evaluate directly the share
of total activity duration devoted to travel. Instead, the dependent
variable of the model was chosen to be the travel time to social/recreation
destinations, and all the independent variables were multiplied by total
activity time for social/recreation. The estimation of such a model
yields results which are different from the model which would have as a
dependent variable the share of total activity duration devoted to travel,
since different assumptions are made on the unobserved error term of the
regression. However, unbiased predictions of the share of total activity
duration devoted to travel can be obtained by dividing the right and left
hand side of the regression by total activity duration. It should be
added that the relative efficiency of the estimated model with respect to
the model whose dependent variable is the share of total activity time
spent travelling, clearly depends on the underlying distribution of the
unobserved error term. Note that the le and R2 are not reported because
they are not available; the software used for estimation, in fact, does
not compute R2 or 3 correctly for the model specification used.
82-
Dependent variable: Travel time to social/recreation destinations
Mean : 32.08430
Sample size :261
R 2  n.a. -2 n.a.
a - 24.8804
Definition: T- total social/recreation duration
Constant x T
En (household income) x T
Accessibility social/
recreation x T
Coefficient
-. 39115
.04514
-. 02355
t-statistics
3.30622
3.86574
2.16992
TABLE 6.9
Model of Travel Time to Social/Recreation Destinations
83
Model of Travel Time to the Remaining Activities Destination
This model was estimated, in a fashion similar to the social/recreation
travel share model, using as dependent variable travel time to remaining
activities, and by multiplying the independent variables by the total
duration of remaining activities (Table 6.10). Similar caveats apply to
this model specification as to the model of travel time for social/recreation
activities. A different specification than the one used in the shopping
and social/recreation model was, however, chosen, because it is assumed
that travel to the remaining activities is most sensitive to the possession
of a driver's license. Travel to activities such as personal business
and/or outdoor recreation has, in fact, characteristics which are signi-
ficantly dependent on the possession of the license. Accessibility for
shopping and social/recreation has a positive sign indicating that when
travel cost (or time) increases, the share of travel to remaining activities
decreases. In this model, accessibility and the driver's license possession
acts only as a proxy for desired vehicular mobility. It is thus reasonable
to expect a positive effect on activity duration of increased accessibility
and possession of a driver's license.
Summary
The specification of the models of travel time estimated here is a
simplification of the form presented in equation (6.3). It was however
decided to adopt this simplification in order to streamline the estimation
and prediction phases of the research, and to remain within the allocated
analysis budget.
84
Dependent variable: Travel time to remaining activities
Mean: 33.59890
Remaining activities: Medical, outdoor recreation, personal business, serve
passenger.
Sample size: 354
2 -2R -n.a. R - n.a.
a - 25.1284
Definition: 1 a total duration of remaining activities
Coefficient t statistics
constant x T .30230 5.05435
1 no
T x Driver's License -.06011 3.02851
0 yes
(Accessibility shopping +
accessibility social/recreation) x T .00320 1.43756
TABLE 6Z0
Model of Travel Time to the Remaining-Ac tivities Destinations
85
Accessibility has a negative sign in the shopping and social/recreation
travel share models indicating that a decrease in transportation level-of-
dervice (increase in cost, in-vehicle travel time or out-of-vehicle time)
would cause an increase in the share of total activity time spent travelling.
For the remaining activities, the sign of the coefficient of the accessi-
bility measure is positive, suggesting that the travel share of remaining
activities would decrease in case of a decrease in transportation level-
of-service.
86
CHAPTER VII
IMPLICATIONS OF THE ESTIMATED MODELS
7.1 Introduction
In order to clarify some of the implications of the activity pattern
models, this chapter analyzes aggregate predictions derived from the models.
Two general types of model predictions are discussed. The first presents'
the impact of level-of-service policies on predicted activity duration and
travel time. The second analyzes the change in aggregate activity duration
due to changes in socioeconomic characteristics, with specific focus on
current trends in female labor force participation and possession of a
driver's license.
7.2 Activity Patterns for Transportation Level-of-Service Changes
The models presented in Chapter VI are sensitive to level-of-service.
Specifically,, a change in out-of-pocket costs, or in travel time to'
destinations, will have an effect on the predicted activity patterns,
i.e., on activity duration and travel time to the activities. It is the
purpose of this section to report the impact of transportation level-of-
service changes on aggregate activity patterns.
The policies tested included changes in automobile operating costs, and
in out-of-vehicle and in-vehicle time. No attempt is made to investigate
the destination and mode choice implications of the changes. Rather,. the
emphasis is on the shifts in total activity duration and the travel time
to activities. In particular, changes in travel time are an indication of
changes in vehicle-miles travelled, or combustion emissions. In order to
simplify the analysis, and to limit the analysis cost, only automobile
87
related policies are tested. The models are however sensitive to public
transportation policies, and such policies could be tested. The three
level-of-service policies discussed in this section are, among the auto-
mobile related policies, those which are the most often considered by
transportation planners (and politicians). Schemes for implementation of
these policies include added gasoline or roadway taxes, parking restrictions,
signallization, speed limits, one-way streets, etc.
