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Household activity-travel behavior : implementation of

within-household interactions

Citation for published version (APA):

Anggraini, R. (2009). Household activity-travel behavior : implementation of within-household interactions. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR657789

DOI:

10.6100/IR657789

Document status and date: Published: 01/01/2009

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Household Activity-Travel Behavior:

Implementation of Within-Household

Interactions

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op dinsdag 1 december 2009 om 16.00 uur

door

Renni Anggraini

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Dit proefschrift is goedgekeurd door de promotor:

prof.dr. H.J.P. Timmermans

Copromotor: dr. T.A. Arentze

Copyright © 2009 R. Anggraini Technische Universiteit Eindhoven,

Faculteit Bouwkunde, Urban Planning Group

Photo by: Aldy Fithrico

Cover design: Tekenstudio, Faculteit Bouwkunde

Printed by the Eindhoven University of Technology Press Facilities

BOUWSTENEN 141 ISBN 978-90-6814-623-4 NUR-code 955: Bouwkunde

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PREFACE

This thesis is the result of my PhD study that I have accomplished as a member of the Urban Planning Group, Eindhoven University of Technology. Without the help, contribution and support of many people, family, friends and colleagues, I would not have been able to complete this PhD research project. I would like to thank everyone who has supported and assisted me during this time, and especially express my gratitude to those who have assisted me by providing valuable feedback on my work at various stages.

First of all, it is a great honor for me to have worked under the supervision of Professor Harry Timmermans. I acknowledge and show my profound respect to him as a highly reliable advisor. He is a very encouraging and inspirational advisor, always providing interesting and promising research directions. I would also like to thank my co-promoter, Theo Arentze, for his considerable support. Throughout my study, Theo provided me very detailed technical and conceptual support both in theoretical and practical aspects, especially in computer programming. As my research concerned the refinement of the ALBATROSS system, it was not an easy task for me to understand somebody else’s work and algorithms. The bi-weekly meetings with Harry and Theo have improved my knowledge of activity-based analyses and research in general. Their feedbacks and comments on papers and the thesis manuscript were very impressive and improved my English writing skills. Without their assistance, it would have been impossible for me to finalize this PhD research. Thanks to Harry and Theo! I really loved working with both of you.

I would like to thank the University of Syiah Kuala for financing my PhD research through the TPSDP Project-Dikti during my first two years. Special gratitude goes to Prof. Dr. Samsul Rizal, Dr. Alfiansyah Yulianur, Dr. Mustanir, Dr. Ismail AB, Dr. Moch. Afiffudin, Danker Schaareman, and all staff for their efforts to the successful of my research. I would also like to express thank the Eindhoven University of Technology for financially supporting me for the

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I would also like to thank my colleagues in the Urban Planning Group. I enjoyed pie time, lunch time and chatting on many occasions. In particular, I show my appreciation to Mandy van de Sande-van Kasteren, Anja van den Elsen-Janssen and Ingrid Dekkers-de Bruijn for their splendid secretarial support and kindness, and other colleagues including Astrid Kemperman and Aloys Borgers for their inspiration. I will never forget the help of Peter van der Waerden and Leo van Veghel who picked me up at Schiphol airport on day one. Thanks also go to my colleagues, Marloes Verhoeven, Claudia Pelizaro, Linda Nijland, and Han Qi who were very generous giving away their home stuff. I would also like to thank my dear friends and family, Ina Rosyid, Inne Harjanto, Dianti-Oki, and Luluk-Nandra who were welcoming my children to their homes, especially when my husband was away to Indonesia and I could not pick up the children from school. Thanks also to Ella Meilinda and Rinaldi Husin families who visited us frequently in Eindhoven and made our stay in Holland more cheerful. It was also a sweet memorable time with Vivi, Desi, Dianti, Runi and Leila for cooking together during Ramadhan. Especially to Desi and Ferdi: thanks a lot for guiding me in computer programming.

Special thanks also go to my brothers and sister, Yudi Kurnia, Susi Andriani, and M. Fadhilla Ismali who always supported me in every possible way, and to my mother and my late father, for giving me everlasting support and pray for my education and life. I thank God for having all of you in my life. Thanks also to my parents-in-law for support and kindness. Last of all, I would like to thank my dearly-beloved husband, Aldy Fithrico, and our lovely kids, Alyauma Akmal Kalani and Alzhira Hana Fitriani. Their presence and love were really delightful and allowing me to enjoy our time in Holland. Thanks for all support, especially during the injury time of finalizing the thesis, when my husband and son helped me to produce the author and subject indexes.

Finally, I thank the many people who contributed to my life and ask forgiveness from those I have omitted unintentionally. Thank you all!

