Lissy La Paix, Transport Research Centre TRANSyT, Universidad Politécnica de Madrid, Av. Profesor Aranguren, Madrid,

Transcription

1 How urban environment affects travel behaviour? Integrated Choice and Latent Variable Model for Travel Lissy La Paix, Transport Research Centre TRANSyT, Universidad Politécnica de Madrid, Av. Profesor Aranguren, Madrid, Michel Bierlaire, École Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering (ENAC), Transport and Mobility Laboratory (TRANSP-OR), Lausanne, Switzerland, Elisabetta Cherchi, DTU Transport, Technical University of Denmark, Department of Transport, Bygningstorvet 116 Vest, 2800 Kgs. Lyngby, Andrés Monzón, Transport Research Centre TRANSyT, Universidad Politécnica de Madrid, Av. Profesor Aranguren, Madrid, Abstract The relationship between urban environment and travel behaviour is not a new problem. Neighbourhood characteristics may affect mobility of dwellers in different ways, such as frequency of trips and structure of the tours. The concept of tour in this context relates to a set of trips during the study day. At the same time, qualitative issues related to the individual s attitude towards specific behaviour have recently become important in transport modelling contributing to a better understanding of travel demand. Following this research line, this paper aims to study the effect of neighbourhood characteristics in the choice of the type of tours performed. We assume that neighbourhood characteristics can also affect the individual propensity to travel and hence the choice of the tours throughout the propensity to travel. Since the propensity to travel is not observed, we employ hybrid choice models to estimate jointly the discrete choice of tours and the latent variable. The propensity to travel is indicative of the tendency to undertake trips, and it is related to the individual socio-economic characteristics and the neighbourhood characteristics. The discrete choice model simulates the choice among tours characterised by different purpose for the main activity and the number of intermediate stops performed. The data used in this study comes from a survey conducted in 2006 and 2007 in Madrid. A total of 943 individuals were interviewed in 3 different neighbourhoods (CBD, urban and suburban). The results show that neighbourhood attributes have indeed a significant impact on the choice of the type of tours either directly and through the propensity to travel. The propensity to travel has a different impact depending on the structure of each tour and increases the probability of choosing more complex tours, such as tours with many intermediate stops. Finally, as expected, the hybrid models show a major improvement into the goodness of fit of the model, compared to a classical discrete choice model that does not incorporate latent effects. Keywords: Neighbourhood, tour-based, discrete choice, latent variable

