DO ATTITUDES AFFECT BEHAVIORAL CHOICES OR VICE-VERSA: UNCOVERING LATENT SEGMENTS WITHIN A HETEROGENEOUS POPULATION

Transcription

1 DO ATTITUDES AFFECT BEHAVIORAL CHOICES OR VICE-VERSA: UNCOVERING LATENT SEGMENTS WITHIN A HETEROGENEOUS POPULATION Sivam Sarda Arizona State University, Scool of Sustainable Engineering and te Built Environment 660 S. College Avenue, Tempe, AZ Tel: ; ssarda@asu.edu Sebastian Astroza Universidad de Concepción, Department of Industrial Engineering Edmundo Larenas 219, Concepción, Cile Tel: ; sastroza@udec.cl Sara Koeini Arizona State University, Scool of Sustainable Engineering and te Built Environment 660 S. College Avenue, Tempe, AZ Tel: ; skoeini@asu.edu Irfan Batur Arizona State University, Scool of Sustainable Engineering and te Built Environment 660 S. College Avenue, Tempe, AZ Tel: ; ibatur@asu.edu Ram M. Pendyala Arizona State University, Scool of Sustainable Engineering and te Built Environment 660 S. College Avenue, Tempe, AZ Tel: ; ram.pendyala@asu.edu Candra R. Bat (corresponding autor) Te University of Texas at Austin Department of Civil, Arcitectural and Environmental Engineering 301 E. Dean Keeton St. Stop C1761, Austin TX Tel: ; bat@mail.utexas.edu and Te Hong Kong Polytecnic University, Hung Hom, Kowloon, Hong Kong Marc 2019

2 ABSTRACT Tis paper is concerned wit unraveling te contemporaneous relationsip tat exists between attitudes and coice beaviors. Attitudes, perceptions, and preferences may sape beaviors; likewise, beavioral coices exercised by individuals may offer experiences tat sape attitudes. Wile it is likely tat tese relationsips play out over time, te question weter attitudes affect beaviors or beaviors affect attitudes at a specific cross-section in time remains unanswered and a fruitful area of inquiry. Various studies in te literature ave explored tis question, but ave done so witout explicitly recognizing te eterogeneity tat may exist in te population. In oter words, te causal structure at play at any point in time may differ across individuals, tus motivating te development of an approac tat can account for te presence of multiple segments in te population, eac following a different causal structure. However, te segments are unobserved to te analyst, necessitating te adoption of a latent segmentation approac to identify te extent to wic alternative causal structures are prevalent in te population. Tis study utilizes a data set tat includes attitudinal variables to examine relationsips among attitudes towards transit, residential location coice, and frequency of transit use (te latter two variables constituting coice beaviors). Results suggest tat tere is considerable eterogeneity in te population wit te contemporaneous causal structures in wic beaviors sape attitudes more prevalent tan tose in wic attitudes affect coice beaviors. Tese findings ave important implications for transport modeling and policy development. Keywords: causal analysis, beavioral coices, attitudes, latent segments, joint models

3 1. INTRODUCTION Tis paper is concerned wit exploring te relationsip between attitudes, perceptions, and values on te one and and beavioral coices on te oter and. Tere is a vast body of literature in a number of disciplines tat as clearly demonstrated a strong inter-dependent relationsip between attitudes and beaviors (Wicker, 1969; Norman, 1975; Fisbein and Ajzen, 2010; An and Back, 2018). In te transportation context, attitudes about various transportation options as well as personality traits tat describe te innate proclivities and preferences of te individual are likely to be strongly associated wit residential and work place location coices (Cao et al., 2010; Bat, 2015a, Ettema and Nieuwenuis, 2017), mode coice (Heinen et al., 2011; He and Tøgersen, 2017), parking coice (Soto et al., 2018), veicle ownersip and type coice (Acker et al., 2014; Coo and Moktarian, 2004), activity engagement and time use patterns (Arcer et al., 2013; Frei et al., 2015), and willingness to participate in te saring economy and adopt new tecnologies (Astroza et al., 2017; Lavieri et al., 2018; Egbue and Long, 2012; Alemi et al., 2018). Te question tat motivates tis researc is: Do attitudes affect beavioral coices or do experiences obtained troug te exercise of beavioral coices sape attitudes? A number of studies ave utilized attitudinal variables and factors as explanatory variables to explain travel coices and beaviors (Ory and Moktarian, 2005; Seraj et al., 2012; Heinen et al., 2013; Bat et al., 2016; Cen et al., 2017). Tese variables are combined wit te usual socio-economic and demograpic variables, built environment variables, and variables tat describe te options in te coice set to predict beaviors. In most, if not all instances, tese studies ave reported tat attitudinal variables contribute significantly to explaining te coice beaviors of interest. More recently, owever, a growing body of literature reports tat te directionality of te relationsip between attitudes and beaviors is actually one in wic beaviors sape attitudes (Kroesen et al., 2017; Kroesen and Corus, 2018). According to tese studies, contrary to assumptions embedded in most models, beavior influences attitudes. Tese studies suggest tat, wen tere is dissonance (inconsistency) between attitudes and beaviors, people are more prone to adjust teir attitudes to align wit beaviors as opposed to adjusting teir beaviors to align wit attitudes. Wile attitudes and beaviors mutually influence eac oter over time (Kroesen et al., 2017), and attitudes temselves may cange as more information becomes available (Seela and Mannering, 2019), te question as to weter attitudes affect beaviors or beaviors affect attitudes at any point in time remains an intriguing one wit very important implications for transportation demand forecasting and te design and implementation of policy interventions aimed at saping beaviors. If it is true tat beaviors affect attitudes (rater tan te reverse), ten information campaigns and strategies aimed at resaping attitudes may not ave te desired and intended effects. Policy interventions would need to directly target beavioral coices by providing individuals te opportunities to obtain alternative experiences first-and by actually trying new and different mobility options; alternative beavioral experiences would ten bring about canges in attitudes tat would furter reinforce desirable beaviors as individuals adjust teir attitudes to reduce dissonance (Kroesen et al., 2017). Wile previous literature as often caracterized a uni-directional relationsip between attitudes and beaviors, tere is significant evidence of te existence of a bi-directional relationsip as well (Dobson et al., 1978, Kroesen et al., 2017; Kroesen and Corus, 2018). Tis study treats bot attitudinal variables and beavioral coice variables as endogenous in nature, tus recognizing endogeneity associated wit estimating relationsips between tese dimensions of interest. Treating bot attitudes and beaviors as endogenous variables requires te specification 1

