With the rapid development of urbanization and motorization, urban commute trips are becoming increasingly serious due to the unbalanced distribution of residence and workplace landuse types in most Chinese cities. To explore the inherent interrelations among residence location, workplace, and commute trip, an integrated model framework of joint residenceworkplace location choice and commute behavior is put forward based on the personal trip survey data of Beijing in 2005. First, to extract households’ different choice characteristics, this paper presents a latent class model, clusters all households into several groups, and analyzes the conditional probability of each group. Second, the paper integrates the residence location and workplace together as the joint choice alternative, employs the socioeconomic factors, individual attributes, household attributes, and trip characteristics as explanatory variables, and formulates the joint residenceworkplace location choice model using mixed logit method. Estimations of the latent class model show that four latent groups fit the data best. Further results of the joint residenceworkplace location choice model indicate that there exist significantly different choice characteristics in each latent group. Generally, the integrated model framework outperforms traditional location choice methods.
In most Chinese cities, with the rapid development of urbanization and motorization, the density of urban landuse is increasing very fast, and the spatial distribution of residence location and workplace is turning to be unbalanced. As a result, the urban transportation systems, especially the commute trips, are facing more and more serious problems.
During the past two decades, integrated models of urban landuse and transportation systems have been studied extensively, especially the residential location choice models using decision behavior approaches. As a competitive tool, the discrete choice model was used widely in the location choice models. Lerman (1976) [
More recently, Li et al. (2014) [
With some models focusing on location choice of specific household types (such as twoearner or single worker households), most of the above works have analyzed the location choice behavior using data of all kinds of households. However, there should exist different choice characteristics for different households. Jiao and Harata (2007) [
Fortunately, the latent class model (LCM) has been used in the category analysis widely. Lazarsfeld (1950) [
To analyze the different residence location and workplace choice characteristics according to household types, one key feature of this paper is to formulate a latent class model and to extract the inherent household groups. Another key feature is to further combine the residence location and workplace together as the choice alternatives and present the joint residenceworkplace location choice models for each latent class using mixed logit methods.
The rest of this paper consists of the following contents. The general model framework is proposed in Section
The theory of LCM is based on the probability distribution principles and loglinear models, with the objective to explain the interrelations among manifest variables using the least latent categories and to achieve the local independence. The LCM is mainly used to analyze the categorical data. Compared with continuous variables, the biggest difference of categorical variables is that their values are discrete, with each value denoting different attribute or classification, for instance, gender, residence location, trip mode, and so forth.
Mixed logit (ML) model is a kind of discrete choice model. To assume the parameters subject to some random distributions, it is capable of incorporating the random taste variations of different households, as well as the spatial correlations among different land locations. Therefore, the ML model is widely used in location choice researches.
The LCM is a kind of model to transform the probabilities of categorical variables to some parameters, that is, probabilistic parameterization. There are two kinds of categorical variables in classical LCM: manifest variable and latent variable. Meanwhile, there are two groups of parameters: latent class probability and conditional probability.
The manifest variable can be observed directly, for example, time, distance, and so on. It is also called observable variable or measureable variable. However, the latent variable cannot be observed directly, for instance, psychological expectation, individual preference, and so forth.
A latent class model can be formulated as
Similar to MNL model, NL model, and GEV model, the mixed logit model is also based on the assumption of random utility maximization. With rather flexible formulation in the structure, it mainly has the following advantages:
Similar to our previous work [
To incorporate random taste variations in the model,
Based on the fundamental theory of discrete choice analysis, the mixed logit model can be formulated as
Therefore, the unconditional probability for decision maker
To explore the inherent characteristics of urban residence location choice and workplace choice, this paper further formulates the latent class model for commute trips based on the personal trip survey data of Beijing in 2005. The study area is divided into eight zones according to the urban districts: Xicheng, Dongcheng, Chongwen, Xuanwu, Haidian, Chaoyang, Fengtai, and Shijingshan. Based on the thorough analyses of influence factors of residence location and workplace choices, we introduce the following five variables into the LCM: residence location, workplace, commute distance, commute mode, and household monthly income. Here residence location, workplace, and commute mode are discrete variables; however, commute distance and household monthly income are continuous in nature. For convenience, these two continuous variables are also discretized and transformed to categorical variables. For the important commute mode, we mainly select five modes, that is, walk, bicycle, bus, subway, and car.
Variables in the latent class model are summarized in Table
Variables in the latent class model.
Variable  Symbol  Values 

Residence location 

Xicheng/1, Dongcheng/2, Chongwen/3, Xuanwu/4, Haidian/5, Chaoyang/6, Fengtai/7, Shijingshan/8 
Workplace 
 


Commute distance 

<4/1, 4–8/2, 8–12/3, 12–16/4, 16–20/5, >20/6 


Commute mode 

Walk/1, Bicycle/2, Bus/3, Subway/4, car/5 


Household monthly income (Chinese Yuan) 

