Discrete Dynamics in Nature and Society

Volume 2015, Article ID 908387, 8 pages

http://dx.doi.org/10.1155/2015/908387

## Joint Residence-Workplace Location Choice Model Based on Household Decision Behavior

^{1}School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China^{2}China Patent Information Center, Beijing 100088, China

Received 11 July 2014; Accepted 26 August 2014

Academic Editor: Geert Wets

Copyright © 2015 Pengpeng Jiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Residence location and workplace are the two most important urban land-use types, and there exist strong interdependences between them. Existing researches often assume that one choice dimension is correlated to the other. Using the mixed logit framework, three groups of choice models are developed to illustrate such choice dependencies. First, for all households, this paper presents a basic methodology of the residence location and workplace choice without decision sequence based on the assumption that the two choice behaviors are independent of each other. Second, the paper clusters all households into two groups, choosing residence or workplace first, and formulates the residence location and workplace choice models under the constraint of decision sequence. Third, this paper combines the residence location and workplace together as the choice alternative and puts forward the joint choice model. A questionnaire survey is implemented in Beijing city to collect the data of 1994 households. Estimation results indicate that the joint choice model fits the data significantly better, and the elasticity effects analyses show that the joint choice model reflects the influences of relevant factors to the choice probability well and leads to the job-housing balance.

#### 1. Introduction

Integrated land-use and transportation models are most important for both urban planning and transportation planning, and many researches have explored the interdependences between land-use and transportation systems. In the urban land-use pattern, one most important type is residence location, as well as the workplace. These two land-use types influence households’ trip pattern greatly. Based on the personal trip survey (PT survey) data of more than 10 Chinese cities, such as Beijing, Shanghai, and Dalian, more than eighty percent of household daily trips are commute trips; that is, these trips depart from residence location and are directed to workplace, or vice versa. Therefore, it is very important to reveal the inherent mechanism of residence location and workplace choice behavior, especially for fast developing Chinese cities.

As an important behavior analysis approach, discrete choice model has been extensively used in the location choice researches. Lerman [1] and McFadden [2] have formulated residential location choice models using discrete choice method more than 30 years ago. Based on the above pioneering researches, Timmermans et al. [3], Waddell [4], Waddell [5], Ben-Akiva and Bowman [6], Sermons and Koppelman [7], Sermons [8], and Sermons and Koppelman [9] have further developed many models to describe households’ residence location choices using discrete choice approaches too.

In more recent years, Bhat and Guo [10], Miyamoto et al. [11], Bhat and Guo [12], Guo and Bhat [13], and Jiao and Harata [14] have also proposed several residential location choice models using different discrete choice methods. Bhat and Guo [10] put forward a mixed logit model to analyze the residential location choice behavior and considered random taste variations in their model, as well as the spatial correlations among different residential locations. Miyamoto et al. [11] also proposed a residential location choice model using mixed logit method and used a stochastic process to formulate the spatial correlation. Bhat and Guo [12] formulated a joint mixed multinomial logit-ordered model to present the residential sorting effects and applied it to comprehensively examine the impact of the built environment, transportation network attributes, and demographic characteristics on residential choice and car ownership decisions. Guo and Bhat [13] explored different conceptualizations to represent neighborhoods in residential location choice models and described three alternative ways to construct operational units to represent neighborhoods. Jiao and Harata [14] presented a mixed logit framework to identify residential location choice behavior in different households and integrated a “direct parametric representation” approach to capture the correlation between spatial units, as well as a comprehensive structure of zonal accessibility to reflect the effects of employment, school, shopping, and recreational opportunities. Most recently, Li et al. [15] formulated a multiobjective optimization model to distribute residential spatial units integrating three objectives. All the above models obtained rather significant results.

As for workplace choice, it has also been extensively studied using similar methods in the framework of disaggregated travel models, for example, Abraham and Hunt [16] and Levine [17].

Most above models of residence location or workplace choice often assume that one choice dimension is exogenous to the other; that is, residence location choice is conditional on predetermined workplace, or vice versa. However, there exist strong interdependences between residence and workplace locations, and such kinds of interdependences have been studied in several existing researches. Waddell [4] questioned it through an empirical study using data of the metropolitan area of Dallas-Fort Worth (Texas, USA). Waddell et al. [18] developed a discrete choice model of joint residence location and workplace choice using methods of latent market segmentation for one-worker households and put forward a methodology for accommodating different sequential decision-making processes. Li et al. [19] also formulated a joint decision model of residence location and workplace using nested logit method and applied it to Beijing city. Ibeas et al. [20] specified a nested logit model and a cross-nested logit model to investigate the existence of spatial correlation between residence and workplace locations and found out that the inclusion of spatial correlations in the model fits the data significantly better.

To revise the residence location and workplace choice models with the assumption that residential location and workplace are chosen independently of each other, that is, without decision sequence, one key feature of this paper is to cluster the households into two groups, choosing residence location first and choosing workplace first, and to formulate the residence location and workplace choice models under the constraint of decision sequence. Another key feature is to further combine the residence location and workplace together and to present the joint choice model.

The rest of this paper is organized as follows. The basic models for all households without decision sequence are proposed in Section 2. Clustering households into two groups, the revised models with decision sequence are presented in Section 3. The joint residence-workplace location choice model is put forward in Section 4 based on the combined choice alternatives. A questionnaire survey is implemented, and the data is illustrated in Section 5. The estimation results of three groups of models are reported and compared in Section 6, as well as the elasticity effects analyses. Conclusions and further researches are summarized in the last section.