In order to simplify the computation of the predictions, changes in
the value of the endogenous variables are predicted only for a limited
number of market segments. All the prediction values were computed from
the estimated models using a programmable pocket calculator. For level-
of-service policies, predictions are computed for only one "average"
individual. Moreover, it was assumed that there is only one destination
available for each alternative activity. The values of level-of-service
and land-use characteristics used refer to that single destination and
are sample averages. Home-work based shopping accessibility for workers
is, for simplicity, assumed constant across all policies and equal to the
average value observed in the sample. The values of the variables (socio-
economic, level-of-service, and land-use) for the base case are listed in
Table 7.1. The results of the policy predictions measures, and their
definition is:
1) Activity duration given participation is the predicted
activity duration, conditional on participation in the activity.
2) Probability of participation is the probability that activity
duration for the activity will be non-zero.
3) Unconditional activity duration is the predicted duration
independent of the probability of participation.
88
Table 7.1
Base Values for the Exogenous Variables of the Activity5Duration
Models for Use in Level-of-Service Policy Predictions
Socioeconomic
Dummy for sex = .5; Dummy for driver's license = .4; Dummy
for travel to work or school = .5; Dummy for household size = .6;
Household size = 1.85; Dummy for child = .1; Dummy for role = .2;
Automobiles owned = 1.3; Income = $13,500/year.
Level-of-service for Shopping Travel
Dummy for automobile mode = .9; Out-of-vehicle time = 2 minutes;
In-vehicle travel time = 6 minutes; Out-of-pocket travel cost = 30o;
Distance = 3 miles.
Land-use for shopping travel
Retail employment density = 30 retail employees per net commercial
acre; Retail employment = 200 employees; Home-work based shopping
accessibility = -4.8 .
Level-of-service for Social/Recreation Travel
Dummy for automobile mode = 1; Out-of-vehicle time = 3 minutes;
In-vehicle travel time = 10 minutes; Out-of-pocket travel cost = 50;
Distance = 5 miles.
Land-use for Social/Recreation Travel
Population - 900; Total zonal employment = 100 employees; Vacant
area = 5.0 acres.
89
4) Travel time given participation is the travel time to the
activity derived from the activity duration given parti-
cipation in the activity.
5) Unconditional travel time is the travel time to the
activity derived from the unconditional activity duration.
6) Total unconditional travel time is the sum of the
unconditional travel times for all the activities
modelled. (Table 7.2).
7.2.1. Doubling Out-of-Pocket Costs
The policy of doubling out-of-pocket (operating) costs does not have
a major effect on activity duration, or travel time, for any of the three
activity types. This is due to the relatively small effect of travel cost
on the accessibility. The doubling of automobile operating costs decreases
the probability of participation in shopping and social/recreation activities
by .6% and .8% respectively. Expected duration and travel time for the same
two activities, however, changes by smaller percentages. Note that, for
shopping and social/recreation, travel time given participation increases,
while unconditional travel time decreases. This indicates that partici-
pation in activities will require longer travel times, since individuals
will choose different destinations with lower access costs. However, the
reduced frequency of activity participation will cause an overall decrease
in travel time (-.3% and -1.2% for shopping and social/recreation trips,
respectively).
7.2.2 Doubling Out-of-Vehicle Time
The doubling of out-of-vehicle time has a much more significant effect
on activity patterns than the doubling of cost. Most significant are the
changes in travel time and in the probability of participation in activities.
90
Vul' y S.
Me-a~ v. e---its. i.s J
A.-Iswimy --- - 2 -- --
-9. 19 i .95 125.5-
With
i.menge with
G ai. uct to - - -
La ocase l1
Expucted
valu.9 3.9 23.ill
.LJ1hUs with
tvbir..i LU - - -
bass Cia
a 16.52 11.92 30. 6
ChA: El with
4, : resapect to - -
*0 Lapuccad C
* 4 Viluc 31.33 29.03 24.55
a Cissmgu with
s inepucito -. - -
I ue5.6 3.5 5.9
S ruapuct 10 - - -
bie rass ill
Eapi. LedIA wlle I15.0
2 . Citaugu vsill.
I k mub i in -veh ic leu t in J eh t im -u t-- uI-p m. bL cOO L
* 2 1 2 3 1 1 2 3
91.11 145. Y5 117.12 - IO.I1 140.32 126.55 92.06 150.69 126.72
-3. -3. -. -22 -. 1 .8 .1 -.2 -.1
17.1 10.0 23.2 16.4 6.3 22.4 f 11. 11.6 23.7
-3.6 -15.4 -2.5 -5.4 -30.2 -5.9 -. 6 -.6 -. 6
15.77 14.64 29.65 14.50 11.62 m.40 16.41 11.73 30.54
14- 1.--.4
-4.5 -15.3 -3.3
31.82
-15.4
31.13 21.43 32.45
-35.2 -7.4
33.67 21.61
-.7
31.40
.1 - 4
29.14 24.72
1.6 7.9 -5.8 16.0 -13.1 .2 .6 .6
5.5 3.1 5.4 j 5.i 2.3 4.5 f 5. 3.4 5.3
-1.3 -9.3 -6.2 -5.0 -19.1 -18.3 -.3 -1.2 -1.1
14.0 12.9 14.9
-6.4
=1 -14.1
() 1scludcp out-af-vshiclr tam and in-vhicl gmlw.