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TABLE OF CONTENTS

Preface List of Figures List of Tables CHAPTER 1 INTRODUCTION 1

1.1 Shifting Paradigms in Travel Demand Modeling 1

1.2 Household Decision Making 3

1.3 Aims and Outline of the Thesis 3

References 6

CHAPTER 2 LITERATURE REVIEW 7

2.1 Introduction 7

2.2 Analytical Studies on Household Decision Making 8

2.2.1 Car Allocation and Usage Decisions 8

2.2.2 Task and Time Allocation Decisions 8

2.2.3 Joint Activity Participation 13

2.3 Partial Models of Household Decision Making 15

2.3.1 Car Allocation 15

2.3.2 Task Allocation 16

2.3.3 Joint Activity Participation 23

2.3.4 Travel Arrangements 24

2.4 Household Decision Making in Comprehensive Activity-Based Models 26

2.4.1 Constraint-based Models 27

2.4.2 Simulation Models 27

2.4.3 Utility-Maximizing Models 29

2.4.4 FAMOS 30

2.4.5 CEMDAP and CEMDAP-2 31

2.5 Conclusions 32

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iv CHAPTER 3

FRAMEWORK 44

3.1 Introduction 44

3.2 ALBATROSS and Household Decision Making 45

3.3 The New Version of ALBATROSS 46

3.3.1 Activity-Travel Diary Data 48

3.3.2 The ALBATROSS Process Model and Extension to Include Household Decision Making 51

3.3.2.1 The Mandatory Activity Module 57

3.3.2.2 The Non-Work Activity Module 59

3.4 Derivation of Decisions from Decision Tree 60

3.4.1 Discrete Choices 60

3.4.2 Continuous Choices 61

3.4.3 Goodness-of-Fit Measures 63

3.4.3.1 Discrete Choices 63

3.4.3.2 Continuous Choices 65

3.5 Conclusions and Discussion 65

References 66

CHAPTER 4 CAR ALLOCATION BETWEEN HOUSEHOLD HEADS IN CAR-DEFICIENT HOUSEHOLDS: A DECISION MODEL 68 Abstract 68

4.1 Introduction 69

4.2 ALBATROSS Process Model 71

4.3 Data 74

4.4 Car Allocation Model Specification 74

4.5 Empirical Analysis 77

4.5.1 Descriptive Analysis 77

4.5.2 Decision Tree Induction 79

4.5.3 Deriving Impact Tables 80

4.5.4 Condition and Action Variables 82 4.5.5 Results 84 4.6 Summary and Conclusions 90

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CHAPTER 5

MODELING JOINT ACTIVITY PARTICIPATION AND

HOUSEHOLD TASK ALLOCATION 93

Abstract 93

5.1 Introduction 94

5.2 The Activity Scheduling Process Model 95

5.3 Models Specification 97

5.3.1 Activity Selection 97

5.3.2 Activity Allocation 98

5.4 Data 98

5.5 Analyses 98

5.5.1 Decision Tree Induction 98

5.5.2 Deriving Impact Tables 99

5.5.3 Condition and Action Variables 101

5.5.4 Results: Activity Participation Tree 104

5.5.5 Results: Task Allocation Tree 107

5.6 Conclusions and Discussion 109

References 111

CHAPTER 6 CONTINUOUS CHOICE MODEL OF TIMING AND DURATION OF JOINT ACTIVITY 112

Abstract 112

6.1 Introduction 113

6.2 Overview of ALBATROSS Model 114

6.3 Data Description 117

6.4 Variable Specification 119

6.5 Methods 123

6.5.1 Decision Tree Induction 123

6.5.2 Deriving Impact Tables 124

6.6 Results 124

6.7 Conclusions and Discussion 127

References 129

CHAPTER 7 HOUSEHOLD LOCATION CHOICE MODELS FOR INDEPENDENT AND JOINT NON-WORK ACTIVITY 131

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vi

7.2 Location Decisions in the Existing Model 133

7.3 Household Location Decisions (Joint Activity) 136

7.4 Data 138

7.5 Overview of Condition and Action Variables 138

7.6 Decision Tree Induction and Impact Table Methods 142

7.7 Descriptive Analysis 143 7.8 Results 145 7.8.1 Independent Activity 146 7.8.2 Joint Activity 148 7.9 Conclusions 149 References 151 CHAPTER 8 CAR ALLOCATION DECISIONS IN CAR-DEFICIENT HOUSEHOLDS: THE CASE OF NON-WORK TOURS 153

Abstract 153

8.1 Introduction 154

8.2 Data Description 155

8.3 Methodology 155

8.3.1 Car Allocation Decisions 155

8.3.2 Decision Tree Induction 159

8.3.3 Impact Tables 160

8.3.4 Condition and Action Variables 160

8.4 Descriptive Analysis 163

8.5 Results 165

8.6 Conclusions 168

References 170

CHAPTER 9 THE INTEGRATION MODEL 171

9.1 Introduction 171

9.2 Test of Validity Using MON Data 172

9.2.1 Frequencies 172

9.2.2 Indicators 176

9.3 Test of Sensitivity 178

9.3.1 Synthetic Populations 178

9.3.2 Scenario 178

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CHAPTER 10

CONCLUSIONS AND DISCUSSION 190

SUMMARY 194 Appendix 199 Author Index 247 Subject Index 250 List of Publications 255 Curriculum Vitae 257

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viii

List of Tables

TABLE 3.1 Classification of Activities in a Household in ALBATROSS 49 TABLE 3.2 Socio-Economic and Situational Attributes used in

ALBATROSS 49

TABLE 3.3 Accessibility Measures used in ALBATROSS 50

TABLE 4.1 Defining Car Allocation Decisions in Households 75

TABLE 4.2 Distributions of Households across Household Composition and SEC (%) 77 TABLE 4.3 Distributions of Household Heads across Household Composition and Work Status of Household Heads by Gender (%) 78

TABLE 4.4 Work Duration Statistics by Work Status and Gender 78 TABLE 4.5 Work Duration Statistics by Day of the Week and Gender 78 TABLE 4.6 Condition Variables for Car Allocation Model 83 TABLE 4.7 Frequency Distribution of Work Status across the Action Variables 85 TABLE 4.8 Confusion Matrix for the Training and Validation Sets 89 TABLE 4.9 Impact Tables of Condition Variables of Car Allocation Model 89 TABLE 5.1 Activity Classifications in a Household 96

TABLE 5.2 Condition Variables for Decision Tree Models 102

TABLE 5.3 Impact of Condition Variables of HH Activity Participation Model 105

TABLE 5.4 Impact of Condition Variables of Task-Activity Allocation Model 108

TABLE 6.1 Independent and Joint Activity Frequency (percentage) 117

TABLE 6.2 Average Duration (minutes) 118

TABLE 6.3 Definitions of Condition Variables 121

TABLE 6.4 Duration Tree Model 126

TABLE 6.5 Start-Time Tree Model 128

TABLE 7.1 Condition Variables of Independent and Joint Activity 140

TABLE 7.2 The Percentage of Performing Independent Activity at the Same Location as Previous and/or Next Activity 143

TABLE 7.3 The Percentage of Performing Joint Activity at the Same Location as Previous and/or Next Activity 144

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TABLE 7.4 The Percentage of Performing Independent and Joint Activity by Available Distance and Location Size Band in Prisms 144 TABLE 7.5 Results of Location Decision Tree Models 145

TABLE 7.6 Impact Table for Independent Activity 147

TABLE 7.7 Impact Table for Joint Activity 149

TABLE 8.1 Itinerary of Male-Female Heads in a Particular Household 159 TABLE 8.2 Condition Variables for Car Allocation Model 161 TABLE 8.3 Primary Activity of a Tour of Male – Female 164 TABLE 8.4 Percentage of Getting a Car by Male/Female across Work

Status 164

TABLE 8.5 Average Duration of Non-work Tour(s) across Work Status

(in minute) 164

TABLE 8.6 Results of the Car Allocation Model to Non-Work Tours 166 TABLE 8.7 Impact Table of Car Allocation Decision to Non-Work Tour