2 1 Introduction Since 1954 (Mitchell, Rapkin 1954) many researchers have studied the important but highly complex relation between travel demand and land use. One of the major problems discussed in the past literature was the relative importance of urban form characteristics versus socio-economic characteristics to explain trip frequency. The conclusion from these early studies (Kitamura et al and Hanson 1982) was that the total number of trips is largely determined by demographic and socio-economic factors but it is not strongly associated with land use characteristics. The trip frequency has been the major focus also in the recent literature, but authors mainly refer only to specific purposes (Limanond, and Niemeier, 2004) or to specific category of people (Paéz et al 2007; Schmöcker et al. 2005; Roorda, 2009; Morency et al. 2011). Few authors studied the relationship between land use characteristics and tours, but they focus only on specific types of tours such as shopping tour (Agyemang-Duah et al. 1995) or type of activity (Naess 2006). Bhat (1999) instead use land use variables to model specifically the number of stops in the tours. More recent, Shiftan (2008) and Shiftan (2000) analyzed the effect of land-use policies through an activitybased analysis. Particularly, Shiftan (2008) analyzes five sub-models describing: tour type, timing of activities, choice of mode and primary destination, work-based sub-tour and choice of location of intermediate stops. Other study reported an operational implementation of an activity-based travel demand model to represent total daily demand and travel as an activity pattern and a set of tours (Bowman et al. 1999). Similarly to the present paper, those studies analyzed tours and intermediate stops but do not consider latent variables. In this paper we aim to study the effect of land use and socio-economic characteristics in the discrete choice among different tours structures. In particular we defined tour structures in terms of type of main activities of the tour and number of stops realised during the tour for other purposes than the main activity. At the same time, following the recent literature on the effect of latent factors into the discrete choice we believe that the discrete choice among type of tours can also be affected by unobservable attitudes towards travel that is not reflected in the explanatory variables (Ben-Akiva et al. (1999), Ben-Akiva et.al (2002a), Ben-Akiva et.al (2002b)Walker and Ben-Akiva (2002), Atasoy et. al 2010; Hurtubia et. al 2010; Yáñez et. al 2010),. To study this effect we used a hybrid model where the latent variable measures the propensity to travel of each individual, while the discrete choice is the type of tours. Both the latent variable and the discrete choice are a function of the individual socio-economic and land use characteristics, but the tour choice is also a function of travel characteristics and a function of the latent variable. In this way we are able to measure the effect of the land use and socio-economic characteristics have on the choice of tours directly and indirectly through the propensity to travel. Only few authors have analyzed the individual s activity-travel decision process including psychological factors. Accounting for latent factors explaining attitude toward lifestyle is important to control for selselection, i.e. for the tendency of people to choose locations based on their travel abilities, needs and preferences, see Litman (2005; Cao et al., 2008). Handy et al. (2005) used a quasi-longitudinal design to investigate the relationship between neighbourhood characteristics and travel behaviour while taking into account the role of travel preferences and neighbourhood preferences in explaining this relationship. The analysis shown that differences in travel behaviour between suburban and traditional neighbourhoods are largely explained by attitudes. In particular, they found a self-selection issue in levels of driving between different neighbourhoods. Similarly, Walker and Li (2007) and Kitrinou et al. (2010) used an integrated choice and latent variable models for the residential location choice. Particularly, Walker and Li (2007) incorporate the latent classes to represent two latent life-styles (auto-oriented households and transit-oriented households) and the choice model is used for the residential location choice. They make explicit connection between demographics, lifestyle and residential location; and the impact of urban forms on environment and health. 2

3 As far as we know, our study is the first attempt to study the relationship between neighbourhood type and tour structure with hybrid choice models. Our study is carried out in the context of Madrid, where data on trips and activities performed by a sample of families living in three neighbourhoods with different characteristics (in terms of urban density, land-use and transport supply) were available. From the two approaches now available on the estimation of hybrid choice models, the present study uses the advantage of simultaneous estimation, by estimating jointly latent and choice model. The paper is organized as follows: Section 2 is a description of the general framework of integrated discrete choice and latent variable model and the model specification used for this specific application. Section 3 is a description of the case study of Madrid and the variables used for the model estimation. Section 4 includes the empirical results of the hybrid choice model estimated. And Section 5 is the conclusion the paper and we also identify future research. 2 Integrated choice and latent variable model The present work follows the general framework and methodology proposed by Ben-Akiva et al. (1999, 2002b), and generalized by Walker (2001), for incorporating latent variables into choice models via the integration of choice and latent variable models. This general framework is based on the assumption that the individual s utility for each alternative depends on a vector of measurable attributes, as with any random utility choice model, but it also depends on unknown variables (latent variables). These latent variables cannot be directly measured, but the modeller has available indicators that are manifestations of the latent constructs and hence allow identification of the latent constructs. The integrated choice and latent variable structure explicitly models the latent variables that influence the choice process. To specify both the discrete choice and the latent variables, two types of equations are required: a measurement equation that links the unobservable latent variable to its observable indicator and a structural equation that links the observable to the latent variables and models the behavioural process by which the latent variables are formed. 2.1 Model Specification As explained above, the objective of this paper is to study the impact of the propensity to travel (PT) on the choice of the tour complexity for 3 primary activities (home, work/study and shopping/others). For this purpose we estimate a hybrid model where the latent variable measures the PT, while the discrete choice is among types of tour. Propensity refers to the natural or acquired tendency, inclination, or habit in a person or thing. This might be thought of as a general willingness to do something, which, at the same time, influences how much carry out an action1. Following this definition, in our paper, the propensity to travel (PT) is defined as the individual tendency to travel, and it is measured by the daily trip frequency. The main motivation to select the propensity to travel as latent variable is because we believe there could be an unobservable attitude that affects the discrete choice model, but it is not reflected in the explanatory variables. As for the discrete choice, we select the type of tour because it incorporates an explicit representation of temporal-spatial constraints among activity stops within a tour. Tour in this context is defined as a sequence of trip segments that start and end at home, which is consistent with Bowman et al. (1999). 1 In the psychological literature Propensity is used often with specific meanings, such as Propensity to Trust others (Mayer et al., 1995), Risk Propensity as the tendency of a decision maker either to take or to avoid risks (Sitkin and Pablo, 1992) or Propensity effect as a reversal of the traditional hindsight bias (Roese et al,. 2006). 3