<2500/1, 2501–3500/2, 3501–5500/3, >5500/4 
In the third column, the number after the slash line “/” is value of the corresponding categorical variables.
Based on the variables in Table
Based on the above symbols and equations, we can further formulate the conditional probability of latent variable
Using (
Based on the clustered household groups from the LCM, we can further formulate residence location and workplace choice models for each kind of household using mixed logit method, just like our previous work [
Variables in the mixed logit model.
Variable  Symbol  Remark 

House renting price 
FJ  Continuous 


Commute distance 
DI  Continuous 


Commute time 
TT  Continuous 


Household monthly income 
INC  Discrete: 


Population density 
POP  Continuous 


Number of employment opportunities 
EMP  Continuous 


GDP of workplace 
GDP  Continuous 
In the third column, the number after the slash line “/” is value of the corresponding categorical variables.
In this model, we assume that households make residence location and workplace choices simultaneously, that is, the joint location choice. Since there are eight zones in the study area, totally we have 64 choice alternatives; that is, each residenceworkplace location pair denotes one alternative.
Based on many estimation experiments, commute distance and commute time are assumed to be corresponding to the unfixed parameters
Using (
Based on the personal trip survey data of Beijing, we can estimate the integrated model of joint residenceworkplace location choice and commute behavior.
Parameter estimation of latent class model is usually implemented using two kinds of iterative algorithms based on maximum likelihood method: expectation maximization algorithm and NewtonRaphson algorithm. The iterative process consists of two steps: the first step is to achieve the maximized value from a starting number, which is taken as the initial estimation value in the algorithm and the second step is to estimate again from the result of the first step, until the process arrives at the accuracy requirement.
To obtain the LCM with bestfit ratio, this paper makes use of the maximum likelihood method for estimation. The progress of estimation begins by fitting a complete independence model with
Based on several estimation experiments, the fit criteria of the proposed LCM are summarized in Table
Fit criteria of the LCM.
Number of latent classes  Likelihood ratio chisquare  AIC  BIC  

Value 



13148.723  <0.001  64326.826  64490.171 

11145.600  <0.001  62425.088  62758.060 

9404.705  0.053  60731.082  61233.680 






8845.764  0.057  60255.852  61097.705 
From Table
The detailed parameter estimation results are further summarized in Table
Estimation results of the LCM.
Latent class  1  2  3  4  Variable values 

Residence location  
1  0.057 

0.018  0.000  Xicheng 
2  0.052 


0.000  Dongcheng 
3  0.001  0.000  0.019 

Chongwen 
4  0.004  0.018  0.000 

Xuanwu 
5 

0.002  0.000  0.000  Haidian 
6 

0.005 

0.001  Chaoyang 
7  0.051  0.004  0.002 

Fengtai 
8  0.060  0.008  0.000 

Shijingshan 
Workplace  
1  0.092 

0.000  0.024  Xicheng 
2  0.092 


0.004  Dongcheng 
3  0.015  0.014  0.011 

Chongwen 
4  0.016  0.037  0.000 

Xuanwu 
5 


0.000  0.002  Haidian 
6 



0.000  Chaoyang 
7  0.030  0.048  0.000 

Fengtai 
8  0.009  0.013  0.000 

Shijingshan 
Commute distance  
1 

0.083 


<4 
2 




4–8 
3 


0.086  0.111  8–12 
4 


0.023  0.012  12–16 
5  0.070  0.068  0.014  0.017  16–20 
6  0.081  0.062  0.000  0.005  >20 
Commute mode  
1  0.097  0.031 

0.133  Walk 
2 

0.214 


Bicycle 
3 


0.165  0.114  Bus 
4  0.061  0.063  0.000  0.000  Subway 
5 



0.229  Car 
Household monthly income  
1  0.156  0.068  0.158 

<2500 
2  0.250  0.198  0.269 

2501–3500 
3 


0.269 

3501–5500 
4 



0.021  >5500 


Latent class probability  47.55%  11.00%  21.30%  20.15% 
From Table
From the above analyses, we can further find out that the differences among four latent classes are distinct. Moreover, the clustered results from the LCM method are much more logical than those from traditional simple cluster analysis methods [
The joint residenceworkplace location choice model based on mixed logit is estimated using maximum simulated likelihood (MSL) method, which was proved to be rather effective and efficient by Bhat and Guo (2004) [
Using the above method, the joint residenceworkplace location choice model is estimated as though that all households tend to choose residence location and workplace simultaneously; that is, these two kinds of landuse types influence each other. The estimated mean values of all parameters are reported in Table
Estimation results of four latent classes.
Variables  Class 1  Class 2  Class 3  Class 4 