4 and estimation of joint equations model systems tat accommodate error correlations, making it possible to account for te presence of correlated unobserved attributes tat simultaneously affect bot attitudes and beaviors. Tis study aims to develop a joint equations model of attitudes and beaviors tat explicitly recognizes te package nature of te relationsip among tem. However, unlike previous studies, tis researc effort explicitly recognizes tat tere may be population eterogeneity wit respect to te nature of te relationsip between attitudes and beaviors. Wile undoubtedly mutually reinforcing, attitudes may influence beaviors for some folks and beavioral coices may affect attitudes for oters at a specific cross-section in time. A multitude of directional relationsips between attitudes and beaviors may exist in te population and it would be of interest to determine te extent or degree to wic eac of te directional relationsips is prevalent in te population at a specific cross-section in time. By determining te degree to wic eac relationsip exists in te population, and te caracteristics of eac market segment (in terms of socio-economic and demograpic caracteristics, for example), it would be possible to design policy interventions, beavioral experiences, and information campaigns tat are appropriately targeted and implemented to acieve desired outcomes. Because te segments in te population are not known a priori, tey are considered latent and determined endogenously witin a joint modeling framework. Tus, te model estimated in tis paper takes te form of a joint equations model system wit latent segmentation, similar to tat presented in Astroza et al. (2018). Te model system includes a model component tat endogenously assigns individuals to different causal segments, and tis component is coupled wit a simultaneous equations model component tat relates attitudes and beaviors to one anoter in a manner consistent wit te latent segment to wic te beavioral unit as been probabilistically assigned. Tis metodology makes it possible to identify te caracteristics of te subgroups tat predominantly depict alternative causal structures. Te model system in tis study is estimated on a data set derived from te 2014 Wo s On Board Mobility Attitudes Survey conducted in te United States. In addition to an extensive battery of attitudinal variables, te survey includes information about people s beavioral coices including use of various modes of transportation, residential location type coice, and car ownersip. Tis particular study examines te nature of te relationsips between attitudes toward transit and two beavioral coice variables, namely, residential location coice and frequency of use of transit. By considering multiple beavioral dimensions, tis study seds ligt on te extent to wic attitudes affect beavior (or vice versa) in te context of different beavioral coices, and identifies te relative presence of different latent segments (following different decision structures) in te population. Te remainder of tis paper is organized as follows. Te next section offers a description of te data. Te metodology is presented in te tird section, model estimation results are presented in te fourt section, and te description of te latent segments is presented in te fift section. Concluding tougts are offered in te sixt and final section. 2. DATA DESCRIPTION Te data set used in tis study is derived from te 2014 Wo s On Board Mobility Attitudes Survey (Transit Center, 2014), an online survey administered to a sample residing in 46 diverse metropolitan areas in te United States. Te data set includes information for 11,842 respondents wo responded to te survey. After filtering records for missing data, 9,600 observations were 2