Model 166

TABLE 9.1 Some Relevant Variables at the Aggregate Level 174 TABLE 9.2 Observed and Predicted of the Old and New Versions 180 TABLE 9.3 Comparison between Base-line and Scenario on

Socio-Demographic Characteristics 181 TABLE 9.4 Predicted Scenario Effects on Some Variables/Indicators:

Old Model Version 182

TABLE 9.5 Predicted Scenario Effects on Some Variables/Indicators:

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x

List of Figures

FIGURE 3.1 Main Steps in the Scheduling Process of Current

ALBATROSS 53

FIGURE 3.2 Generation Modules in ALBATROSS 53

FIGURE 3.3 The Process Model for Mandatory Activities 54

FIGURE 3.4 The Process Model for Predicting Locations of Work

Activities 55

FIGURE 3.5 The Process Model for Predicting Locations of Work-Related

and Non-Work Activities 55

FIGURE 3.6 The Process Model for Non-Work Activities 56

FIGURE 4.1 Schematic Representation of Main Steps of the ALBATROSS

Process Model 72

FIGURE 4.2 The Process of Car Allocation Model for Work Tours 75

FIGURE 4.3 Examples of Distinguished Cases 76

FIGURE 4.4 Car Allocation Tree Model with 5 Major Branches 87

FIGURE 6.1 Household Activity-Travel Scheduling Process of

ALBATROSS 116

FIGURE 6.2 Start-Time Profiles every 30 minutes for each Activity 118 FIGURE 7.1 The Process Model for Predicting Location of Non-Work

Activities 135

FIGURE 8.1 The Process of Car Allocation Decisions for Non-Work

Tour 157

FIGURE 8.2 An Example of Defining Car Allocation Decision Cases in

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Chapter 1

INTRODUCTION

1.1 SHIFTING PARADIGMS IN TRAVEL DEMAND MODELING

Travel demand modeling has been considered a fundamental area in transportation research for decades. It has been customarily used in urban planning and transportation engineering to predict transport demand and evaluate the possible consequences of spatial, infrastructure, and socio-economic policies. The traditional paradigm, still dominant in planning practice, is the trip-based, four-step modeling approach. The four-step model is a primary tool for forecasting future demand and performance of a transportation system. In order to assess the impact of infrastructure investments and other policies, models that predict long term travel demand were deemed critical in evaluating alternative investment and other policies. The four-step model is achieving this goal by breaking down the decisions that ultimately lead to traffic flows into trip generation, destination choice, choice of transport mode and route choice. These four subsequent decisions are modeled separately and independently. Originally, traffic zones served as the unit of aggregation; later travel behavior of individuals was simulated. Predicted flows are then used to determine future road capacity needs. For more details see Ortuzar and Willumsen (1994)and McNally (2007).

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interdependencies that may exist among the various choice facets. The model forecasts turned out to be very unreliable and failed to assess especially the secondary effects of policy measures correctly. The models lacked any explanation in terms of human decision making. Furthermore, the models disregarded constraints such as intra-household constraints, situational constraints, space-time constraints, and institutional constraints. They also neglected the dependencies between travel mode, departure time and destination choice.

When in the 1990s, policy shifted from long-term investment strategies to short-term market-oriented solutions, the need to develop transport demand models that could predict behavioral responses to policy measures was expressed in the academic research community and was somewhat echoed in policy agendas. It led to the development of activity-based models, which view travel as the result of people organizing their activities in time and space. Activity-based models are founded in behavioral theory and focus on the interdependencies between activity generation, transport mode choice, destination, stop pattern and route choice, in the context of multiple constraints that limit the choices of individuals and households. Moreover, temporal dimensions were added to increase the sensitivity of the model. Activity-based models also predict the timing and duration of activities.

While the vast majority of planning organizations continue to rely on traditional models, academic research suggests that activity-based approaches promise greater predictive capability, more accurate forecasts, and especially more realistic sensitivity to policy changes (McWethy, et al., 2002). Recognition of the various interdependencies in activity timing and other travel attributes allow greater realism in models of travel demand. Moreover, activity-based modeling is better suited to current transportation planning interests. In general, activity-based models focus on activities as the unit of analysis as opposed to trips as the unit of analysis in trip-based models. This shift has enabled the models to address issues related to substitution of non-travel alternatives. Focusing on activity episodes also permits the incorporation of constraints such as time constraints related to opening hours, work schedules, expected activity duration, and multi-day scheduling of activities.

Different modeling approaches have been suggested in the literature, and each of these has led to operational models. The dominant approach is based on the principle of utility-maximization and corresponding discrete choice models. Observed activity-travel patterns are viewed as the results of individuals maximizing their utility. The potential of discrete choice models has been recognized from the mid 1970s onwards. The shift from trip-based via tour-based to activity-based models simply meant

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increasing complexity. Typically some nested structure is assumed and the parameters of the model are estimated using the principle of utility-maximizing behavior.

A second approach is focusing primarily on time use. An example is AMOS/PCATS (Kitamura and Fujii, 1998), which was later operationalized for the State of Florida (FAMOS). CEMDAP, developed by Bhat and his co-workers (2004) is an example of a hybrid system. It consists of a series of separate submodels, which are linked in a micro-simulation system. Each submodel applies advanced econometrics.

Finally, rule-based models have been developed. These models assume that choices are context-dependent. Logical rules are extracted from empirical observations for each stage of an assumed process model. An example is ALBATROSS (Arentze and Timmermans, 2000, 2004, 2005) which has been developed for the Dutch Ministry of Transportation, Public Works and Water Management.

1.2 HOUSEHOLD DECISION MAKING

The aim of introducing more interdependencies in the models is not only concerned with interdependencies in choice facets, but also with interdependencies between the decisions of individuals. It was realized that in many cases, it is not the individual, but rather the household that makes decisions. Households are relevant in at least three situations. First, the activity-travel patterns of household members need to be synchronized in time and space for joint activities, such as dinner or a family outing. Second, resources may need to be allocated to individual household members. In turn, resource allocation decisions may limit subsequent choices of individual members. For example, if one member uses the car in a single-car household, other household members cannot use the car at the same time, implying their action space may be limited. Thirdly, some activities are household activities, implying that only one household member has to conduct that activity. In turn, such task allocation decisions influence other aspects of activity-travel programs.

An examination of the literature shows that although the topic of household decision making has been high on the research agenda for many years, most activity-based models of transport demand are still based on individual travel patterns.