Acliv ; sa. -1. Shappiag
2. SucWaL/r-:rsatota
1. Srmainiag *a.. iLvLlwm. Ndical. OuL4uur RecrMation,
pctcwual bubaess, Sarve Pssenger.
Knyarcs ul bui1: hrstl.
tii lr.va1
for .xvl-of-Srviru Policita
1.-A
i - .1
Particularly sensitive to out-of-vehicle time is the social/recreation
activity; this policy causes a 15% decrease in the participation rate
with a 9% decrease in the total travel time generated by social/recreation
trips. Shopping is less sensitive to the policy, and the decrease in
total travel time is 2%.
7.2.3 Doubling In-Vehicle Travel Time
The policy of doubling in-vehicle travel time has a significant effect
on activity patterns. Note that the largest change is predicted in the
probability of participation in social/recreation trips, a drop from 11.9%
to 8.3%. Also the unconditional expected travel time decreases from 3.5
to 2.8 minutes, a drop of 19%. The predicted decrease in unconditional
travel time to the remaining activities is 18%.
7.2.4 Summary
The changes in non-work activity duration due to level-of-service
policies all have the expected sign. A cost or time increase causes
activity duration for all activities to decrease. Note that the pricing
policy yields changes in predictions which are much smaller than the
changes in prediction due to travel time policies. For all non-work
activities the travel time changes due to the pricing policy is negligible.
However, the out-of-vehicle time policy decreases non-work travel time
by 6.4% and non-work participation 5.8%. The in-vehicle time policy
decreases non-work travel time by 14.1% and trip generation by 12.1%.
7.3 Future Changes in Activity Patterns
This section illustrates the effect of socioeconomic and demographic
variability on activity duration. Sensitivity of expected activity
92
duration to socioeconomic and demographic characteristics is tested by
varying the values of the relevant independent variables in the models.
Furthermore, specific emphasis is placed on two relevant trends, the
increased participation of females in the labor force, and the increased
desire of individuals for vehicular mobility, as represented by the
increased rate of issuance of driver's licenses.
7.3.1 Implications of Socioeconomic Characteristics
In order to test the implications of the socioeconomic characteristics
on.activity duration, a segmentation of the population into relatively
homogeneous markets is performed. The dimensions of stratification used
are four: sex, work (or school) travel, possession of a driver's license
and age. The share in the population of the 12 markets derived from the
proposed stratification is illustrated in Table 7.3. Note that, by
definition,children (under 17 years of age) do not possess a driver's
license. This implies that the market segments of children with driver's
license are void. The value of the independent variables which were not
used in the stratification is assumed to be the average value of that
variable in the corresponding market segment. The predictions which were
derived from the above classification (for the three activity types across
the twelve market segments) are presented in Tables 7.4, 7.5 and 7.6.
The effect of a single variable on the activity duration of the
population as a whole is tested by modifying the base case share of the
market segments. As an example, in order to test the effect of'an in-
crease in the possession of driver's licenses, the share of individuals
with driver's licenses is increased by 1% with respect to the base case.
93
Work or Frequency Market
School Driver's in the Segment
Sex Status [icense Age Population Number
Under 17 -
Yes
Went- to Over 16 .2034 1
work or
school
Under 17 .0263 2
No
Over 16 .0071 3
Male
Under 17 -
Yes
Did not go Over 16 .1181 4
to work or
school
Under 17 .1174 5
No
Over 16 .0114 6
Under 17 -
Yes
Went to Over 16 .0818 7
work or
school
Under 17 .0249 8
Female No
Over 16 .0171 9
Under 17 -
Yes
Did not go Over 16 .2091 10
to work or
school
Under 17 .1195 11
No
Over 16 .0640 12
TABLE 7.3
Definition and Frequency of the Market
94
Segments in the Population
Market 
-1
1 2 3 4 5 6 7 8 9 10 11 12 ighted
Measure
Expected
duration
given part- 92.33 '80.13 '77.51 106.31 76.72 88.08 101.01 104.67 81.25 112.41 80.40 92.67 95.3058
icipation
[min]
Probability
of partic- .1802 .0974 .0822 .2870 .0778 .1496 .2461 .2744 .1043 .3340 .0990 .1827 .206642
ipation
Uncondition-
al expected 6.64 7.80 6.37 30.51 5.97 13.18 24.85 28.72 8.47 37.54 7.96 L6.93 20.8664
duration
(*) Weighted by the frequency in the population
TABLE 7.4
Base Measures of Shopping Duration
Ln
Market
egment 1 2 3 4 5 6 7 8 9 10 11 12 Weighted
sum(
Measure
Expected
duration
given part- 155.8 133.1 126.3 160.1 141.8 129.3 163.6 139.1 131.8 168.2 148.5 135.1 153.78
icipation
[min]
Probability
of partic- .136 .062 .045 .153 .088 .052 .167 .079 .058 .186 .110 .067 .1316
ipation
Uncondition-
al expected 21.2 8.2 5.6 24.5 12.4 6.7 27.3 11.0 7.7 31.2 16.3 9.1 20.71
duration
r)
(*) Weighted by the frequency in the population
TABLE 7.5
Base Measures of Social/Recreation Duration
r
%0
ON
Market
egment 1 2 3 4 5 6 7 8 9 10 11 12 Weighted
Sum (*)
Measure
Expected
duration
given part-131.46 110.56 111.87 152.14 116.17 128.00 125.45 105.94 107.17 144.72 111.18 122.22 129.61
icipation
[min]
Probability
of partic- .254 .134 .141 .376 .164 .233 .218 .110 .116 .333 .137 .199 .2438
ipation
Unconditior
al expected 33.36 14.79 15.74 57.28 19.09 29.83 27.33 11.67 12.46 48.21 15.24 24.31 32.83
duration
(*) Weighted by the frequency in the population
TABLE 7.6
Base Measures of Remaining Activities Duration
The relative shares of the three other dimensions (sex, work or school
travel and age) is maintained constant, In general, in order to maintain
the relative shares of the other stratification dimensions constants, an
iterative procedure is required. As an example, increasing the share of
the market segments for individuals that possess a driver's license (market
segments 1, 4, 7 and 10) would, if not adjusted, increase the share of male
in the population. The prediction results for a 1% increase in the male
population share and an identical increase in the share of individuals
going to work or school and in the share of individuals possessing a
driver's license are reported in Table 7.7. Note that the increase in
male population share has a negative effect on shopping and social/
recreation duration and a positive effect on remaining activities duration.