#### 2. Residence Location and Workplace Choices without Decision Sequence

In this section, the residence location and workplace choices are assumed to be independent of each other.

##### 2.1. Residence Location Choice without Decision Sequence

Essentially, the household decision behavior influences the residential location choice greatly. Using the discrete choice method, the random utility theory is employed to describe such decision behavior. The following equation is formulated to indicate whether a household will choose a location as the residence place or not: where is an indicator to denote whether household selects spatial unit to reside or not; is the utility for household to select spatial unit ; is the total number of spatial units in the choice set.

Usually, the utility function may be divided into two items: the systematic item and the random item :

In a mixed logit formulation, the deterministic term can be further represented as below:where and are parameters to be estimated, is the fixed parameter, is the unfixed parameter subject to a logarithmic normal distribution; and are explanatory variables, for example, spatial unit information, household information, travel related information, and so forth; is the number of explanatory variables corresponding to the fixed parameters; is the number of explanatory variables corresponding to the unfixed parameters.

Based on the above formulations, the choice probability for household to choose spatial unit is presented as a mixed logit formulation:

Using to represent the density function of the logarithmic normal distribution, the unconditional choice probability for household to choose spatial unit is therefore the integral of over all possible variables of :

According to the factors households pay most attention to when they make the residence location choice, the explanatory variables include the following: : household travel time between residence location and workplace; : household travel distance between residence location and workplace; : household travel cost between residence location and workplace; : regional housing price around residence location; : regional population around residence location; : number of regional rail transit stations around residence location; : regional floor area ratio (FAR) around residence location.

According to several estimation experiments, and are assumed to be corresponding to the unfixed parameters .

Therefore, (5) can be further represented as

In this model, the unfixed parameter is assumed to follow the following logarithmic normal distribution: where is the random variable, and and are the expectation and variance of , respectively.

##### 2.2. Workplace Choice without Decision Sequence

Similar to the residence location choice model, the mixed logit method is employed to model the workplace choice.

According to the factors households pay most attention to when they make the workplace choice, the explanatory variables include household travel time , household travel distance , household travel cost , and : household annual income; : number of regional employment opportunities around workplace; : regional gross sale of consumer goods around workplace.

Based on several estimation experiments, and are also assumed to be corresponding to the unfixed parameters .

Therefore, the workplace choice model without decision sequence is represented as

In this model, the unfixed parameters and are also assumed to follow the logarithmic normal distribution as shown in (7).

#### 3. Residence Location and Workplace Choices with Decision Sequence

In the above two models, we assume that residence location choice and workplace choice are independent of each other; that is, people choose locations without decision sequence. However, some households tend to choose workplace first and then choose residence location according to the constraint of workplace, or vice versa. Both of these sequential choice processes are present in the population in a proportion that is unknown to the analyst. Fortunately, the cluster analysis provides an effective method to differentiate them. In this section, we relieve the strong assumption, cluster all households into two groups, and formulate the residence location and workplace choice models with decision sequence.

In this research, a large amount of information about the households is collected through a questionnaire survey, and seven groups of preference data are extracted to represent the households’ preferences when they choose residence and workplace locations, including the following:(1)residence location is adjacent to workplace;(2)traffic is convenient;(3)commute is convenient;(4)housing price is acceptable;(5)there are good schools nearby;(6)geographic position is good;(7)residential community environment is excellent.

Based on the above 7 groups of preference data, cluster analysis is then implemented to cluster all households into two categories, choosing workplace first, and then choosing residence location conditional on workplace, or vice versa. The detailed data and clustering results are described in Section 5.

Using survey data of clustered households, we can formulate the residence location and workplace choice models with decision sequence, respectively. For the convenience of comparison between different models, we use the same explanatory variables here as models without decision sequence. Therefore, the residence location choice model with decision sequence is the same as (6), while the workplace choice model with decision sequence is the same as (8). Here the unfixed parameters and are also assumed to follow the logarithmic normal distribution as shown in (7).

#### 4. Joint Residence-Workplace Location Choice

As stated above, there exist strong interdependences between residence and workplace locations, and in most time they influence each other, and households tend to consider these two choice problems together. It is often unreasonable to simply assume that households choose residence location or workplace first. Therefore, we assume that both residence location and workplace choices are made simultaneously as an instantaneous bundle and then model the interdependence based on such assumption.

In this model, we take the residence-workplace location pairs as new choice alternatives. To model the joint location choice behavior, all explanatory variables influencing residence location and workplace choices are incorporated within the joint choice model

The definitions of all variables in (9) are the same as the above, and the unfixed parameters and are also assumed to follow the logarithmic normal distribution as shown in (7). Since the residence-workplace location pairs are taken as the choice alternatives, the number of alternatives increases dramatically.

#### 5. Data

To testify the above three groups of models, we collected the field data of 1994 households in Beijing city through a questionnaire survey. The residence and workplace locations in the data cover all districts of Beijing city, including 6 urban districts and 10 suburban districts.

Table 1 provides a summary of household characteristics in the survey data used, and the distributions of household structure, household income, car ownership, and commuting mode are included. The clustered result of households choosing residence or workplace first is also shown in the table.