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models of transport demand are still based on individual travel patterns. The goal of this thesis therefore is to systematically model household decision making processes in an activity-based framework with a special focus on resource and task allocation and joint activity participation. More specifically, this study represents an attempt to improve ALBATROSS (Arentze and Timmermans, 2004). This model was one of the few of its generation that did include aspects of household decision making by simulating the decisions of one household member, and then based on the outcome of this, model the decision process of another household member.

The aim of this thesis is primarily to refine the ALBATROSS model to represent household-level decision making more explicitly so that the interaction between persons can be captured well. In particular, the following elements will be further elaborated:

1. Joint activity participation choice was not modeled in the sense that the required synchronization in case of joint activities was not imposed as a constraint. We will attempt to model joint activity participation in a more consistent manner. 2. Activity allocation to each household head was an implicit decision step. In this

study, we will model this step explicitly.

3. Car allocation to each male and female head was also an implicit decision, in particular for those households with more drivers than cars. The car allocation problem will now also be modeled explicitly in this study.

The aim of refining ALBATROSS is to make it more comprehensive and applicable for household-level decision making. Household heads need to trade-off activity needs and mobility in the context of joint activity participation, household task allocation and mobility. Joint activity participation needs compromise when the activity is done by male and female jointly.

In order to achieve these goals, some component of the process model underlying ALBATROSS is elaborated or re-designed in terms of household decision making. Moreover, a new much larger data set (the MON-data) is used, implying that the decision rules that are derived are based on more (household) data. The structure of this thesis follows the process model underlying ALBATROSS.

Before going through the chapters that make up this thesis, it should first be noted here that most chapters are based on previously published conference papers or journal articles. Intrinsically, this format leads to some overlap between some of the chapters, especially regarding parts of introduction, methods used and descriptions of data

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collection efforts, although every attempt has been made to write each paper in such a way that transitions from one chapter to another are as smooth as possible.

Chapter 2 starts by discussing the literature review in the area of household decision making in urban travel demand modeling. Chapter 3 further continues to discuss the general framework underlying the model system. It motivates the potential advantages of a rule-based system. In terms of modeling, the challenge is to extract decision rules from observed activity-travel patterns. Throughout the thesis, a CHAID-based decision tree induction method is used as in the basic model. Chapter 4 describes the results of the first household decision. It is concerned with the problem of car allocation decision to work tours focusing on car-deficient households, i.e. households where the number of drivers is higher than the number of cars, the decision who or no-one at all uses the car to go to work is modeled.

Chapter 5 discusses the results of the model for generating non-work activities. Two different models are developed, one for joint activity participation and one for household task allocation, focusing on two-heads households. A classification of activities is developed and activity types that likely relate to the needs at the household level are identified. .

Chapter 6 specifies two subsequent models: duration and start-time models for non-work activities conducted jointly by the male and female head of a household. Specifically, the study investigates the timing of non-work activities related to household and family activities, such as household tasks (e.g., escorting persons, grocery shopping) and non-task activities (i.e., social and leisure activities). The analysis focuses on two-heads households (with or without children) and the joint activities in their schedules.

Chapter 7 re-estimates location choice models in the context of household decision making. It consists of two primary models for respectively independent and joint non-work activities. As in the basic model, the concept of detour time is used. This concept considers relative locations to the previous and next activity as the unit of analysis for defining location choice. By applying that concept, distances between locations that may be combined in a single trip-chain can be captured well.

Chapter 8 models the car allocation decision to non-work tours. This chapter is similar to chapter 4 that is concerned with the car allocation decision to work tours. Nevertheless, the way of defining the car allocation decision is quite different given the

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Chapter 9 discusses the integration of these sub-models into the integral ALBATROSS model. It intends to prove that the simulation of sequential choice facets and observations are little different.

Finally, Chapter 10 summarizes this study, reflects on the results and identifies some avenues of future research.

REFERENCES

Arentze, T.A. and Timmermans, H.J.P. (2000), ALBATROSS: A Learning-based

Transportation Oriented Simulation System. EIRASS, Eindhoven University of

Technology, The Netherlands.

Arentze, T.A. and Timmermans, H.J.P. (2004), A Learning-Based Transportation Oriented Simulation System, Transportation Research Part B, 38, 613-633.

Arentze, T.A. and Timmermans, H.J.P. (2005), ALBATROSS 2.0: A Learning-based

Transportation Oriented Simulation System. EIRASS, Eindhoven University of

Technology, The Netherlands.

Bhat, C.R., Guo, J.Y., Srinivasan, S., and Sivakumar, A. (2004), A Comprehensive Econometric Microsimulator for Daily Activity-Travel Patterns, Transportation

Research Record, 1894, 57-66.

Kitamura, R. and Fujii, S. (1998), Two Computational Process Models of Activity-Travel Behavior. In: T. Gärling, T. Laitila and K. Westin (eds.), Theoretical

Foundations of Travel Choice Modeling, Elsevier, New York, pp. 251-279.

McNally, M.G. (2007), The Four Step Model. In: Hensher, D.A. and K. Button (eds.)

Transport Modeling, 2nd Edition, Pergamon, Oxford, pp. 55-73.

McWethy, B.L., Lemp, D.J., and Kockelman, M.K. (2002), From Aggregate Methods to Microsimulation: Assessing the Benefits of Microscopic Activity-Based Models of Travel Demand. In: Proceedings of the 86th Annual Meeting of the

Transportation Research Board, Transportation Research Board, National Research

Council, Washington D.C.

Ortuzar, J.deD. and Willumsen, L.G. (1994), Modelling Transport (second edition), Wiley, Chichester.

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Chapter 2

LITERATURE REVIEW

2.1 INTRODUCTION

As briefly discussed in the introduction, the activity-based approach to travel demand forecasting represents an attempt of improving the integrity of demand forecasting models by explicitly modeling various dependencies. These dependencies are not only concerned with the various choice facets (generation, destination, transport mode, etc), but also with dependencies between members of the household. The focus on the household as opposed to the traditional focus on the individual is especially important in the context of task and resource allocation and joint activities. Although the importance of the household level has been recognized in seminal work, except for some analytical studies, only recently there have been attempts of modeling these phenomena (Timmermans, 2006).