5 retained for analysis and model estimation. Table 1 presents a socio-economic and demograpic profile of te sample. Overall, te sample provides te ricness of variation and diversity of information necessary to undertake a study of tis nature. Among individual caracteristics, te sample as a sligtly iger proportion of women. About one-fift of te respondents in tis sample are 65 years and above and more tan one-alf of te sample as an educational attainment of college graduate or iger. About 40 percent of te sample is employed full-time, wile anoter 12.5 percent are employed part-time. Te sample spends a fair amount of time online, wit 34 percent indicating tat tey spend 4-8 ours online per day wile five percent of te sample indicated an our or few ours per week. Among ouseold attributes (te rigt column of Table 1), just about 20 percent of te sample as ouseold income less tan $35,000, wile 23.7 percent of te sample as ouseold income greater tan or equal to $100,000. Just about 38 percent of te sample reports ouseold sizes of tree or more, and nearly 70 percent of te sample resides in detaced ousing units wic is consistent wit te statistic tat 61 percent of te sample resides in ousing units owned by te ouseold. Wit respect to transit ricness, 61 percent of te sample reports residing in cities tat may be caracterized as transit progressive (Transit Center, 2014), i.e., cities were tere is a substantial presence of transit modes. Only four percent of te sample resides in ouseolds wit zero veicles, and 25 percent of te sample reported residing in ouseolds wit no workers (consistent wit te age distribution noted earlier). About 40 percent of te sample indicated tat te distance to te nearest transit station is less tan 0.5 mile, wile 38.6 percent reported tat te nearest transit station is more tan one mile from te residence. Te sample is well distributed across te country, wit te largest proportion (23.9 percent) drawn from te West Coast. Among endogenous variables (left column bottom of Table 1), urban dwellers account for 27.8 percent of te sample. Anoter 32.4 percent of te sample resides in suburban and small town locations tat ave mixed land use; te remaining 39.8 percent reside in suburban and small town/rural locations tat would not be caracterized as aving mixed land use. Just about one-alf of te sample reports tat tey never use transit at all even toug it is available. Seventeen percent report using transit at least once per week. Te tird endogenous variable of interest in tis study is te attitudes towards transit (transit proclivity). Tis endogenous variable constitutes a factor derived by conducting a factor analysis on 10 attitudinal statements in te survey data set. Tese attitudinal statements pertain to feelings about transit and are terefore used to derive a transit proclivity or propensity factor. Table 2 presents te attitudinal statements, te percent of te sample agreeing or disagreeing wit eac statement, and te factor loadings. After a number of trials, it was found tat tree of te statements ad insignificant factor loadings, and ence te final factor was based on seven of te ten attitudinal statements. Te loadings are intuitive and suggest tat te factor represents a propensity or proclivity towards using transit as a mode of transportation. Te results of te factor analysis were used to compute factor scores for eac individual in te sample. Tis continuous factor score was used in te model estimation effort to retain te variation in transit proclivity represented by te factor. Tis continuous factor score does not ave a specific underlying scale, but simply represents te range of lower and iger positive attitudes towards transit. Tus, we do not sow any specific descriptive statistics for tis variable in Table 1. 3

6 TABLE 1 Socio-economic and demograpic caracteristic of te sample (N=9600) Individual Caracteristics Exogenous Variables Value (%) Houseold Caracteristics Exogenous Variables Value (%) Gender Houseold income Female 53.5 < $25, Male 46.5 $25,000 to $34, Age category $35,000 to $49, years 0.2 $50,000 to $74, years 17.2 $75,000 to $99, years 22.8 $100, years 19.2 Houseold size years 19.2 One years and above 21.4 Two 44.2 Education attainment Tree and more 37.9 Hig scool or less 17.0 Housing unit type Tecnical/training beyond ig scool 5.1 Detaced Housing 69.4 Some college 26.2 Apartment ousing 28.2 College graduate or iger 51.7 Oters 2.4 Employment status Home ownersip Employed full-time 40.4 Rent 28.1 Employed Part-Time 12.5 Own 61.0 Not Employed 6.1 Living family rent-free or oter 10.9 Oter (student, retired, omemaker) 41.0 Presence of kids Time spent online Presence of kids 0-4 years 8.0 More tan 8 ours per day 18.0 Presence of kids 5-15 years to 8 ours per day 34.0 Presence of kids years to 4 ours per day 42.0 Transit Ricness A few ours per week or an our per week 5.0 Deficient 38.6 Endogenous Variables Progressive 61.4 Residential location coice (RLC) Veicle ownersip Urban 27.8 Zero 4.0 Suburban and small town mixed land use 32.4 One 30.7 Oter suburban and small town + rural 39.8 Two 42.6 Frequency of transit use (FTU) Tree or more 22.8 Frequent: once per week or more 17.0 Number of employed persons Infrequent: less tan once per week 32.6 Zero 25.0 Never (but as available) 50.4 One 35.3 Attitudes Toward Transit (ATT) Factor Score Two or more 39.7 Scale-less underlying continuous variable Distance from ome to nearest transit station Less tan 0.5 mile mile 21.4 More tan 1 mile 38.6 Geograpic Region Norteast 16.3 Sout 18.5 West/Soutwest 19.0 West Coast 23.9 Midwest

7 TABLE 2 Transit Attitudes and Factor Loadings Attitudinal Statements Agree (%) Neutral (%) Disagree (%) Factor Loading (Std Error) I like te idea of doing someting good for te environment wen I ride transit (base) I am not sure I know ow to do all te tings to make te bus or train trip work I worry about crime or oter disturbing beavior on public forms of transportation I feel safe wen riding public transportation (0.037) Public transit does not go were I need to go (0.023) Riding transit is less stressful tan driving on congested igways (0.049) It would be easier for me to use transit more if I were not so concerned about traveling wit people I do not know (0.025) My family and friends typically use public transportation (0.062) I like to make productive use of my time wen I travel I sometimes take public transit to avoid traffic congestion (0.135) Te tree endogenous variables considered in tis study are as follows: Residential Location Coice (RLC): Tree categories Urban; Suburban + Small Town wit Mixed Land Use; and Suburban + Small Town/Rural witout Mixed Land Use Frequency of Transit Use (FTU): Tree categories Frequent (once or more per week); Infrequent (less tan once per week); and Never Attitude Towards Transit (ATT): Continuous factor score Te tree endogenous variables may be related in six possible different causal structures. It is entirely possible tat all six causal structures are prevalent in te population, i.e., tere is at least some fraction of te population following eac of te causal structures. However, te estimation of a joint simultaneous equations model system tat involves tree mixed endogenous variables and six different latent segments is computationally callenging, and te interpretation of results obtained from suc a large-scale model estimation effort may prove difficult. In order to reduce te size of te problem, four plausible causal structures (and ence, four possible latent segments) are considered and included witin te scope of tis paper. Because te intent of tis paper is to unravel relationsips between attitudes and beaviors, te four causal structures were attitudes (ATT) come first in te causal ierarcy and attitudes (ATT) come last in te causal ierarcy are considered. Te two causal structures were attitudes (ATT) act as a mediator between residential location coice (RLC) and frequency of transit use (FTU) are omitted from te scope of tis modeling exercise. Te four causal structures may be depicted as follows: 5