4 Figure 1 shows the framework of the integrated latent variable and choice model we used in our formulation. As in the typical general framework of the hybrid models, the right portion of Figure 1 represents the latent variable model (i.e. the PT ) while the left part represents the discrete choice among a set of possible types of tours. Terms in ellipse represent unobservable (latent) constructs, while those in rectangles represent observable variables. We assumed that socioeconomic (SE) and neighbourhood characteristics (LU) play a role in both the latent and discrete choice model, while the travel attributes (LOS) only affect the choice of the type of tour, because this information only exists once a tour has started. The solid arrow that links travel attributes and neighbourhood characteristics to the observed decision of type of tour represents the structural equations that control the decision making process. Similarly, another solid arrow links the PT with the observed decision. The dashed arrows represent instead the measurement equations. Fig. 1 Framework for the Integrated Choice and Latent Variable Model Latent variable model As in the general framework, we need the distribution of the latent variable, the number of trips, given the observed SE and LU characteristics. Let be PT the latent variable, and and two vectors of explanatory variables respectively for the socioeconomic and the neighbourhoods characteristics, the structural equation for PT is specified as follows: Where is the propensity to travel for individual n. is a vector of SE characteristics with elements, is the vector of neighbourhood attributes with elements, and are two vectors of parameters associated to the SE and neighbourhood characteristics respectively, while is the error term Normal distributed with zero mean and standard deviation. We also need the distribution of the indicators conditional on the values of the latent variable. The measurement equation for propensity to travel ( ) is specified as follows: Eq. 1 4

5 where is l th indicator of the latent variable ( ), is the associated parameter to be estimated and is the error term, Normal distributed with zero mean and standard deviation Discrete Choice Model Analogously to the latent variable model, also for the discrete choice model, we need the distribution of the utilities ( that individual n associates to each type of tour j and a measurement equation to identify the choice. The utility function is expressed as a function of a vector of socioeconomic characteristics ), a vector of neighbourhood characteristics, a vector of attributes of the tour and the propensity to travel of each individual n. Eq. 2 Note that the discrete choice and the latent variable models can include different attributes, hence the vectors and can be different between equations (1) and (3). The parameters associated to these attributes in the discrete choice are of course different from those in the latent variable. jn is the error term extreme value distributed with mean zero and standard deviation. In our formulation, the discrete alternatives j are represented by the following types of tours: j=1 is HOME: no trips during the day. j=2 is a Home-Work-Home tour (HW/SH), which includes, Simple tour from home to work and back, Simple school tour from home to school and back. j=3 is a Work/school tour with at least 1 additional stop for another activity (HW/SH+), and includes Work tour with an intermediate stop at home. Work tour with an intermediate stop at home, plus 1 or more additional stops. Work tour with a work-based sub-tour, and any number of additional stops. j= 4 is a Simple tour from home to shopping and back (HOH/SHOP) or a Simple tour with purpose other than work or school or shopping. j = 5 is a Shopping tour with at least 1 additional stop for another activity (HOH+/SHOP+) or a tour with purpose other than work or school, with at least 1 additional stop for another activity. The choices are mutually exclusive. A hierarchy of activities was established in order to construct the tour track, and subsequently the tour complexity. The hierarchy of purposes was created and used to identify primary activity and secondary activity among the others activities during the day, in the case of several trips and/or stops. The trip s main purposed was defined based on the following prioritized order of activity purposes reported by survey participants: 1. Work 2. Work-related 3. Studies: University or school 4. Accompanying: Pick-up/drop-off to someone 5. Shopping 6. Leisure: social, entertaining trips and Sports 7. Others: Other home, Medical 5 Eq. 3

