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Contents : Conditional Choice Modelling of Time Allocation Among Spouses in Transport Settings. Theory and Empirical Findings 1 Aloys Borgers1 Frank Hofman2 and Harry Timmermans1 Urban Planning Group/EIRASS Eindhoven University of Technology Eindhoven The Netherlands E-mail: a.w.j.borgers@bwk.tue.nl 2 Transport Research Centre (AVV) Ministry of Transport Public Works and Water Management Rotterdam The Netherlands EJTIR 2 no. 1 (2002) pp. 5 - 17 Received: March 2002 Accepted: June 2002 As part of a wider rule-based model of activity behaviour this paper explores the possibility to build a suite of linked conditional choice models to predict the amount of time spouses in a household spend on a set of activities together and alone. First a choice model is used to predict the probability and hence the amount of time the spouses spend together and alone. Conditional on the outcome of this choice model a second model predicts the amount of time that is spent by each spouse separately on a set of activities as a function of sociodemographics car availability and work status. The model is estimated using a small sample in Hendrik-Ido-Ambacht and Zwijndrecht in the Netherlands. The results indicate the model to have face validity. Rho-square values are also high. 1. Introduction Recently the development of activity-based models has been advocated by an increasingly larger number of researchers in transportation research (see e.g. Timmermans 2000). This plea for activity-based models is related to the understanding that discrete choice models focusing on trips or tours rather than activities have reached their limits (e.g. Axhausen and G rling 1992 Bhat and Koppelman 1999). Several developments including an increased participation of women in the workforce changes in the institutional context and the colonisation of the night potentially have a dramatic impact on activity-travel patterns. The mechanisms underlying such change cannot be easily captured by conventional discrete choice models except if one is willing to make rather ad hoc largely non-testable assumptions. 6 Conditional Choice Modelling of Time Allocation Task allocation among spouses is another important development in this regard. Changing role patterns may induce a change in the allocation of tasks with the household. Consequently particular activities may be organised differently in time and space potentially resulting in shifting travel patterns. An interesting study on the relationship between task allocation and aspects of mobility and travel patterns was conducted by BGC (1995). In particular the authors examined the relationship between the number of tasks defined as paid work school volunteer work and in-home maintenance that are performed and aspects of travel patterns. They concluded that females who combine more tasks have a higher car ownership and car availability rate. There was also evidence that if individuals performed more tasks their mobility was higher and their travel patterns were more complex. This relationship was especially strong for women. There is also consistent evidence that the work commute of women is shorter (see also Hanson and Hanson 1980 Singell and Lillydahl 1986 Gordon et al. 1989 Turner and Niemeier 1997). In addition to this basically empirical descriptive research there have been some attempts of modelling activity participation and related travel of couples. For example Golob and McNally (1997) used a structural equation model to investigate the relationship between activity participation and travel. 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 their model predicts that the female's travel for maintenance activities increases more than proportionally to the increase in the female's participation in maintenance activities. To further increase the relevance of activity-based models a separate (sub)model of task or time allocation within households is required if one wishes to capture change in time allocation on activity-travel patterns. The current paper explores the possibility of developing such a model. The paper is organised as follows. First we will outline the theoretical underpinnings of the suggested approach followed by a discussion of the specification of the model. This is followed by a discussion of the data collection. Next we will discuss the results of the estimation. Finally we draw some conclusions and discuss some avenues of future research. 2. Theory Assume that spouses are faced with a set of activities that they need or wish to accomplish during a particular time horizon. Each activity takes a certain amount of time. Some activities are spent together by the spouses while the remaining time is spent to conduct personal activities or fulfil household responsibilities. If we group the latter two categories the problem can be conceptualised as a hierarchical choice process. First a decision needs to be made regarding the amount of time spent together to conduct particular activities. This results in a number of hours left for each spouse to conduct mandatory and discretionary activities. Given the amount of time left the time allocation of each spouse can be predicted by relating the time spent on various activities to a set of independent variables. Note that although we Aloys Borgers et al. 7 used this hierarchical conceptualisation this does not imply that the actual decision-making process also proceeds along these lines. It is primarily a convenient way to capture the empirical relations if any in the data. We conceptualise that various factors influence the time allocation to activities. In particular we assume 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. We included the presence and age of children in the household because the presence of children especially when they are young may induce particular activities such as bringing/getting them to/from school. The socio-economic status of the household has been included in the model to examine the possibility that role patterns may vary across households of different socio-economic status. Age has been included primarily for the same reason but also because the amount of time spent on particular activities may be partly age-dependent. The number of cars available in the household was included to reflect the notion that a spouse's flexibility to conduct a particular activity pattern within some space-time prism is influenced by the availability of a car. If a car is not available and a spouse is dependent on other means of transportation the possibilities to reach particular destinations and to become engaged in trip-chaining are reduced resulting in a different activity pattern and associated time allocation. Finally work status was included because the amount of time spouses have to spend on work which is a mandatory activity directly influences the time left for discretionary