8 Structure 1 RLC (R) Structure 3 ATT (A) RLC FTU ATT RLC FTU + RLC ATT RLC + ATT FTU Structure 2 FTU (F) Structure 4 ATT (A) FTU RLC ATT FTU RLC + FTU ATT FTU + ATT RLC Note: RLC = Residential Location Coice FTU = Frequency of Transit Use ATT = Attitude towards transit (Transit propensity) Te first two structures are tose were beaviors affect attitudes towards transit (ATT), wile te latter two structures are tose were attitudes towards transit (ATT) influence beaviors. Te relationsip between residential location coice (RLC) and frequency of transit use (FTU) may go eiter way. On te one and, residential location may engender transit use; on te oter and, te frequency of transit use may motivate an individual to seek a residential location tat supports te level of transit use undertaken and desired by an individual. 3. MODELING METHODOLOGY In te case were bot attitudinal and beavioral coice variables are represented as continuous variables, it is econometrically feasible to identify and estimate bidirectional causal models tus enabling an explicit portrayal of te mutually reinforcing relationsip tat exists between attitudes and beaviors. However, wen te beavioral coice variables of interest are not continuous (and, are often discrete in te context of travel beavior), ten a bidirectional causal model is not identified, and identification restrictions must be imposed for logical consistency purposes (Pendyala and Bat, 2004). Tis necessitates te estimation of recursive joint equations model systems wen considering multiple endogenous variables of different types. In oter words, wen dealing wit discrete coice variables (or, more generally, limited dependent variables), te joint equations model system can reflect te influence of attitudes on beaviors or te influence of beaviors on attitudes, but not bot (after accommodating for unobserved covariance effects) It sould be noted, owever, tat te recursive joint equations model system tat depicts unidirectional relationsips does not necessarily imply a sequential ordering in te decision mecanism. By estimating bot attitudes and beaviors in a joint equations framework, wile recognizing te presence of unobserved correlated attributes tat affect multiple dimensions, te system of equations portrays jointness in te determination of attitudes and beaviors wile recognizing tat one dimension influences te oter. A more detailed discussion about te important distinction between sequentiality and simultaneity in te coice processes at play may be found in Astroza et al. (2018). Anoter important note ere is tat inference about causality is inextricably tied to observations of individuals and teir coices over time. In oter words, longitudinal data is very desirable for any effort aimed at unraveling and identifying causal relationsips and structures. Generally, cause-and-effect patterns play out over time, involve leads and lags, and are inerently dynamic in nature. Altoug te profession as seen te collection of longitudinal panel survey data on occasion, te prevailing norm continues to be te collection of (repeated) cross-sectional 6

9 data from a sample of te population. In te absence of true longitudinal panel data, it is virtually impossible to unravel cause-and-effect relationsips tat transpire over time. Terefore, te analysis in tis paper sould be construed as depicting contemporaneous causation, i.e., te causal relationsips tat exist at a single snapsot in time. Individuals are making a bundle of coices jointly (involving attitudes, residential location coice, and frequency of transit use), and te causal relationsips depict te nature and direction of influence among te endogenous variables and capture te reasoning or logical flow of tougt tat an individual may exercise. For example, an individual may reason at any cross-section in time tat e or se likes te idea of riding transit (positive attitude) and terefore resides in a residential location tat facilitates a ig level of transit use. Te logical flow of relationsips among te dimensions represents a contemporaneous causation, te notion tat beavior is caused at te moment of its occurrence by all te influences tat are present in te individual at tat moment (Lewin, 1936). 3.1 Te Joint Model of Beavioral Coices and Attitudinal Factor Te remainder of tis section describes in detail te model formulation adopted in tis paper. Consider an individual q (q=1, 2, 3,, Q) facing a multi-dimensional coice system comprised by one continuous variable (attitudes towards transit), one ordinal variable (frequency of transit use), and one nominal variable (residential location). Te discussion starts wit te formulation for eac type of variable, and ten presents te structure and estimation procedure for te multi-dimensional system. For tis section, assume tat te individual belongs to a specific segment. Let y be te continuous variable (corresponding to te attitudes towards transit score) for individual q given tat e/se belongs to segment. Let y γ s in te usual linear regression fasion, were s is a column vector of exogenous attributes as well as possibly te observed values of oter endogenous variables, γ is a column vector of corresponding coefficients, and is a normal standard scalar error term (te variance of is normalized to one for all segments, because, toug y is a continuous variable, it represents a scale-less latent factor score in our empirical analysis tat is constructed from oter observed indicators). Note tat some elements of γ can be zero for some of te exogenous variables, indicating tat te corresponding exogenous variables do not impact coice-making in segment. Furter, because latent segmentation is used as a way to introduce, across te segments, eterogeneity in te recursive effects among te endogenous variables, γ will necessarily be zero on some of te endogenous variables witin eac segment (see Astroza et al., 2018 for a detailed explanation). Let tere be one ordinal variable for te individuals. In te empirical context of te current paper, te ordinal variable corresponds to te frequency of transit use and as tree different levels: never, infrequent (less tan once per week), and frequent (once per week or more). Let te ordinal index for te individual given tat e/se belongs to segment be j ( jl 1,2,3) and let n q be te actual observed value. Ten, assume an ordered-response probit (ORP) formulation as: * * y z, j nq if, n 1 y, n, j {1, 2, 3}, were z is a column vector of q q exogenous attributes as well as possibly te observed values of oter endogenous variables, is a column vector of corresponding coefficients, and is a standard normal scalar error term. Similar to te case of te continuous variable, can be zero on some of te endogenous variables 7