6 According to this hierarchy, the primary activity is used to classify the tour into five categories that compose the alternatives of the choice model. Therefore, the model involves five alternatives mutually independent: The choice model was built assuming extreme value distribution for the error terms of the alternatives; hence the probability of individual n choosing the alternative j is the probability of choosing the alternative conditional on the observed and unobserved variables: Where is the choice set of the individual n. Since PT is unknown, then the probability of individual n choosing alternative j is the integral: Eq. 4 Eq Estimation method Two approaches can be used to estimate the hybrid model: sequential and simultaneous. Simultaneous approach allows estimating both the latent variable and discrete choice model together. While the twostage approach consists of estimation separately of the latent variable; and after uses these parameters in the discrete choice model. See McFadden (1986), Train et al. (1987), and Morikawa et al. (2002), Golob (2003) and Bollen (2005) for more details on the sequential approach. We estimated our models using simultaneous estimation because it leads to more efficient estimates (Ben-Akiva et. al, 1999). Since the estimation of hybrid models is computationally intensive, we estimated a reference model with the structure of multinomial logit. This model, which does not include the latent variable, will be used afterwards for comparison purpose. In the hybrid model the latent variable and the discrete choice were estimated jointly. In the integrated model, we estimated the joint probability of observing both the choice j for individual n and the latent variable. Since the latent variable is a function of the distribution of its error term, we then needed to integrate fit it over the distribution of. Moreover, PT is unobservable but the number of trips is its manifestation, hence we can use the indicator of to improve the accuracy of estimates of the structural parameters as well as to allow for their identification purposes. Therefore, adding the indicators to the integral, we obtained the following expression: Eq. 6 Since structural and measurement equations are assumed to be normally and independently distributed, the densities of and are given respectively by: Eq. 7 Eq. 8 The maximum likelihood is obtained, as always, from maximizing the logarithm of the likelihood function ( ) over the unknown parameters: 6

7 Eq. 9 Where the binary variable characterizes the individual decisions and it is defined as: 10 and C n is the choice set of each individual, i.e. the set of alternatives available for each individual. 3 Empirical Application 3.1 Data characteristics The data used in this work comes from a survey conducted with the aim to analyse the influence of the type of questionnaire (activity-based against travel-based) on the mobility patterns (Madrigal, Monzón 2007). The survey was conducted in 2006 and then repeated (although not with the same individuals) one year later, in One of the reasons for repeating the survey was the need to enlarge the sample and to increase a new type of neighbourhood. In fact, in 2006, the survey included two zones of Madrid: the CBD and an urban area; in 2007 a suburban area was added. The three neighbourhoods included in the survey have the following characteristics: CBD: this area (called Chamberí) corresponds to one of the 22 neighbourhoods of the Central Business District of Madrid. It is a traditional neighbourhood where several historical buildings are located and where people live mainly in apartments. It is characterised by good transit (bus and metro) and rail services and by a gross income level that ranks 4th amongst the neighbourhoods of Madrid City. In 2004 the income of Chamberí was also 40% higher than the mean of the Region of Madrid. Urban: this area (called Pozuelo de Alarcón) is located 15 km west to the Madrid CBD but it is inside Madrid City. This is a car-oriented neighbourhood, where the supply of public transport services is limited. Urban dwellers tend to live in single family houses or detached houses. Pozuelo's average income level ranks the highest amongst the municipalities of the Region of Madrid. It was 66% higher than the mean of the Region of Madrid in Suburban: this area (called Algete) is located 30 km north-east to the Madrid CBD, in the Metropolitan Ring. This district has lower available gross income and fewer transit services than the other two selected neighbourhoods. The average income is lower than Pozuelo s inhabitants. It was 17% higher than the mean of the Region of Madrid in Data were collected during a working-day using a travel diary. The sample includes 345 households and 943 individuals. All individuals older than 4 years were interviewed. The complete sequences of trips made in a day were then collected, with all their characteristics. Socio-economic characteristics were also gathered from each individual of the interviewed families. Then, household location, origin and destinations from the survey were geocoded and integrated into geographic information System (GIS) that included public transport network and street data 2. 2 The public transport network was facilitated by the Department of Human Geography of Complutense University of Madrid. 7