This suggests that men devote more time than women to activities such as
personal business, serve passenger, etc. Somewhat surprising is the small
changes caused by an increase in the share of workers (or students) in the
population. This suggests that individuals who do not work (or do not go
to school) allocate, at least during a weekday, most of their extra "leisure"
time not to more out-of-home activities but to more in-home activities.
As expected the increase in the share of individuals possessing a driver's
license has a large positive effect on the duration and frequency of
participation of all- the activity types.
7.3.2 Implications of Socioeconomic Trends
This section examines the implications of two major socioeconomic
trends.: the increase in the female labor force participation and the
increase in the possession of driver's licenses. The two trends are
98
ni Dl Ranrantinn
Remaining
Aptfvtuiit
Measures 1 2 3 1 2 3 1 2 3
Expected
Value 95.3 20.6 20.8 153.7 13.1 20.7 129.6 24.4 32.9
LayI fo
U
@pp
Change with
irespect2to 0.0 -.1 -.2 0.0 -.1 -.2 0.0 .1 .1
base case[2
Expected
Value 95.3 20. 20.8 153.9 13.2 20.7 129.6 24.4 32.8
0 04
0uChange with
respect to 0.0 0.0 -.1 0.0 0.0 -.1 0.0 -.1 -.1o ".
0U"base case [2)
Expected
Value 95.4 20.8 21.0 153.Q 13.2 20.R 129.8 24.5 33.0
Change with
V resp ct to .1. 5 .. 6 . 1 . .. .4 .1 -.4 -.5
base case[]
>GW Change with
~,respect to .1 .5 .6 .1 .4 . .4 .1 .4 .5
base case [2)
Measures: 1. Activity duration
given participation [min]
2. Probability of participation [%]
3. Unconditional
activity duration (min]
TABLE 7.7
Effect of Socioeconomic Characteristics on
Activity Duration.
99
At ti li Shnnin
analyzed separately, and net of any other socioeconomic trend, It is
assumed that the representative trends were those observed to have occured
in the period 1969 to 1974. All the predicted changes in activity duration
reported in this section refer to the expected change over this "typical"
five year period.
The trends are derived from national data collected and tabulated by
the U.S. Bureau of the Census (1975). It was also assumed that national
trends would be valid in predictions for the Minneapolis-St. Paul metro-
politan area.
Female Labor Force Participation
While the growth in participation of men in the labor force is
parallel to the growth in the adult population (9.67% vs. 9.88%), the
growth in women's participation is more pronounced. Between 1969 and
1974, the increase in female labor force has been 17.09%. This is
7.12% above the adult population growth.
In order to compute the predicted activity duration for this scenario,
the frequency of females over sixteen who went to work is increased
by 7.21%. The frequency of females over sixteen who did not go to work
is decreased accordingly. The results of the predictions are reported in
(*)The 17.09% increase includes both employed and unemployed women. How-
ever, in 1974 because of the very bad employment prospects, many women
had effectively dropped out of the labor force, and do not appear in this
increase. The true long run rate of increase of the femal labor force
participation might thus be underestimated by the 1969 to 1974 trend.
This includes the entire market segments 7 and 9.
100
Table 7.8. Note that, although work has a negative effect on activity
duration, the model predicts an increase in activity duration for shopping
and social/recreation. This is due to the fact that the frequency of
working women with driver's licenses (market segment 7), within the class
of working women, is much higher than the frequency of non-working women
with driver's licenses within the class of non-working women. Assuming
the new entrants into the labor force acquire licenses in the same pro-
portion as their already working counterparts, this implies that an
increase in the proportion of working women would increase the frequency
of individuals in possession of a driver's license. Thus the decrease
in shopping and social/recreation duration due to more working women is
offset by the stronger effect of increased proportion of drivers. For
the remaining activities, however, the negative impact of work on activity
duration is not completely offset by the positive effect of driver's
license. The effect on non-work activities of increased female parti-
cipation in the labor force on the population as a whole is a decrease in
the probability of participation of .04% and a decrease in the unconditional
duration of .03%. These changes in aggregate predictions are very small,
but it should be remembered that the fraction of the population which is
affected by the trend represents only 10% of the total population.