activities. According to our conceptualisation first we assume that spouses have to choose between spending time together and spending time alone and second we assume that spouses have to choose on how to spend time among several activities. Therefore the problem at hand is a choice problem. Multinomial logit models including these variables as contextual effects were used to predict time allocation by the two spouses on a set of activities. First a binomial logit model was estimated to predict the amount of time spent together. This model is specified as follows: ptogether exp(Vtogether )/exp(Vtogether ) + exp(Valone ) where ptogether palone Vtogether Vtogether Valone Valone X c0 is the proportion of time spent together is the proportion of time spent alone is the structural utility of spending time together defined as c0 +X is the structural utility of spending time alone defined as 0.0 represents the characteristics of the households and the spouses is a constant to be estimated is a set of parameters to be estimated. (1) Note that the probability that spouses will spend time together has been directly related to the amount of time available during one week. The structural utility of spending time together depends on a set of characteristics of the household and the spouses. 8 Conditional Choice Modelling of Time Allocation Next a conditional choice model was estimated to predict the time a spouse will spend on a particular activity. This multinomial logit model has the following form: pas exp(Vas )/ exp(Va 's ) a' (2) where pas Vas Vas cas as is the proportion of time spent on conducting activity a for spouse s is the utility of spending time on activity a for spouse s defined as cas +asX is a constant to be estimated for activity a and spouse s is a set of parameters to be estimated for activity a and spouse s. Because the total amount of time spent alone by spouse s is known (Palone) these proportions can be translated into the time spent on particular activities. The utility of activity a is supposed to be a function of the set of characteristics X. Note that the constant for one of the activities has to be set at zero. Finally a multinomial logit model was estimated to predict the time spent on each activity by both spouses together: pa exp(Va )/ exp(Va ' ) a' (3) where pa Va Va ca a is the proportion of time spent on conducting activity a by both spouses together is the utility of spending time on activity a by both spouses defined as ca +aX is a constant to be estimated for activity a is a set of parameters to be estimated for activity a. Again the proportion of time spent on activity a can be translated into the amount of time spent on activity a by multiplying Pa by the predicted time spent together (Ptogether). 3. Data collection The data for the formulated model were collected in the Spring of 1998. This data collection was a follow-up of the collection of diary data required to estimate the Albatross model (Arentze et al 2000). Respondents participating in the original data collection effort were asked if they were willing to participate in the collection of additional data. A total of 223 respondents agreed and these constitute the sampling frame for the present study. After a reminder 75 two-person households and 33 single households returned the filled-out questionnaire representing a response rate of 56% and 57% respectively. Of the latter group 18 respondents were women and 15 men. However these single household respondents were not used for the analysis reported in this article. Respondents were requested to jointly express the amount of time they typically spend alone and together on a set of 27 different activities which were later grouped into activity classes. Aloys Borgers et al. 9 The following activity classes were distinguished: (1) sleep eat drink and personal care (2) work out of home including travel time (3) shopping services including travel time (4) inhome non-leisure (5) in-home leisure (6) out-of-home leisure (7) bring/get activities and (8) other. Respondents had to express the amount of time in a free format e.g. minutes per day or hours per week. All time expenditure data were re-coded into the number of hours per week. 4. Analysis and results Because we assume that the probability that a particular task will be conducted by the spouses can be described by multinomial logit models standard methods of estimating multinomial logit choice models may be used to estimate the model. In this particular study iterative reweighted regression analysis was applied which produces maximum likelihood estimates. The observed time expenditures for each activity constitute the dependent variable. The effects of the independent variables were estimated by coding the implied categories as a series of dummy-coded indicator variables. This implies that each variable with say L categories or levels is coded as L - 1 indicator variables. One of the categories or levels is chosen as a base and coded 0 on all indicator variables. Each indicator variable corresponds with a specific category or level as indicated by a code of 1 while all other categories are coded 0 on that variable. When interpreting the following results it should be remembered that all effects describe the differences between the corresponding activity and sociodemographic group and the time spent on the "other" activity class by young households of lower social-economic status with one car without children between 4 and 18 years of age and both spouse working less than 4 hours per week. Figure 1 presents the categorisation and labels of the independent variables. Note that the categorisation of the presence of children is based on the age at which children go to primary and secondary school. Socio-economic status was measured by means of household income. High socio-economic class was defined as twice the modal income level low socio-economic status was defined as lower than modal income and medium socio-economic class was defined in between. The categorisation of age was set at 50 years of age to represent the before and after WW-II generations. The work status was defined as no work' (max. 4 hours per week) part-time' (5-32 hours) and full-time' (more than 32 hour per week). As explained in the theory section we have conceptualised the modelling process of time allocation by spouses to a set of activities in terms of a suite of linked choice models. A first model predicts the amount of time spent by both spouses together. This model will result in a predicted amount of time left for each spouse to spend on activities by themselves. The allocation of this time to a set of activities is predicted by another set of choice models one for men and one for women. Finally time spent by men and women together will be allocated to the activities. The results are reported next.

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