10 witin eac segment (structural eterogeneity). For identification conditions, set,0,,3, and,1 0. Only one tresold,,2, is ten estimated. Let tere be one nominal (unordered-response) variable for te individuals. In te empirical context of te current paper, te nominal variable is residential location, wic as I=3 alternatives (sown in Table 1). Using te typical utility maximizing framework, it is possible to write te utility for alternative i for individual q given tat e/se belongs to segment as: U qi β, x qi qi were x qi is a column vector of exogenous attributes as well as possibly te observed values of oter endogenous variables, β is a column vector of corresponding coefficients, and qi is a normal scalar error term. Let te variance-covariance matrix of te vertically stacked vector of errors ε [( 1, q2,. 3 )] be Λ. Again, β can be zero on some of te endogenous variables witin eac segment. Define U ( U 1, U2, U3)'. Several important identification issues need to be addressed for te nominal variable. First, one of te alternatives as to be used as te base wen introducing alternative-specific constants and variables tat do not vary across te alternatives. Tis is because only utility differences matter in terms of te nominal variable coice. For future reference, let u be te vector of utility differences wit respect to te cosen alternative for te nominal variable and let Λ be te corresponding covariance matrix. Also, because only utility differences matter, only te covariance matrix of te error differences is estimable. Taking te difference wit respect to te first alternative, only te elements of te covariance matrix Λ of u ( U2 U 1, U3 U 1) is estimable. Te jointness across te different types of dependent variables may be specified by writing * te covariance matrix of te [41] vector y u, y, y as: Σ * Σ uy uy Var ( y ) Ω Σ * 1 *, (1) uy y y Σ * 1 uy were Σ * is a 2 1 vector capturing covariance effects between te u uy vector and te scalar * y, Σuy is a 2 1 vector capturing covariance effects between te u vector and te scalar y, and Σ * y y is te covariance between yy * y and y. Te covariance matrix in Equation (1) needs to be mapped appropriately in terms of a corresponding covariance matrix (say Ω) for te vector * U, y, y, wit appropriate identification conditions imposed on Ω to recognize tat only utility differences matter for te nominal variable. Te approac to do so is discussed in detail in Bat (2015b). Tis needs some additional notations and discussion, wic are omitted in te interest of brevity. Next, let be te collection of parameters to be estimated: [, φ,,2, ; Vec( Ω)], were Vec( Ω ) represents te vector of estimable parameters of Ω. Ten te likeliood function for te individual q given tat e/se belongs to segment may be written as: 8

11 were Lq( θ ) 1 ( y ) Pr low, s ψ u ψup,, (2) ( y s ) ( u Ω ) du, 1 3 Du * u =( u, y), te integration domain for te probability D u u ψlow, u ψ up, { : } is simply te multivariate region of te elements of te u vector determined by te range (,0) for te nominal variable and by te observed outcome of te ordinal variable. Tat is, ψ low, (,,, n q 1) and ψ up, (0,0,, n q ), and R (.) is te multi-variate normal density function of dimension R. 3.2 Segmentation Model Te derivation tus far is based on te notion tat individual q belongs to a single segment. However, te actual assignment of individual q to a specific segment is not observed; but it is possible to attribute a probability ( 1,2,, H ) to individual q belonging to segment. Te conditions tat 0 1 and 1 must be met. To enforce tese restrictions, following H 1 Bat (1997), te following logit link function is used: exp( μ wq ) H, (3) exp( μ w ) j1 were w q is a vector of individual exogenous variables, and μ 1 0 serves as a vector identification condition. Defining θ [ θ 1,..., θ; 1,..., ] μ μ, ten te likeliood function for individual q is: H L q ( θ) Lq ( θ ) q segment ), (4) 1 and te overall likeliood function is ten given as: L( θ ) L q ( θ). (5) q Typical simulation-based metods to approximate te multivariate normal cumulative distribution function in Equation 1 can prove inaccurate and time-consuming. As an alternative, te Maximum Approximate Composite Marginal Likeliood (MACML) approac (Bat, 2011), wic is a fast analytic approximation metod, is used. Te MACML estimator is based solely on univariate and bivariate cumulative normal distribution evaluations, regardless of te dimensionality of integration, wic considerably reduces computation time compared to oter simulation tecniques used to evaluate multidimensional integrals. For a detailed description of te MACML approac in te specific case of a joint system of continuous, ordinal, and nominal variables, te reader is referred to Bat (2015b). j j 9