Driver's License Possession
Statistics show that the share of adults possessing a driver's
license is increasing. The increase in share appears, for all practical
purposes, only in the group of adult women. The rate of increase of
possession of driver's licenses in this group over the typical five year
101
TABLE 7.8
Activity Program Changes for Increased Female
Labor Force Participation (*)
Activity
Duration given
participation
Probability of
participation
Unconditional
duration
Shopping
.0175
.0526
.0408
Social/
Recreation
.0204
.053
.116
Remaining
* 041
-. 127
.175
(*) Measures are percent changes with respect to base case
102
Total
-.04
-.03
AL a
period (1969 - 1974), net of population growth, is 13.8%, In order to
compute the predicted activity duration due to this trend, the share of
adult women with a driver's license is increased by 13.8%. The share of
adult woemn without a license is decreased according. The results of the
predictions are reported in Table 7.9. All the predicted changes have
the expected sign.
The increase in the share of women drivers over non-drivers has
the effect of increasing the proportion of adults and workers in the
population. Note that, while work has always a negative effect on
activity duration, the effect of adult age is positive on the shopping
duration and negative on social/recreation duration (the age variable
does not appear in the model of remaining activities). The negative
effects of work and adult age (on social/recreation only) have not,
however, altered the directionality of the changes in activity duration
for any of the three activity types. The effect on all non-work activities
of the increased possession of driver's licenses is an increase in the
probability of participation of 2.8% and in the unconditional duration of
3.4%.
7.3.3 Summary
The changes in non-work activity duration caused by changes in socio-
economic characteristics all have the expected sign. In particular, the
possession of a driver's license and sex are the most important deter-
minants of activity duration. Moreover, it is interesting to point out
that the results of the models suggest that the effect on activity duration
of going to work or school is very small. This implies that, if in the
103
TABLE 7.9
Program Changes for IncreasedPossession of
Driver's License (*)
Activity
Duration given
participation
Probability of
participation
Unconditional
duration
Shopping
.951
3.239
4.066
Social
Recreation
639
2.715
3.196
Remaining
. 799
2.498
3.070
(*) Measures are percent changes with respect to base case
104
Activity
2.8
3.4
Total
future the work duration of individuals were to decrease, people would
devote only a fraction of the additional time availeble to them to out,-.
of-home activities; most of the additional time would be devoted to in-
home activities.
The two scenarios of increased female participation in the labor
force and increased possession of driver's licenses also have the expected
effect on activity duration. A .9% increase in unconditional activity
duration is predicted for the latter trend And a .03% decrease is pre-
dicted for the former, both over a five year period.
105
CHAPTER VIII
SUMMARY AND CONCLUSIONS
8.1 Summary
This research has addressed the theoretical and empirical issues in
modelling the duration of non-work out-of-home activities. The primary
objective of this research is to advance the state-of-the-art in non-work
travel demand modelling. Specifically, past research has neglected to
regard travel demand as demand derived from basic commodities such as
activities. The decision to travel is, in almost all cases, not generated
by the pleasure of driving, or sitting in a bus, but primarily by expecta-
tions on the activity to be performed at the destination of the trip.
The.theoretical approach proposed here is derived from conventional
consumer theory. It explicitly recognizes the impact of transportation
level-of-service and land-use on activity duration. However, because
of the complexity of the problem, it was not possible to solve analytically
the proposed theoretical model. Nevertheless, based on the implicit
solution and a priori considerations, it was assumed that accessibility,
a composite measure of level-of-service and density of opportunities,
should appear explicitly as a variable in the models of activity duration.
Other variables which have been proposed in the current literature as
determinants of activity patterns have also been included in the models.
These variables are socioeconomic and demographic characteristics and
include sex, work status, age, household size, child rearing responsabi-
lities and income.
106
The shifts in non-work activity programs due to transportation
level-of-service changes are significant, primarily for travel time
policies (in- and out-of-vehicle times). In particular, a decrease
in the speed of travel decreases activity duration for all the activities
modelled and decreases the total time individuals spend travelling.
The effect of the cost policy (out-of-pocket cost) is an order of
magnitude smaller than the effect of the travel time policies. This
is due, primarily, to the low importance individuals attach to travel
cost when deciding on participation in discretionary activities.
Note that a change in activity duration corresponds, in the framework
developed for this research, to a change in probability of participation
in the activity. Although a rigorous relationship between probability
of participation and trip generation has not been developed, nevertheless
it can be reasonably assumed that, everything else being equal, a de-
crease in the probability of participation in a given activity corresponds
to a decrease in trip generation, and viceversa. Thus, among other
things, by showing that non-work activity programs are sensitive, at least
in the short run, to the level-of-service of the transportation system,
it is possible to infer that trip generation is also sensitive to
level-of-service.