8 3.2 Variable description As mentioned in section 2, the explanatory variables used in our model are: Socioeconomic characteristics of the individuals. Neighbourhood characteristics. Many variables were tested (see La Paix et al., 2010a) for a description of the variables available) but only Neighbourhood type (CBD) and commercial ratio (comm) were significant in this study and then used in the final formulation.travel attributes: The unique travel related variable in our model is travel time. Table 1 Definition of explanatory variables Parameters in the Variable latent variable Socio-economic Characteristics ( ) Gender 4-13 years Base category Definition 0=Male 1=Female years Yes=1; otherwise years Yes=1; otherwise years Base category years Yes=1; otherwise 0 More than 64 years Yes=1; otherwise 0 Female married Yes=1; otherwise 0 Worker Yes=1; otherwise 0 Student Yes=1; otherwise 0 Unemployed Car ownership (1) Base category 0= no car 1= otherwise Driver License Yes=1; otherwise 0 Interaction car ownership * holding a driver licence Yes=1; otherwise 0 Interaction Adult * Child presence Yes=1; otherwise 0 Neighbourhood Characteristics ( ) CBD Yes=1; otherwise 0 Urban Yes=1; otherwise 0 Worker Density Ratio of worker density at origin/destination Commercial land-use Ratio of urban retails origin/destination Number of bus stops and metro Presence of bus and metro station in the residence area. Calculated for a 600 meters radio Attributes of tours ( ): Travel time Longest Trip Travel time 8 Parameters in the discrete choice model Base category It is important to mention that many attributes were tested but only those listed above were significant in our models. A detailed description of all the variables built and tested (also in other models) can be found in La Paix et al. (2010a, 2010b) and La Paix et al. (2010). In particular, to describe the characteristics of the neighbourhoods, several variables were tested, such as dwelling type, population density in the municipality, mixed land use (percentage of land use in the zone of origin and/or destination for residential,