12 4. MODEL ESTIMATION RESULTS Model specifications tat incorporate latent segments can prove to be computationally callenging to estimate (Astroza et al., 2018). To elp facilitate te identification of good starting values for model parameters, te study employed a strategy of first estimating four different causal structures separately and independently, assuming tat te entire sample constituted a single segment. Te parameter estimates from tese independent models were used as starting values for te fullfledged model wit latent segmentation. Also, to elp inform te specification of te joint model, we started wit obtaining best specifications for te individual models corresponding to Residential Location Coice (RLC), Frequency of Transit Use (FTU), and Attitude Towards Transit (ATT), and using tese to inform te joint modeling wit multiple segments. Models wit different numbers of latent segments were estimated and compared. It was found tat te model wit four latent segments (i.e., all four causal structures considered in tis study) offered te best fit compared to models wit one, two, or tree latent segments. For te four-segment model, te log-likeliood value at convergence is 164, and, wit 242 parameters, te Bayesian Information Criterion (BIC) is 165,486.8; te corresponding BIC values for te one, two, and tree segment models are larger at 166,257.3, 165,932.5, and 165,599.2 respectively. Just to explore furter, a five-segment model was also estimated and evaluated (by adding one of te causal structures in wic attitudes act as a mediator between residential location coice and frequency of transit use), and te fit was found to be inferior to te four segment model (BIC for te five segment model was 165,525.1). As suc, te remainder of tis section is dedicated to discussing results for te four-segment model. In te interest of brevity, te joint equations model estimation results for eac of te four causal structures are not presented in full. Rater, complete estimation results are presented for one causal structure for illustrative purposes (Table 3). In general, te effects of exogenous variables on endogenous variables do not vary by causal structure, and tere is no reason tat tey sould. Te exogenous variable influences are largely based on patterns of relationsips witin te data set and tere is no reason for tese relationsips to vary across te causal structures considered. Indeed, an examination of te detailed model estimation results for te four causal structures sows tat te exogenous variables depict similar coefficient values and signs. A brief description of te influence of various exogenous variables on te endogenous variables of interest is provided ere. Tese relationsips can be seen in Table 3. An examination of exogenous variable influences sows tat women respondents sow a lower inclination to reside in urban areas relative to non-urban areas. Admittedly, tis result needs to be interpreted wit care, because residential locations are likely to be based on all individuals in a ouseold. However, since te survey used ere was an individual-based survey (only one individual responded per ouseold), and tis result came out to be statistically significant, we left it in to potentially reflect te notion tat, at least witin te group of single adult ouseolds, women prefer non-urban settings. Women respondents also are more likely tan men to use transit and ave a more positive attitude towards transit. Younger individuals (particularly below 35 years of age) are more likely to be urban dwellers wen compared wit older individuals. Older individuals (35 years or above) use transit less frequently tan teir younger counterparts; consistent wit tis finding, younger individuals below te age of 35 years are found to ave a more positive attitude towards transit. College graduates are found to favor urban residential location type, as do tose employed full time. Time spent online is significantly related to te endogenous variables considered in tis paper; tose wo spend more tan eigt ours per day online are more likely to reside in urban and suburban mix areas, sow a propensity towards iger 10

13 frequency of transit use, and demonstrate a more positive attitude towards transit. It is likely tat tose wo are tecnology oriented prefer transit-oriented urban lifestyles (Hong and Takuria, 2018). Among ouseold attributes, ome ownersip is negatively associated wit urban and suburban mix residential coice and negatively associated wit transit use, but positively associated wit attitudes towards transit. It appears tat ome owners are positively disposed towards transit, and teir infrequent (or non-existent) use of te service does not provide a sufficient basis to cange tat perspective. Lower incomes are associated wit urban living and iger propensity to use transit. Individuals in larger ouseolds are less likely to favor urban residential locations and are less inclined to use transit, presumably because of te lifecycle stage and need to fulfill ouseold obligations. Tis is furter reinforced by te finding tat te presence of cildren negatively impacts urban residential location coice and propensity to use transit. As expected, ouseolds wit ig levels of veicle ownersip (tree or more veicles) are less likely to reside in urban and suburban mix areas, depict a lower propensity to use transit, and ave more negative attitudes towards transit. Te exact nature of te causal relationsips involving veicle ownersip is unknown and merits furter investigation. Veicle ownersip is actually an endogenous mobility coice variable, but as been treated in tis study as an exogenous variable for simplicity. It is entirely possible tat veicle ownersip is affected by residential location coice, propensity to use transit, and transit attitudes; exploring te causal influences tat sape veicle ownersip remains a task for future researc efforts. Tose wo reside in transit progressive cities are more prone to using transit and ave a more positive attitude towards transit, wile tose in te Sout region of te United States (wic is generally more sprawled and autooriented) ave a lower propensity to use transit and a ave a more negative attitude towards transit. In general, all of te exogenous variable impacts are consistent wit expectations and demonstrate tat socio-economic and demograpic variables play a significant and important role in saping attitudes and mobility/location coices. For eac of te segments, we could not reject te ypotesis tat te diagonal terms in te 2 2 covariance sub-matrix of te differenced error terms corresponding to te residential location coice alternative utilities were 1.0 and tat all te off-diagonal elements in te sub-matrix were 0.5. Tis implies tat te error terms of te residential location coice alternatives are independently and identically distributed. Assuming tat te error term in te base alternative in eac dimension is independent of te error terms in oter dimensions, and scaling te variance of te utilities of eac alternative error term in te residential location coice model to one, te implied covariance (correlation) matrix among (1) te urban residential location utility (UL), (2) te suburban/small town mix residential location utility (SUBT), (3) te propensity underlying frequency of transit use (FTU), and (4) ATT factor score is presented toward te bottom of Table 3 for causal structure 1 (we present only te lower diagonal elements because of te symmetric nature of tis matrix). Tere are statistically significant error correlations, and we found tis to be te case for every causal structure considered in tis paper. In general, te error correlations for te oter causal structures ad te same signs as tose for te first causal structure in Table 3, clearly indicating tat, in eac segment, tere is a residual association between te dependent variables not captured by te explanatory variables included in te model specification. Tis result justifies te use of a joint package approac to model relationsips among te endogenous variables considered in tis study. Not surprisingly, te positive correlation in te second column and last row of te covariance (correlation) matrix suggests tat unobserved factors tat increase te utility of residing in an urban area increases positive views of transit, even if tese factors do 11