The importance of socioeconomic characteristics is also significant.
Specifically, the possession of a driver's license, which represents
the desire for vehicular mobility, has a large impact on activity duration.
While the percentage of adult women who have a driver's license has been
increasing at a rate of approximately 2.7% per annum. This trend applied
107
to the estimated models suggest that, in the future, more time is going
to be spent in non-work out-of-home activities.
A major trend, which offsets somewhat the previous, is the one that
indicates that more and more women are entering the labor force. While
the pure effect of work participation is a decrease in activity duration
for all activities, it is expected that working women would possess
relatively more driver's licenses than non-working women, and thus would
have higher travel mobility. The combined effect of increased work
duration and driver's license possession due to this trend is an increase
in shopping and social/recreation duration. Another major finding of
this research indicates that a work duration decrease would not increase
significantly the duration of weekday non-work activities. In particular,
it is suggested that, in the future, if work hours were to decrease, the
"new" leisure time available would not be devoted primarily to more out-
of-home activities, but mostly to in-home activities.
The estimation of the simultaneous shopping duration model for the
two heads of household has not been entirely satisfactory. This is
due primarily to the large standard error for the estimated coefficients,
and to the model form assumed (Nelson and Olson, 1977), which, although
the best available at present, is not well adapted for the problem at hand.
It was, nevertheless, possible to derive some preliminary conclusions.
In particular, the estimated models suggest that the equation for the male
head of household (the husband) should include the shopping activity
duration of the female head of household (the wife).
108
Also the results of the models for heads of household suggest that
estimation of models of activity duration for different population groups
would yield' coefficient estimates which can be significantly different
from those estimated on the full cross-section of the population.
8.2 Recommendations and Directions for Further Research
8.2.1 Near Term Recommendations
The results of this research have provided useful insights in the
modelling of activity duration and participation. Nevertheless, issues
and problems, which for various reasons were not addressed, have surfaced
both during the research, and in the analysis of the results. It is the
purpose of this section to provide guidance to future researchers in
this field, so that they might continue the work presented here, extending
it, and avoiding some of the problems that were encountered.
The primary issue regards the size of the estimation sample. Strict
budget constraints for this research have dictated a significant reduction
in the sample size for model estimation. This, combined with the high
iariability of the observed activity durations and participation is assumed
to be the major cause of the somewhat poor statistical properties of the
estimated models. It is suggested, for future research, to use a larger
sample of observations (>5,000 individuals). Note however that the costs
of estimation of limited dependent variable models with such a sample
size can be very high (>$100 per model).
A second important issue is the itaprovement. of the models for
prediction of travel time. The models presented in this research are
multivariate regressions which predict the share of total activity duration
109
which is devoted to travel for each given activity. A better model, which
was not adopted for this research because of the limited computer budget
available, is based on the explicit use of travel demand models such as
a destination and mode choice model. This model derives directly from
the models of activity duration and a travel demand model conditional on
activity duration and does not require any additional model estimation.
Some of the empirical results also have suggested some areas in which
further investigation seems appropriate. In particular, the issue of
joint travel of members of the household has not been investigated. This
was primarily due to the potential computational problems that could have
been generated by the sorting of joint household travel from individual-
level trip information. In fact, trip information is recorded at the
individual level and the recorded data does not permit to identify expli-
citly the members of the household (or friends) with whom a trip might
have taken place. It is however possible, by matching information such
as trip origin and destination, start and end time, and mode, to determine
whether a given trip was made with one or more household members. Data,
nevertheless, cannot be obtained on friends or other individuals who might
share a ride in the vehicle but who are not members of the household.
Neglecting joint travel causes an evident overprediction of the value
of time, since it is expected that actual travel costs are lower than
those used for model estimation. Travel costs for an automobile trip to
a shopping mall with two occupants in the vehicle are double-counted in
the individual activity duration model. An additional issue which was
considered secondary to this research is the impact of vehicular mode
110
choice on activity patterns. It is hypothesized that individuals choosing
public transportation for their mode to work are less likely to participate
in descretionary activities than individuals choosing private automobile.
This is primarily due to the fixed nature of the route and fare structure
of the transit system,.which does not favor deviations on the home-work,
work-home trip.
With regard to the estimation of the econometric models, two issues
are of interest. First, it is suggested to estimate the model form pro-
posed by Westin (1975) with a larger sample size. It is hypothesized
that the larger sample size would improve the reliability of the estimates
and thus yield acceptable coefficients. A Westin type model was estimated
with the smaller sample size available for this research. The coefficient
estimates were, however, highly unreliable. This problem is discussed in
more detail in Chapter V. Second, it is suggested to develop an alternative
to the simultaneous limited dependent variable model developed by Nelson
and Olson (1977) which is used in this research to estimate joint activity
duration models. Two possible estimation procedures could be developed.
One is the full information maximum likelihood (FIML), which is to be
considered a technique of last resort, since it involves the repeated
evaluation of the cumulative multivariate normal distribution for which
no close form solution exists. A second procedure would require the
development of an equivalent of the two stage least squares estimator for
the simultaneous limited dependent variable model. For experimental pur-
poses the first procedure (FIML) is to be preferred because it yields
estimates with all the desirable statistical properties. For repeated
111
model estimation, however, the development of a limited information maximum
likelihood estimation procedure is required in order to reduce model
development costs.