House renting price  −0.9568 
−0.1823 
−0.1734 
−0.2153 


Commute distance 
−0.1953 
−0.1174 
−0.5049 
−0.2662 


Commute distance 
0.3115 
0.1762 
0.2878 
−0.1417 


Commute time 
−0.03623 
−0.0305 
−0.0128 
−0.0582 


Commute time 
−1.14 
−0.0139 
7.69 
−2.10 


Household monthly income  1.0919 
2.0387 
1.0537 
1.3504 


Population density  0.9441 
−0.9983 
−0.1624 
−0.0763 


Number of employment opportunities  0.0648 
0.0665 
0.1113 
0.2311 


GDP of workplace  0.3617 
0.2288 
0.3973 
0.1594 
Here M means “mean value”; S.D. means “standard deviation.”
From Table
For all latent classes, we can get the following results from the signs of parameters.
The expected negative sign of house renting price shows that with other conditions fixed, households tend to live in areas with rather low housing price.
Both commute distance and commute time between residence location and workplace have negative signs as expected, which indicates that households tend to jobhousing balance when they consider their residence location and workplace choices; that is, proximity to workplace is very important for households to choose residence location; at the same time, proximity to residence location is also very important for households to choose workplace.
The positive sign of household monthly income is also consistent with expectation, which means that households are more likely to reside or work in places which could bring them higher income.
The sign of number of employment opportunities is positive, showing that job opportunities are a rather important factor influencing households’ residence location and workplace choices. It means that people tend to live and work in locations with more opportunities.
GDP of workplace has the expected positive sign, indicating that households are more inclined to work in places with good economic environment.
A very interesting thing is that there is an exception in population density; that is, in latent class 1, the parameter is positive, while in latent classes 2, 3, and 4, the parameters are negative. Characteristics of each latent class could explain such exception. In class 1, most households live in Haidian and Chaoyang districts, which are two rather big zones with many residential landuses, but the residence density is not very high; therefore, households tend to locate in places with high population density, which is also a kind of reflection of population clustering effect. Conversely, in classes 2, 3, and 4, most households live in other six districts of Beijing, which are rather small areas with very high residence density; therefore, households in these three classes tend to reside in areas with low population density, which reflects that low residence density and comfortable community environment are more important for these people.
Further comparisons of the estimations among four latent classes reveal the following results.
For all 4 latent classes, the magnitude of household monthly income is much bigger than other parameters. It indicates that this factor is much more important than other factors for household residence location and workplace choices. Moreover, house renting price also has rather big magnitude, showing that housing price is also a very important factor in location choices.
For latent class 1, house renting price, population density, and GDP of workplace have much bigger magnitudes, showing that these three factors are more important for households in Haidian and Chaoyang districts to make their residence location and workplace choices.
For latent class 2, much bigger magnitudes in population density and GDP of workplace again prove their importance. As stated before, the sign of population density is negative, because most households in class 2 reside in Xicheng and Dongcheng districts, which locate at the center city of Beijing, with very high residence density. Therefore, different from class 1, these households tend to live in areas with low population density and comfortable environment.
For latent class 3, commute distance has rather big magnitude, which means that people consider more about commute distance when they make residence location and workplace choices. Results from the latent class analyses give the reason; that is, most households in this group use walk and bicycle in commute trips, and these two kinds of modes are more sensitive on trip distance.
For latent class 4, the magnitude of number of employment opportunities is obviously bigger than others. Once again, the reason can be achieved from the latent class analyses. Most households in this group reside and work in Fengtai and Shijingshan districts, which are relatively underdeveloped in economic level. There are less employment opportunities in these two districts than other six zones, and income is also rather low. Therefore, households in this group pay more attention to number of employment opportunities in residence location and workplace decision behaviors.
Generally, all the estimation results are consistent with expectations. The detailed analyses based on latent classes explore many interesting and logical results.
This paper addresses an integrated model of joint residenceworkplace location choice and commute behavior using latent class and mixed logit methods. The general model framework consists of two single models. We first present a latent class model to extract households’ different choice characteristics and cluster households into several groups. Based on the latent class analyses, we further combine the residence location and workplace together as the joint choice alternative and formulate a joint residenceworkplace location choice model using mixed logit method. A large amount of data is extracted from the personal trip survey data of Beijing in 2005 for case study. Estimation results of the latent class model show that households are properly clustered into four groups, and every kind of household has different characteristics. The mixed logit models for all four latent classes are then estimated, respectively, using maximum simulated likelihood method. Estimated parameters show that all the estimations are consistent with expectations. For all latent classes, household monthly income and housing price are much important for residence location and workplace choices. Further comparisons of the estimated parameters among four latent classes prove that there exist much big differences in the location choice behaviors, and the joint residenceworkplace location choice model using latent class and mixed logit methods is very effective.
Future researches are directed towards the following aspects. The first is to employ more recent socioeconomic data, census data, and trip survey data and to update the case studies of this research. The second is to further explore the differences among different decision makers, for instance, male, female, and children in the same household and to analyze more detailed choice behaviors. The third is to track the development histories of residential and employment landuses based on panel data.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research has been supported by National Natural Science Foundation of China Project (51208024), Beijing Philosophy and Social Science Project (14CSC014), Beijing Nova Programme (Z151100000315050), Science and Technology Project of Ministry of Housing and UrbanRural Development of China (2013K56), and the Importation and Development of HighCaliber Talents Project of Beijing Municipal Institutions (CIT&TCD201404071).