14 not necessarily increase te actual use of transit. A possible explanation is tat a variety seeking individual (wo likes to try different experiences) may like to reside in an urban location (were tere is a variety of amenities in close proximity) and ave a positive attitude towards alternative (a variety of) modes of transportation. Te correlations in te tird column suggest tat unobserved factors tat lead to residing in suburban and small towns reduce transit use propensity as well as positive attitudes toward transit. Tese results are clear evidence of unobserved residential self-selection effects (see Bat and Guo, 2007 for a detailed discussion). Tose wo intrinsically (due to unobserved individual factors) do not ave positive views about transit and are not very likely to use transit and are likely to locate temselves in suburbia. Table 4 presents a summary of te endogenous variable effects, wic are of interest in te context of understanding relationsips among dependent variables under different causal structures (and so te estimates of all te causal structures are sown in Table 4). Note tat tese are true causal effects after cleansing any relationsips among te endogenous variables caused by spurious unobserved correlation effects. In general, it can be seen tat te relationsips are significant and consistent wit expectations, indicating tat tese tree endogenous variables affect one anoter in beaviorally intuitive ways after accommodating unobserved covariances. In causal structure 1 (RLC FTU; RLC + FTU ATT), it is found tat tose in suburban and small town locations sow a lower propensity to use transit. Compared to tose in suburban and small town/rural areas wit no mixed land use, te residents of urban and suburban mix areas ave a more positive attitude towards transit (again, tis is after accommodating unobserved factors tat may influence tese endogenous variables). Likewise, frequent and infrequent transit users ave a more positive attitude towards transit tan tose wo never use transit; between tese two groups, frequent users ave a more positive attitude tan infrequent users. In causal structure 2 (FTU RLC; FTU + RLC ATT), it is found tat frequent users of transit are more likely to reside in urban areas and suburban and small town areas wit mixed land use areas rater tan suburban and small town areas witout mixed land use. Transit users also ave a more positive attitude towards transit. Similarly, urban dwellers are likely to ave a more positive attitude towards transit. In causal structure 3 (ATT RLC; ATT + RLC FTU), tose wit a positive attitude towards transit are more likely to favor urban and suburban mix residential locations and exibit a greater propensity to use transit. Tose residing in suburban mix locations depict a lower propensity to use transit tan teir counterparts in oter urban and suburban/rural areas. In causal structure 4 (ATT FTU; ATT + FTU RLC), positive attitudes towards transit lead to a more urban and suburban mix residential location coice (relative to tose residing in suburban/rural locations) and a iger propensity to use transit. Similar to indications in oter causal structures, tose wo use transit more frequently are more likely to coose urban and suburban mix locations for residence (relative to suburban/rural locations), wit tis tendency being particularly ig for urban locations. 12

15 TABLE 3 Illustrative Model Estimation Results: Causal Structure 1 (RLC FTU; RLC + FTU ATT) Residential Location Coice RLC (base: oter suburban & small town + rural) Frequency of Transit Use FTU (never, infrequent, Attitude Towards Transit ATT Explanatory Variables Urban dwellers Suburban and small town mix and frequent) (continuous factor scores) Coef t-stat Coef t-stat Coef t-stat Coef t-stat Constant Individual Caracteristics Gender Female Age category years years years years years years and above Education attainment College graduate or iger Employment Status Employed full-time Time spent online More tan 8 ours per day Houseold Caracteristics Home ownersip Own Houseold income Less tan $35, More tan $75,000 Houseold size Two or more Presence of cildren Presence of cildren 0-4 years Presence of cildren 0-15 years