8.2.2 Long Term Recommendations
The most important long term recommendation involves the data.
In particular, the framework developed within this research is based
primarily on the duration constraint; however little or no data is avail-
able on the scheduling and temporal distribution of the constraint. For
example, if an individual works from nine o'clock to five o'clock every
weekday,it will be impossible for him (or her) to go to the bank, or to
a store, that has those opening hours. Thus, this individual will not
be observed participating in any of the above activities, not because
of limited time available to him, but primarily because of scheduling
conflicts. Other components of activity duration modelling that require
additional investigation, but cannot be analyzed because of the limitations
of currently available data,include the determinants of intra-household
task sharing and activity scheduling, and the determinants of activity
duration. Negligence of the above components could give rise to a signi-
ficant misinterpretation of the "causal" determinants of activity duration.
Thus it is suggested here that, in order to avoid important biases in the
analysis and the prediction, the data to be collected for future research
include more relevant information than currently available in typical
urban transportation surveys.
112
Another area in which further research is recommended is the develop-
ment of improved theoretical and econometric models. It is believed that
the development of an improved theoretical model will permit better
understanding of the activity pattern decision process. And, in order to
best exploit the improvements in the theoretical model, it is probable that
a new econometric approach would have to be developed to evaluate the
parameters.
113
APPENDIX I
THEORY OF ACCESSIBILITY
This appendix presents both the theoretical justification for the
specific functional form adopted, and the empirical application for
actual evaluation of accessibility.
Accessibility in the context of this research, is a measure which
is directly related to the travel choices of decision makers. Specifi-
cally, as Ben-Akiva and Lerman (1977) write "... accessibility... refers
to some composite measure which describes the characteristics of a group
of alternatives as they are perceived by a particular individual."
Clearly accessibility depends on the set of alternatives being evaluated
by the decision maker, and on the characteristics of the decision maker.
Ben-Akiva and Lerman formalize the concept of accessibility as being
"the outcome of an operation on a set of travel alternative". Under the
common assumptions of utility theory and disaggregate demand modelling,
a decision maker t will choose, out of the set of his available travel
alternatives Ctthe one with the highest utility. However, since
utility is (at least from an observer's perspective) a random variable,
the utility of the most desirable alternative cannot be measured. Ben-
Akiva and Lerman suggest, as an alternative to this measure, the expected
value of the maximum of the utilities of the travel alternatives which
is written as:
A(C ) r E[Max (U )] (I.1)t ieC itt
114
where A(Ct) is called accessibility, and Uit is the utility of alternative
i to individual t. Assume a multinomial logit model of choice of the form:
exp(V )
P(iICt) it(.2exp(VI ) (1.2)t iexp(V j
where P(iICt) is the probability that individual t will choose alternative
i given Ct, and Vit is the systematic component of the utility function
Uit (with Uit = Vit +it wheree it is the random utility component).
Given the assumed model of choice, the accessibility can be derived in
closed form as:
A(Ct) = ln E e + Constant (1.3)
ic Ct Ct,-
The first term on the right hand side of (1.3) is the natural logarithm
of the denominator of the multinomial logit model, the constant term can
be omitted since only changes or relative values of A(C ) are of interest.
.t
The final expression for accessibility derived from the above assumptions
is thus:
Vit
A(Ct)1ln Z e (1.4)
t
Assuming that average utility function Vit is linear in the unknown para-
meters, it is written as:
Vit = a!Xit vi (1.5)
115
where x is a column vector of explanatory variables, and is a column
vector of parameters to be estimated. It is necessary at this stage to
extend somewhat the analysis to include the specification of Ct, the set
of alternatives available to individual t. When modelling travel demand,
one has to account for the multiple dimensions of choice with which
decision makers are faced. Specifically, the relevant decisions include
not only all travel choices such as mode, route, destination, etc., but
also travel-related choices such as auto ownership, residential location,
work place, etc.
For modelling activity patterns, it is assumed that work hours, the
mode to work, residential location, and automobile ownership are fixed.
Specifically, it is assumed that non-work activities and the related
travel patterns are short-run decisions, while work, residential location
and automobile ownership are long-run decisions. The distinction between
short and long-run decisions is formalized in the concept of the "hier-
archy of choices".(* Long-run choices, also termed mobility decisions,
are at the top of the hierarchy. The short-run decisions, also termed
non-work activity duration/travel patterns, are made conditional on the
long-run decisions (Figure I.1).
We will hypothesize a similar hierarchy of choices within the short-
run decisions. It is assumed that consumers first decide on activity
duration, and then, conditional on activity duration, choose their travel
(See Ben-Akiva (1973), Lerman (1975) and Adler (1976) for disz:ussions
of alternative choice hierarchies.
116
MOBILITY DECISIONS
Residential Mobility
Residential Location
Labor Force Participation
Work Place
Auto Ownership
Mode of Work
NON-WORK ACTIVITY DURATION/TRAVEL PATTERN
Activity Type and Duration
Tour Type
Tour Schedule
Destinations
Modes
Route Choice
Etc.