The purpose of this chapter is to give an overview of this line of research. First, we will summarize empirical work, followed by recent modeling attempts. Finally, we will discuss how household decision making is treated in existing comprehensive

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activity-2.2 ANALYTICAL STUDIES ON HOUSEHOLD DECISION MAKING 2.2.1 Car Allocation and Usage Decisions

Activity participation and destination choice often depend on the transport modes that are available to individual household members. Car use often means that more destinations can be visited during a single trip or that destinations further away from home can be reached within a given time budget. Especially in car-deficient households in which the number of cars is less than the number of drivers, car allocation and usage is a household decision which impacts many other choice facets of individual activity-travel patterns. Golob, Kim, & Ren (1996) analyzed how drivers are allocated to vehicles in multi-driver/multi-vehicle households. They found that gender, income, work status, age and the presence of small children influenced the number of vehicle miles traveled with the various vehicles. Hunt & Petersen (2005) also found evidence of gender differences.

Almost similar, Vance and Iovanna (2007) also found that gender play a role in determining the probability of car use and the distance driven. Drawing on a panel data collected between 1996-2003 in car-owning households in Germany, the results indicated that although women, on average, perform more non-work travel than men, they were more reliance on other modes than car. Another interesting study is done by Vovsha and Petersen (2007). A model system structure is proposed that can fully address all needs associated with car allocation and use. The core short-term module includes two long-term sub-models: 1) household car ownership, 2) main driver assignment for each car, and four short-term sub-models: 3) individual and joint travel generation, 4) schedule adjustments, 5) mode choice, and 6) car allocation and type choice. However, neither of the existing model system has yet included a full set in a consistent way.

2.2.2 Task and Time Allocation Decisions

One would expect that household characteristics, such as the structure and the number of persons in a household, influence the number and type of activities conducted in the household and therefore task allocation and travel decisions. Household structure also influences where (in-home vs. out-of-home) activities are conducted (Gronau, 1977; Lawson, 1999). A major factor that influences the decision to travel relates to the role of paid work within a household. The amount of time spent on paid work strongly influences the budget available for household consumption, and the total amount of time and the time of day available for other activities. Lee & Hickman (2004), looking

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doubly-censored tobit models. In particular, they compared trip chaining behavior, among five types of households: single non-worker households, single worker households, couple non-worker households, couple one-worker households, and couple two-worker households. They found that household types, defined by the number of household heads and work status, strongly influence activity time allocation in trip chains. The presence of children in the household has a positive effect on the duration of all of-home activities in household trip chaining, except for the duration of out-of-home discretionary activities of households having children under 5 years old. This suggests that the presence of children induces more chaining of trips and more time allocated to these trip chains. Households having more children of 16 years of age and over are more likely to spend time in trip chaining for out-of-home subsistence activities. Finally, they found that flexible work arrangements tend to be correlated with less trip chaining for the work trip.

Another consistent finding in the literature is that the work commute of women is shorter (e.g., Hanson & Hanson, 1980; Hanson & Johnston, 1985; Singell & Lillydahl, 1986; White, 1986; Fagnani, 1987; Gordon, et al., 1989; Hanson & Pratt, 1990; Turner & Niemeier, 1997). It reflects the fact that on average working women are less flexible because they need to combine paid work and household activities. Women are able to combine work and domestic duties primarily by working closer to home, more trip-chaining and relying on social networks (Hanson & Pratt, 1995: Kwan, 1999; Dowling, 2000). Consequently, accessibility considerations are more important to them, both in terms of accepting a job, but also because they need to take care of many other non-work activities. Stopher & Metcalf (1999, 2000) concluded for several cities in the United States that beyond the effects of lifecycle, both gender and working status influence the amount of time allocated to household activities (see also Vadarevu & Stopher, 1996, 1999). Likewise, Schwanen, Ettema & Timmermans (2006) argued that if a spouse works longer hours, s/he has less time for domestic tasks. Relegating household activities to one’s partner may then be a reasonable strategy to cope with this situation. Alternatively, households may consider an overall reduction of household tasks at the household level (Morris, 1990; Presser, 1994). However, such effects are gender-specific in the sense that male’s household tasks do not change much if women work longer hours and women, irrespective of their employment status, continue to carry prime responsibility for these tasks (Morris, 1990; Pinch & Storey, 1992; Hanson & Pratt, 1995; Presser, 2003). There are nonetheless variations. In addition to the impact of class, occupation and lifecycle, gender roles and power differentials among spouses matter (Morris, 1990). Men tend to conduct more household tasks if spouses’ roles orientations are more egalitarian (Huber & Spitze,

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may conduct more tasks in larger households with young children to increase the efficiency of the household or to comply with the prevailing moral climate and gender ideology (Knijn, 2004).

There is also some evidence that good accessibility stimulates out-of-home activity participation and trip making (Boarnet & Crane, 2001; Ettema, Schwanen & Timmermans, 2006). In contrast, poor accessibility, either as the result of the non-availability of a car or as the result of the spatial distribution of facilities relative to home may lead households to assign out-of-home household tasks to one spouse – usually the female – who can combine several tasks in multi-stop activity chains. For example, Strathman, et al. (1994) concluded that the likelihood of forming complex commuting chains is higher for women and high-income households, both of which tend to be “time challenged” groups. If, however, accessibility is better, men may take on more household tasks, because accommodating such activities in their activity schedules is easier (Hanson and Hanson, 1980; Ettema, et al., 2006). Kwan (1999, 2000) found that women’s household activities tend to be more fixed in space and time than those by men, suggesting that such tasks are a structural component of their daily schedules, while men conduct such activities on a “standby/basis”. This interpretation is corroborated by Aitken (2000), who concluded from interviews that fathers responsible for childcare felt they were merely ‘helping out’ their spouses.

Household tasks also have an effect on other in-home and out-of-home activities. For example, Gronau (1977) looked at the effects of an increase in the number of children and the age cohorts of the children. He found that as the number of children in a household increases, the additional time devoted to children is not spent on work at home and leisure. Similarly, Redman (1980) found that family size had a negative effect on meals being eaten outside the home. Golob & McNally (1997) used a structural equation model to investigate activity participation and travel of couples. Activities were classified into three categories: work, maintenance, and discretionary. The total out-of-home duration for these categories was calculated as was total travel time. A series of household and personal characteristics was used as the exogenous variables of the model. They studied four types of direct effects: travel requirements of out-of-home activities, within-person activity interactions, within-person travel interactions, and cross-person interactions. One of the interesting results was that if the male increases his participation in work activities, the female’s travel for maintenance activities increases more than proportionally to the increase in the female’s participation in maintenance activities.