9 commercial or industrial purposes), balance between residence and employment and measures of accessibility. All the available variables were tested in our specifications, as well as several combinations of variables. The final selection of the neighbourhood characteristic was based on statistical grounds. Socioeconomic and neighbourhood characteristics are included in both latent and discrete choice, while the travel attribute is used, of course, only to explain the discrete choices. Table 1 reports the list of explanatory variables used in each model along with an explanation of how they have been coded. The column definition reports the name of the associated parameters as it will be reported in the results. 4 Results Table 2 shows the results obtained using the specifications described in section 2. In particular, the first three columns present the parameters estimated for the latent model, while the last three columns include the parameters estimated from the multinomial logit. The top part of the table displays the results for the discrete choice model, including the latent variable. The lower panel displays the results of latent variable, which consists of a structural equation and one measurement equation. Following the description in section 2, the parameters to be estimated include: 18 parameters (λ) for the SE and neighbourhood characteristics in the latent variables; 1 parameter ( ) associated to the latent variable in the measurement equation (this parameter was constrained to zero, for identification purposes) and 22 parameters (β) for the SE, neighbourhood and LOS attributes in the discrete choice model; apart from that,we needed to estimate the standard deviation ( ) for the indicator of the latent variable (1 parameter) and the standard deviations ( ) for the latent variable). Parameters are estimated using an extended version of the software package BIOGOME (Bierlaire 2003); For further details see Bierlaire and Fetiarison (2009). First of all, it is worth noting that hybrid models require a computationally intensive process to find the right specification. Each parameter was tested as generic and specific for each alternative. Each specification was evaluated on the base of the usual statistics, such as the t-test and the likelihood ratio tests. Thus, the final specification is the best we could find. We first analyze the results from the latent model and then the results from the choice model. We also mainly discuss the results obtained from the simultaneous estimation, while we discuss the comparison with the MNL estimation in the next paragraph. The results shows that the propensity to travel is affected by the individual age. In our model several age categories were tested and the best specification was obtained by fixing the two categories 4-13 and years old, as base reference. The latent model shows that the other four age-groups are more likely to travel than those two reference groups. While individuals less than 13 travel less seems obvious. While do so people between 40 and 49 is less clear. Maybe it depends on our specific sample. Additionally, the results from the latent model also show that the propensity to travel tends to decrease with age (people 65 years old and older show the lowest propensity to make trips, and those less than 21 years have the highest). This decrease is entirely monotonic, and consistent with previous studies in the field of spatial analysis and trip generation (Morency et al. 2011). The propensity to travel is also affected by the dwelling type, but interestingly living in condominium increases the propensity to travel, while living in detached houses decreases the propensity to travel ( and are the only dwelling type coefficients significant at 95%). The effect of neighbourhood type ( and ) confirms the hypotheses that high density residence location increases the propensity to travel.holding driver license ( ) is a useful predictor of the number of trips, which is consistent with other studies. Car ownership ( ) proved positively but not significantly associated to PT, this effect is produced by individuals that choose to stay at home. Finally, as expected, having a job ( ) and study commitments ( ) have almost the same effect on 9

10 the propensity to travel. This is why in the discrete choice model working-tours and study-tours are grouped in the same category. Based on statistical tests and a priori hypothesis about behaviour, in the discrete choice model, the propensity to travel is included in the alternatives 3, 4 and 5, as these are the tours that include at least one additional stop other than the main activity performed. It was assumed in fact that a higher propensity to travel would lead to more intermediate stops. The p-values for the PT coefficients in these three alternatives (, and ) are significant at 95% confidence level. Additionally,, and and bigger in magnitude than, therefore, the higher PT the larger number of intermediate stops. Table 2 Model Estimation Results Hybrid Model Discrete choice Multinomial Logit Discrete choice Name Value Std err p- value Affected alternative Value Std err p- value * , , * * 3, , , * , * * * * * * * * 10

11 Table 2 (continue) Model Estimation Results Hybrid model Latent Model Name Value Std err p-value b_meanatt * * * * * Fit Measures Hybrid Model Multinomial Logit Number of estimated parameters: Sample size: Final log-likelihood: Alt. 1 chosen: 206 Alt. 2 chosen: 437 Alt. 3 chosen: 146 Alt. 4 chosen: 85 Alt. 5 chosen: 69 Rho bar for the init. model Excluded data: 0 Non excluded data: 943 Null loglikelihood: This parameter is non-significant. Constrained to zero after statistical analysis. 11