Figure 1.1
BASIC CHOICE HIERARCHY
117
pattern (Figure 1.2). The above theoretical assumptions imply that.,
when individuals decide on the activity duration, their travel pattern
in indeterminate. It is thus impossible to write the utility for a
specific alternative. It is possible, nevertheless, to define a com-
posite measure, such as accessibility, that describes the characteristics
of the travel pattern for a given activity.
It is assumed that individuals' choice of destination and mode
alternatives vary with the activity performed at the destination. Thus,
in order to compute the accessibility for a particular activity, different
models of destination and mode choice have to be estimated for each activity
type. In the present study three activities are modelled: shopping,
social/recreation and the remaining non-work activities (medical, outdoor
recreation, personal business, and serve passenger). Accordingly three
different accessibility measures need to be developed for the three
activities. Destination/mode-choice models for shopping and social/
recreation activities have already been estimated by Adler and Ben-Akiva
(1976) and Ben-Akiva and Adler (1975) for Washington, D.C.; no model
has been estimated for the remaining activities. It was not feasible
(because of budget constraints) to estimate a completly new model for
the remaining activities. Therefore only two joint destination and mode
choice multinomial logit models were estimated using the model specifi-
cation already available from the two studies mentioned earlier. The
(*)While the scope of the present research is limited to the modelling of
activity duration, a related research currently in progress (Damm,1978) is
investigating the issues involved in the scheduling of activities and travel.
118
ACTIVITY DURATION
Activity Type
Activity Duration
TRAVEL PATTERN
Tour Type
Tour Schedule
Destinations
Modes
Route Choice
Etc.
Figure 1.2
NON-WORK CHOICE HIERARCHY
119
The sum of the shopping and social/recreation accessibilities is used in
the remaining-activities duration model as a proxy for the accessibility
which could not be estimated.
From the reduced sample, home based shopping and social/recreation
trips were sorted. This yielded 128 observations for the estimation of
the shopping model and 77 for the estimation of the social/recreation
model. The preliminary models estimated yeilded a high value of time
(>$100/hour). This was assumed to be due to the small estimation sample.
It was thus decided to constrain the value of time to a smaller value,
and this procedure yielded the estimated coefficients in Tables I.1 and
1.2.
Accessibility from the estimated models was then computed using
equation (1.4). Because the total number of alternative destinations
available to each individuals is assumed to be 1058 (the number of zones
coded for the Twin Cities metropolitan area), for computational sim-
plicity it was decided to draw a random sample of alternative destinations
for the computation of accessibility, instead of enumerating all the
alteratives. A maximum of forty destinations and two modes were selected
for each individual. Note that a selected zone was not considered an
alternative destination in the computation of the shopping or social/
recreation accessibility if, respectively, no stores or no social/recreation
opportunities were available in that zone. If transit were not available
to a given destination, only the automobile mode was considered. Further-
more, the automobile mode was assumed to be non-available for household
or individuals who didn't own a vehicle.
120
TABLE 1.1
Shopping Destination Mode Choice Model
Variable
(t-sta tis tics)
*1 = 0 - 2,999
2 = 3,000 - 3,999
3 = 4,000 - 5,999
4 = 6,000 - 7,999
5 = 8,000 - 9,999
Sample Size: 128
6
7
8
9
10
10,000
12,000
15,000
20,000
25,000
Coefficient
11, 999
14,999
19,999
24,999
+
121
Auto const. [for auto mode only] -8.134
(2.597)
Autos owned [for auto mode only] .7291
(by the hh) (.4258)
Ret. emply. density [retail employees/ -.001761
net commercial acreage] (.5866)
ln retail employment [employees] 1.00
(NA)
-.05 x ovtt [min. one way]/dist [miles
one way] + 3.672
-2.4 x ln (ivtt [min. one way] + ovtt (6.360)
[min. one way]) +
-.02 x optc [c one way]/ hh income [code*I
TABLE I.2
Social/Recreation Destination-Mode
Choice Model
Variable Coefficient
*
See Table 1.1 for income codes.
(t-statistics)
Sample size: 77
122
Auto constant 2.554
(for auto mode) (.3884)
ln(Weighted Attraction Variable) =
ln(.00018 x population +
.00096 x total zonal employment+ 1.00
.00036 x vacant area [1/10 acre]) (NA)
-.21 x ovtt[min. one way]/dist[miles
one way] +
-1.9 x ln (ivtt [min. one way] +
ovtt [min. one way]) + 1.828
-.004 x optc[ one way]/hh income (6.850)
[code*]
The level-of-service used for the evaluation of accessibility (except
for the home-work based shopping accessibility) is the one-way mode-
specific travel time and cost from home to each of the forty destinations.
The home-work based accessibility is the accessibility of destination
and mode alternatives, given that the destinations are reached by a
deviation from the home to work or work to home trip. Since home to work
and work to home trips are assumed exogenous (i.e. they would be performed
anyhow), the travel time and cost to the activities reached by such a
deviation is equal to only the incremental and not to the full travel time
and cost of the tour which includes home, the workplace and the destination.
123
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