Borgers, Hofman, Timmermans & Ponjé (2001) used a stated choice approach for estimating the probability of certain task allocation profiles. The main reason for

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collecting stated choice data was that revealed daily task allocation patterns may be influenced too much by unique factors. Examining task allocation behavior under laboratory conditions as a joint decision making process likely generates more valid data. The problem addressed in this paper was that stated choice experiments typically involve a choice between single alternatives and not between portfolios (a specific combination of tasks). The authors therefore explored alternative approaches of how to measure the influence of experimentally varied factors on task allocation. In a sequel, Borgers, Hofman & Timmermans (2002) estimated a slightly simpler model. They assumed that the presence of children of various ages in the household, the socio-economic status of the household, age, car availability and work status of the spouses influence time allocation decisions. Multinomial logit models, including these variables as contextual effects, were used to predict time allocation of two spouses to a set of activities. First, a multinomial logit model was estimated to predict the amount of time spent together. Next, a conditional choice model was estimated to predict the proportion of time spent by each spouse on conducting a particular activity. Because the total amount of time is known, these proportions can be translated into the number of hours spent on particular activities. Respondents were requested to jointly express the amount of time they typically spend alone and together on 27 different activities, which were later grouped into activity classes. The following activities were distinguished: (1) sleep, eat, drink and personal care; (2) work out of home, including travel time; (3) shopping, services, including travel time; (4) in-home non-leisure; (5) in-home leisure; (6) out-of-home leisure; (7) bring/get activities, and (8) other. Results indicated that if an older child is present in the household, the amount of time spent together significantly increases. The amount of time spent together is less if either spouse works. Time spent on sleeping, eating, drinking and personal care is significantly less when older children belong to the household. The amount of time spent on sleeping, eating, drinking and personal care by men is less if their spouses have a part-time or full-time job. If men have a part-time job, their time allocation to sleeping, eating, drinking and personal care are higher. In contrast, it is significantly less if they have a full time job. Men working part-time spend more hours on shopping, while men working full-time spend less time on shopping. If spouses work, men tend to shop more, but this effect was less significant.

The effects of the work status variables were interesting. If men work part-time, they tend to spend more time on in-home work activities, although the effect was not significant. If they work full-time, they allocate significantly less time to in-home work. If their spouses work, men also tend to spend more time on in-home work activities, but this effect is only significant if their spouses work part-time. If their spouses have a

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activity pattern in the sense that they may spend more time together on other activities. The impact of work status of women is such that working women spend less time on shopping, but this effect is only significant if they work full-time, and then only at the 90% probability level. Time pressure might be the reason for this finding. The pattern of the signs of the work status variables is interesting. Compared to the reference household, time allocation of men to shopping tends to increase if their spouse work, suggesting that men take over some of the shopping responsibilities of their spouses.

Women tend to spend more time on in-home non-leisure activities if they have young children and less time if they have older children compared to the situation where there are no children in the household. This seems to indicate that older children help out. Similar results were obtained for other categories. Overall, the results suggest that task and time allocation in households depends on household type (age, children, number of workers), the utility that is derived from joint versus solo activities, the urgency of conducting particular activities, gender roles and the constraints and possibilities offered by the environment to conduct these activities efficiently in time and space. Ettema & Van der Lippe (2006) investigated task allocation patterns on a weekly basis. The results of their analyses indicated that specialization is a dominant weekly pattern in dealing with time constraints, i.e. each spouse takes primary responsibility for different tasks. The presence of young children and a lower accessibility to jobs and services increases the female's share of household tasks and childcare. This specialization is strongest on Friday and on Wednesday, reflecting school hours and part time work arrangements in the Netherlands. Non-traditional roles and a highly qualified job increase the females' share of paid labor and decrease their share of household and childcare tasks, however this effect is not observed on Fridays, suggesting that women still, more than men, work in part time jobs where Friday is the free day.

Cao and Chai (2007) examined activity time allocation of the male-female household head between weekday and weekend. Based on observations on Shenzhen residents in China, they found the gender role in the household. Men are dominant in out-of-home activities, but women are more dominant in in-home activities. On average, women carry more maintenance responsibilities than men, but men spend more time on work and leisure activities than women, especially on the weekend. On the weekend, Shenzhen’s residents are not as mobile as westerner countries because most people spend time at home and surrounding neighborhoods, especially as for female. Further, the influences of household structure on time allocation of both household heads demonstrated substantial gender-role differences. The results also showed some interesting interpersonal interactions of time allocation. Specifically, the more women

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participate in leisure activities, the more men spend time on leisure activities, but not vice versa. Although not substantial, women’s work activity duration tends to increase men’s leisure activities. During the weekday, as women spend more time on maintenance activities, overall, men as well as women participate in fewer leisure activities. On the weekend, once one household head works, the other tends to carry more maintenance activities.

2.2.3 Joint Activity Participation

Joint participation in activities represents a substantial portion of non-work activities, is an important component of travel during certain time periods and affects individual travel schedules. Joint participation in maintenance and leisure activities and the provision of rides to family members, constrain individual choice sets and affect the saliency of attributes that contribute to the generalized cost of travel alternatives. Therefore, this choice problem has received relatively most interest.

The relative importance of joint activity participation is evident in that joint activities tend to have a longer duration than non-work independent activities, and persons tend to stay out later and travel farther from home (Kostyniuk & Kitamura, 1983). Moreover, Fujii et al. (1999) found that time spent on activities jointly with other household members, particularly with children, was incremental to individual feelings of satisfaction and in decisions to allocate time to joint and independent activities. Several studies have examined the effect of household attributes on joint activity-travel behavior. Kostyniuk & Kitamura (1983) and Chandraskharan & Goulias (1999) found that joint activities involving household heads are significantly affected by the presence of children. Couples without children living at home are more likely to pursue joint out-of-home non-work activities than couples with children. In households with children, most joint activities between adults are at home. In addition, the employment status of the household heads influences whether a joint activity originated from home or from an out-of-home contact point.