12 Therefore, the results show that there is a latent effect of neighbourhood type and socioeconomic characteristics on the selection of the type of tour. These results also show that the effect of the Propensity to Travel (PT) is different depending on the type (or complexity) of the tour performed and depending on the primary activity of each tour. This result confirms our hypotheses about the impact of latent variable propensity to travel : since in discrete choice model only difference between utility of alternatives matters, in this case PT produces an increase in the utility of both working and non-working tours with stops. Analyzing working tours, the results from the hybrid model reveals that there is a higher propensity to have tours with intermediate stops than without stops when the main purpose of the tour is working. Socioeconomic characteristics, as well as land use attributes affect the choice of the type of tour also directly, not only through the latent effect. In particular people of 64 years or older have less probability to make a tour for work (maybe because they are likely to be retired or close to retirement) while they have a higher probability to make a tour for other activities. More interestingly, we also found that commercial land-use, dwelling type and neighbourhood type are significant for the choice of the type of tour. In particular, we found that the proportion of land in commercial-use at origin and destination ( ) significantly affects the probability to make non-working tours with stops ( ). This variable is related to the first trip of the day. Where the area of origin is the residential area, and destination corresponds to the municipality of the first trip destination. When this ratio is high, means that the area of destination has a lower commercial use than the area of origin. This was found to significantly increase tour complexity of non-working tours with high availability of retail outlets at origin significantly increase the complex of the tour. Despite of this influence, the effect for working tours is not clear, commercial retail outlets induce workers to make intermediate stops in residentialarea. Thus, workers could accomplish these activities at destination, in the case of availability of adequate facilities at working places. This result leads to the conclusion that mixed land uses in both residence and working places positively influence tour complexity, or in other words stop making propensity. Similarly, and suggest that higher service employment at residential location is associated with more intermediate stops during a work-tour. Thus, people living in tracts with commercial land use have both more intermediate stops and activities. Therefore, researchers and planners should examine how land use and design attributes influence the utility of each tour, and from there consider how the effect on the choice of tour complexity influences trip generation. It is important to mention that the correlation between the above attributes is not high, so we did not have severe multicollinearity problems as that typically arise when attempting to include several land use variables in a single model. In order to avoid multicollinearity we also calculated ratios between commercial land-use at origin and destination, while dwelling type and neighbourhood type are measured at the place of residence. Several specifications were tested; finally we combined two dummy variables and one ratio. This gives an indication that these results may be less spurious than estimates often obtained for one type binary variables only or density-related variables. We now look at measures of transport supply, which are important because they have a direct policy implication. Our results show that the availability of bus stops and metro stations in the residence area does not influence the working-tours (the parameter specific for working tour was in fact not included in the last specification reported in Table 2) while it affects negatively the probability of making a multi-stops non-working tours (. Additionally, this result shows that, definitely, increasing the accessibility measures increase travel demand. The result does not support the theory of inelastic demand (Ewing et al. 1996, Ewing et al. 1994), which that the number of total trips increase substantially with better accessibility. Finally the significance of the travel time parameter (, which was significant only when included in the utility function of non-working tours-with-stops, means that people travelling for non- 12

13 working purposes give more importance to travel time than people travelling for other purposes. The perception of travel time is negative, as expected, because longer travel time entails less time for intermediate stops. The negative sign indicates that people who travel longer distances during the day are less likely to carry out other intermediate activities or tours with stops. It shows the link between time constraints and an individual s decision process. 4.1 Comparison with MNL When we compare the results with the multinomial logit, it is possible to see that there are some significant differences in the values of the estimated parameters, most notably in parameters for SE characteristics (Age, adult with child and driver). This is because of the absences of the latent variable, the logit model underestimate the importance of SE variables, while overestimate values of land-use variables. Most of the parameters are lower in magnitude, and present higher p-values. However it is important to note that all parameters keep the same sign for both hybrid and multinomial logit models. The hybrid model gives more information about the joint influence of SE and land-use variables. Estimation of hybrid models is computationally intensive; it demands a highly complex simulated likelihood function and estimation time, as also stated by Raveau et. al (2010). However, the parameters obtained from the hybrid model are statistically more significant than parameters obtained from the traditional MNL model: more parameters exhibit p-values smaller than Moreover, the application of hybrid choice models to the relationship between urban environment and travel behaviour leads to richer and more precise results than models without latent variables. Comparing the fit measures, the final log likelihood for hybrid (L= ) is bigger than the log likelihood of the multinomial logit (L= ) indicating a better fit for the hybrid model. The rho bar is also bigger for hybrid model (0.96) than multinomial logit model (0.219). On the whole, the inclusion of latent variables in discrete choice models leads to a superior performance of the models not only by improving model fit but also to achieve better estimators of land use variables, see and. The models presented her show that omitting important latent constructs can lead to mis-specification and inconsistent estimates of all parameters, which is consistent with Walker (2001). A two-stage sequential approach with integration will be conducted for this research in the future. Therefore, hybrid models are preferred for this research. 5 Summary and Future Directions In this paper we studied the effect of land use and socio-economic characteristics in the choice of tour complexity according to 3 primary activities: home, work/ school, shopping/others. A hybrid model was estimated where the latent variable is propensity to travel and the choice model is the discrete choice among tour structures in terms of type of main activities of the tour and number of stops realised during the tour for other purposes than the main activity. Many authors have studied the relationship between urban environment and travel behaviour with different structures of discrete choice models. However, the study of this relationship with hybrid models is new. The empirical results obtained from our case study are also new in this field. This approach has two key advantages. The first is that tour-based analysis provides a better explanation than trip-based because it takes into account temporal and spatial constraints; and the second is that the integrated choice and latent variable model allows to a more detailed analysis of the behavioural process. The main motivation to select the propensity to travel as latent variable is because we believe there could be an unobservable attitude that affects the discrete choice model, but it is not reflected in the explanatory 13