Another interesting study that investigated the effects of children on household travel behavior was done by Senbil, et al. (2008). They examined the impact of children on various household non-commute trips for four different types of non-commute trips, i.e., trips to shopping, restaurant, park and recreation centers, and department store. These variables were regressed against socio-economic and demographic,

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non-commute trips by male and female household heads. Results for linear regression suggest that children can be grouped under general groups, i.e, pre-school, school, for accounting child effect on household travel behavior. Besides, number of children reveals significant results. Also in linear regression analyses, they found that the differentiation outperforms a classical lifecycle classification. Results for seemingly unrelated regression suggest that there is a general complementary among household heads in non-commute trips, except shopping trips which display substitution, albeit minor. Also, for household heads, pre-school children constitute the child group with significant effects on non-commute trips.

Srinivasan and Bhat (2008) examined the joint participation with household members and non-household members along with the generation, location, and scheduling of joint activity episodes. They found that independent activities are different from joint activities in systematic ways. Specifically, joint episodes are of longer durations, significantly likely to take place at the residence of other people, and often confined to certain time periods of the weekday. In addition, within the class of joint episodes, important differences are also observed based on activity type, companion type, and the day of the week. Overall, the empirical results from this study highlight the important need to accommodate intra-household and inter-household interactions in activity-travel behavior analysis. Specifically, some of the key implications of their empirical findings include the following. First, given the sheer magnitudes of joint activity and travel engagement, their results underscore the need for travel demand models to recognize these inter-dependencies for accurate travel forecasts and policy analysis. In particular, inter-personal linkages in activity travel behavior imply that policy actions can also alter the travel patterns of individuals who are not directly “exposed” to the action. For example, when a husband’s work timings change because of work-staggering, the wife’s travel patterns can also change. Second, the timing (i.e., duration and time-of-day) of activity-travel is found to be related to the companion type. Consequently, accurate assessment of soak time distributions for air quality models requires information on joint activity-travel engagement patterns. Third, a high fraction of joint leisure type activities is found to be undertaken at “someone else’s home”. The implication here is that individuals are perhaps not as flexible in their choice of destination location for the pursuit of discretionary-type activities as they have been traditionally assumed in travel-demand modeling. Fourth, the desire to participate in activities with non household members such as friends also generates additional travel to pick-up and drop-off the activity companions. Such travel cannot be realistically captured by individual-level models. Fifth, with the gaining prominence of the need to model weekend travel behavior, accommodating inter-personal interactions assumes even greater significance as joint activity and travel participation levels during weekends are found to be greater than those during weekdays. Finally, to enable the

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development of empirical models that accommodate inter-personal interdependencies, future travel surveys should be suitably enhanced to adopt a more disaggregate activity classification scheme and to collect data on individuals’ activity and travel companions.

2.3 PARTIAL MODELS OF HOUSEHOLD DECISION MAKING 2.3.1 Car Allocation

Petersen & Vovsha (2005, 2006), in addition to car allocation, also modeled car-type choice. First, they simulated which individual and joint activities are conducted and where these activities are conducted. Then, accessibility to the most important activities (work and school) in combination with the household characteristics determines car ownership by vehicle type. Next, generated activities are scheduled and out-of-home activities are distributed by travel tours. Travel needs of the household members are further consolidated through joint travel arrangements. Finally, available household cars are allocated to these tours. The authors argue that numerous feedbacks can be implemented within this framework in order to enhance the integrity of the model system and eliminate possible inconsistencies. Interestingly, they notice that only some of them can be formalized as log-sums in a nested logit model. Other feedbacks are more complicated in nature and require rule-based algorithms. For example, re-scheduling and tour-formation procedures are needed to synchronize tours and enforce joint travel arrangements. If the total time budget proved to be unrealistic in terms of the travel time share, adjustment of certain activities and locations is needed.

The actual model is a multinomial model which predicts the choice of household car. A maximum of 8 choice alternatives is distinguished, varying in terms of five car types (small auto with 4 or less cylinders; large auto with 6 or more cylinders; van; SUV/jeep; truck, and car age in years). If a household has less than 8 cars, unavailable choice alternatives are blocked out. For each tour, assumed known are tour-related attributes (purpose, destination, distance, schedule, number of stops, pure auto tour versus drive-to-transit tour), driver-related attributes (person type, gender, age), joint-travel-related attributes (party type, party size, fully joint versus partially joint tours), household-related attributes (income group), and zonal attributes (area type at the origin, area type at the destination). Purpose, distance, number of stops, driver type, party type, joint activity participation and socio-demographics were used as explanatory variables.

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In particular, cars are allocated to household members such as to maximize household utility, which is assumed to be the sum of household members’ individual utilities. The scope of explanatory variables is largely restricted to travel time and costs of alternative transport modes and trip purpose.

2.3.2 Task Allocation

Wen & Koppelman (1999, 2000) proposed a prototype activity stop generation and tour scheduling model that includes the daily allocation of household maintenance tasks and automobile use. Their model focuses on travel that is generated from participation in activities undertaken to satisfy needs and desires of the household and its members. The model itself is a nested logit model that differentiates between household subsistence (work and work-related business) needs and mobility decisions, the generation of maintenance (grocery shopping, personal and household business) activities (stops) which serve the household in general and each member of the household and the allocation of stops and autos among household members exclusively or jointly. Finally, individual daily travel/activity patterns are derived through the generation of tours, the assignment of stops to tours, and the selection of locations for each stop and travel mode(s) for tours. The highest level is the choice of the number of household maintenance stops. The second level is the allocation of maintenance stops to individuals. The lowest level of the model concerns the allocation of cars to individual household members. The second stage choices, for each adult household member, include the number of tours and the assignment of stops to tours, conditional on the choices of the number of maintenance stops and the allocation of stops and autos. A distinction is made between workers and non-workers. Thus, this model remains restrictive, both in terms of characterization of activity patterns level characteristics and the limited choice facets that are included in the model. Time allocation and the utility derived from different types of activities are not included in the model, although it is an important consideration in leisure and maintenance activities and an essential criterion for decisions regarding joint activity participation. Zhang, Timmermans & Borgers (2002) developed a more general model of task allocation and time use of household members. They assumed that households allocate their time to activities such that household utility is maximized. In contrast to many other models, household utility is not assumed to be a simple sum of household members’ utilities, but also incorporates relative influence and interest. Starting point is the assumption that every household has to perform a set of activities to survive or to give some meaning or pleasure to their daily life. The utility of these activities is assumed to differ between individuals. Role patterns within households and more

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general lifestyle decisions influence the kind of activities that are conducted, the household member primarily responsible for the task, and activity participation and allocation of time across activities (and related travel). Activities are classified into four types, i.e., in-home activities, out-of-home independent, allocated and shared (or joint) activities. An independent activity is an activity, not being a household task that is conducted by an individual household member (e.g., work or attending a football match). Shared activities are those activities that require the presence of more or all household members (e.g., dinner or a family outing). An allocated activity is a household task that is assigned to a specific household member (e.g., daily shopping). Shared activities may be synchronized or non-synchronized. In the former case, household members carry out the activity together. In the latter case, household members share the activity partially. The basic structure of their model was formulated as:

Maximize GUF =G(u1,u2,...,un ) [2.1]

Subject to

j ijt =Ti, for i = 1, 2, …, n [2.2]

where,

GUF stands for group (household) utility function, ij

t is the time of individual i performing activity j,

i

u is household member i’s utility, and

i

T is member i’s available time.