14 variables. The PT for a single individual measures in fact how frequently s/he travels depending on her/his socioeconomic and neighbourhoods characteristics of the where s/he lives and performed other activities during the tour. This latent variable also allows accounting for self-selection effects due to the spurious associations attributable to the simultaneous effect of preferences on both the choice of residential location (and thus built environment) and travel behaviour (Handy et al., 2005; Cao et al. 2009). The results support our hypotheses that PT as latent variable exists, that it is a determinant to tour complexity behaviour, and that it can be explained by observed socioeconomic and neighbourhood characteristics. There are specific effects tested in this empirical study between urban structure variables, such as commercial ratio, neighbourhood type, presence of bus/metro at residence area and so on, and tour complexity according to different primary activities (working, school, shopping and others). The estimated parameters and model fit measures show that the empirical application of hybrid models is clearly more robust than traditional choice models. It is worthwhile emphasising the contribution made by latent variables in the discrete choice model to better understanding individual s decision process. The results from the latent model show that PT is explained by socioeconomic and neighbourhood characteristics. And, there is a latent PT for all alternatives of tour. This effect is clearly different between tour with stops and tour without stops. Additionally, the extent to which this tendency influences the decision for tour complexity strongly depends on the flexibility of the individual s commitments. For example, low propensity to travel represents the behaviour of people who do not have job/study commitments, or aging people or those who are living in a low density area with no commercial retail outlets. And high PT captures the behaviour of people who have to travel daily for work or study, people who need to travel for household commitments or people who undertake multi-stage tours during a working day. Finally, although our model do not consider directly mixed land-use effect, the effect of the neighbourhood type, commercial retail outlets and commercial ratio suggest that mixed land-uses do not encourage propensity to travel and, as consequence trip generation, while positively influences tour complexity and thus stop making propensity. Our results also reveal that higher densities favour tour complexity, and significantly influences propensity to travel, and in turn this propensity positively influence tour complexity. This adds new evidences to the current literature, where often opposite effects of the mixed land-use and density on travel behaviours are reported. For example Limanond and Niemeier (2004) reveal that land use patterns have no impact on the whole shopping tour frequency; Kitamura et al. (1997) suggest that land use policies promoting higher densities and mixtures may not alter travel demand materially unless residents attitudes are also changed. While Cevero and Kockelman (1997) find that land-use diversity reduce trip rates and encourage non-auto travel; Cevero (1996) reports that mixed-use development is more important than density in affecting non-motorized work trip mode shares while Kockelman (1997) reports that density has negligible impact on travel behavior (except with respect to auto ownership) once accessibility is accounted for. A detailed review of these effects is reported in Badoe and Miller (2000). As a future work, the model obtained from the simultaneous estimation will be validated with a sub-sample from the data set. The validation will test the forecasting power of the model. Additionally, some important elasticity will be calculated, such as: travel time, commercial ratio and public transport supply, with the objective of testing the effect on the chosen alternatives. 6 Acknowledgments This research was mainly developed during the stay of the first author at Transport and Mobility Laboratory at EPFL (Transp-OR). The first author would like to thank to Transp-OR staff, for their feedback and useful comments; special thanks go to Bilge Atasoy, for her help in the estimation process. The 14

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