A set of alternative specifications of the group utility function was considered. The

multi-linear group utility function can be specified as follows: n 2 1 n ~ 1 n 1 i i i ii i i n 1 i wiui (w u u ) ... w uu ...u GUF 1 2 1 12 1 2 + + + =

∑ ∑

= > = [2.3] where, i

w is member i’s weight parameter, and

n ~ 1 i

i ,...,w

w12 are the intra-household interaction parameters.

This model assumes that household utility can be derived by weighting the utilities of the individual household members, and adding interaction effects. The weight wi can be interpreted as a measure of a member's power or influence in the group

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decision-interaction parameter, the higher the group’s collective desire to choose a time allocation such that the utilities of all household members are more or less equal.

The GUF in equation (3) finds its theoretical roots in group decision theory (Eliashberg & Winkler, 1981, 1986; Harsanyi, 1955; Keeney, 1972; Messer & Emery, 1980). It can include several GUFs as special cases. The additive-type group utility function only uses the first component of the utility function and can be expressed as:

=

= ni 1wiui

GUF [2.4]

Harsanyi (1955) showed that if the group is to behave in a Bayesian rational manner, then the group utility function must be additive. This model can be arrived at when household members first average their separate utility functions and then maximize the resulting mixture function (Curry, et al., 1991). However, this GUF ignores the interaction among household members. An alternative is a compromise-type group

utility function which can be expressed as:

= = =

= in1wiui in1(ui/n)

GUF [2.5]

Equation [2.5] shows that household members have equal weights. Curry & Menasco (1979) called this the compromise weight. There is some empirical support in other disciplines for such equal weighting (e.g., Davis & Rigeaux, 1974; Munsinger, Weber & Hansen, 1975; Krishnamurthi, 1988), but there is also empirical support of non-equal weights (Molin, Oppewal & Timmermans, 1997, 2000). Hence, it may advisable not to assume equal weights a priori.

Another special case is the capitulation-type group utility function, which takes group interaction into account by assuming that each household member uses other members’ weights (utilities) as his or her own weight (utility) for joint decision-making.

=

= in1wiui

GUF or GUF =

in=1wiui [2.6]

where wi represents the average weight of other members relative to member i and is called capitulation weight, and ui represents the average utility of other members relative to member i and is called capitulation utility.

An alternative to these linear functions are Nash-type functions of a multiplicative form. The group utility function can be expressed as:

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( )

wi

i ui

GUF =

[2.7]

Equation [2.7] shows that this utility function is multiplicative without a reference point. It satisfies Nash’s (1950, 1953) axioms for two-party cooperative games or variations on those axioms. The Nash model assumes that each household member identifies his/her most preferred outcome and the household then compromises by averaging along the resulting negotiation frontier (Curry et al., 1991). Gupta & Livne (1988), however, pointed out that Nash’s definition was particularly inappropriate for multiple-issue bargaining and suggested the following definition.

(

)

wi

i ui ui

GUF =

[2.8]

This type of GUF uses other members’ capitulation utility as a reference point. Curry et

al. (1991) have experimentally tested the validity of this utility function. The reference

point suggests that during negotiations each member can be expected, explicitly or implicitly, to compare each possible agreement against the reference point.

Zhang, et al. (2002) decided to use the multi-linear specification because it is easier to estimate and it is more general. Their model only incorporated binary interaction terms rather than multiple interaction terms. Thus, the estimated model can be formulated as follows:

∑ ∑

= + = > = n 1 i i i ii i i n 1 i wiui 1 2 1(w12u1u2 ) GUF [2.9]

Each member’s utility function is further composed of the utilities from different activities based on the same type of multi-linear GUF.

∑ ∑

+ > = i i i i i i i i i i a1 a2 a1 a1a2 a1 a2 a a a i r u (r u u ) u [2.10] where, i a

u is household member i’s utility for activity ai,

i

a

r is member i’s weight (or relative interest) for activity ai, which reflects the relative importance of each activity making for each member’s utility, and

i ia2

a1

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In particular, they proposed the following utility maximization framework to model household time allocation based on the multi-linear household utility function, subject to each member’s available time constraint.

Maximize GUF =

i(wiui )+

∑ ∑

i i'=i+1(wii'uiui' ) [2.11]

shr i alc i as i shr i ind i is i alc i ind i ia i shr i hom i hs i alc i hom i ha i ind i hom i hi i shr i shr i alc i alc i ind i ind i hom i hom i i u u r u u r u u r u u r u u r u u r u r u r u r u r u + + + + + + + + + = [2.12] Subject to i shr i alc i ind i hom i t t t T t + + + = [2.13] i i' , t t t shr shr i' shr i = = ∀ ≠ [2.14] where, hom i

t is the time staying at home,

ind i

t , tialc and tishrare the time of member i performing out-of-home independent activity (ind), allocated activity (alc) and shared activity (shr), respectively,

i

T is member i’s available time for performing all these activities,

shr i alc i ind i hom i ,u ,u u

u and are the utility functions,

shr i alc i ind i hom i ,r ,r r

r and are their weight parameters, and

hi i

r , riha, rihs, riia, riis and rias are the interaction parameters.

In order to derive operational models of household time use, the following type of utility function for each activity was used.

(

t 1

)

exp

(

x

)

, j {hom,ind,alc}

ln uij = ij +

qβiqj iqjij = [2.15]

(

)

(

shr

)

i q shr iq shr iq shr shr i lnt 1 exp x u = +

β +ε [2.16]

where,εij andεishr are error terms of utility functions, xiqj , xiqshr are explanatory variables and, βiqj and βiqshr are the parameters.

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