16 TABLE 3 Illustrative Model Estimation Results: Causal Structure 1 (RLC FTU; RLC + FTU ATT) (continued) Residential Location Coice RLC (base: oter suburban & small town + rural) Frequency of Transit Use FTU (never, infrequent, Attitude Towards Transit ATT Explanatory Variables Urban dwellers Suburban and small town mix and frequent) (continuous factor scores) Coef t-stat Coef t-stat Coef t-stat Coef t-stat Houseold Caracteristics Veicle ownersip Tree or more Location Caracteristics Lives in Transit Ric City Progressive Region Sout Tresold Parameter Correlation Between Error Terms URB SUB FTU ATT URB SUB FTU ATT URB: Urban residence utility SUB: Suburban and small town mix utility 14

17 TABLE 4 Relationsips Among Endogenous Variables for te Four Causal Structures/Segments Residential location coice (base: suburban and small town+rural) Variables Suburban & Small Urban Dwellers Town Mix Frequency of Transit Use (never, infrequent, and frequent) Attitude Towards Transit (continuous factor score) Coef t-stat Coef t-stat Coef t-stat Coef t-stat Segment 1 (RLC FTU; RLC+FTUATT) Residential Location Coice (base: suburban, small town +rural area) Urban dwellers Suburban and small town mix Frequency of Transit Use Frequent ( once per week) Infrequent (< once per week) Segment 2 (FTURLC; FTU+RLCATT) Frequency of Transit Use Frequent ( once per week) Infrequent (< once per week) Residential Location Coice (base: suburban/small town + rural area) Urban dwellers Suburban and small town mix Segment 3 (ATT RLC; ATT+RLCFTU) Attitude Towards Transit Residential Location Coice (base: suburban/small town + rural area) Urban dwellers Suburban and small town mix Segment 4 (ATTFTU; ATT+FTURLC) Attitude Towards Transit Frequency of Transit Use Frequent ( once per week) Infrequent (< once per week) Goodness of Fit Statistics (Four-Segment Model System) Log likeliood at convergence, L(β) = -164, (242 parameters); Log likeliood wit constants, L(c) = -217, Log likeliood wit no constants, L(0) = -278,366.45; Adjusted (c) = ; Adjusted (0) =

18 5. SIZE AND CHARACTERISTICS OF LATENT SEGMENTS Tis section presents information about te latent segments in te population. As posited earlier in tis paper, it is ypotesized tat different segments in te population follow different causal structures in teir contemporaneous decision-making processes. Tis section offers information about te size and caracteristics of te latent segments to determine te extent to wic beaviors affect attitudes or attitudes affect beaviors in te survey sample of tis study. Table 5 presents te results of te latent segmentation membersip model. TABLE 5 Latent Segmentation Model Segmentation Variables Segment 1 Segment 2 Segment 3 Segment 4 (base) Coef (t-stat) Coef (t-stat) Coef (t-stat) Constant (-6.23) (-8.11) (-9.32) Age years (-2.88) (-3.01) (-3.76) Age years (-2.11) (-2.34) (-3.08) Gender: Female (-3.53) (5.03) (3.32) Lives in transit ric city (-3.31) (-4.10) College graduate or iger (-2.22) (-2.57) Distance to nearest transit station < 0.5 mile (4.12) (-3.21) (-2.18) Hld Income > $75, (-3.25) (5.19) (2.74) Segment Size 41% 25% 21% 13% 3,936 2,400 2,016 1,248 Segment 1 Causal Structure: RLC (R) FTU (F); RLC (R) + FTU (F) ATT (A) Segment 2 Causal Structure: FTU (F) RLC (R); FTU (F) + RLC (R) ATT (A) Segment 3 Casual Structure: ATT (A) RLC (R); ATT (A) + RLC (R) FTU (F) Segment 4 Causal Structure: ATT (A) FTU (F); ATT (A) + FTU (F) RLC (R) Te model offers a first glimpse into te profile of te segments. In general, it appears tat individuals are more likely to belong to te first segment in wic residential location coice affects frequency of transit use, and tese two beavioral coices togeter impact attitudes (see te last row of Table 5 for te segment size information). It is found tat 41 percent of te sample is assigned to tis first segment, wit all oter segments substantially smaller in size (te size of eac segment may be determined based on te procedure discussed in Bat (1997). Te second largest segment is te second segment in wic frequency of transit use affects residential location coice, and tese two coice beaviors togeter sape attitudes. In oter words, te two causal structures (te first and second) in wic beaviors sape attitudes account for two-tirds of te sample. Te oter one-tird of te sample is collectively assigned to te oter causal segments (te tird and fourt segments) in wic attitudes affect beaviors. It appears tat, in te context of tis sample (wic is a rater large sample drawn from diverse areas in te United States), beaviors influence attitudes for a majority of te respondents, consistent wit recent evidence in te literature (Kroesen et al., 2017) wic suggests tat people adjust teir attitudes according to beavioral coices and experiences in an effort to reduce cognitive dissonance. Te results of te effects of exogenous variables in Table 5 indicate tat individuals younger tan 65 years of age are increasingly less likely to belong to te second, tird, or fourt segments (see te progression of coefficients from left to rigt for te two age groups). Women, owever, are more likely to belong to te tird and fourt causal segments tan te first two causal segments. Compared to men, women appear to be more set wit respect to teir attitudes and likely 16

19 to exibit beavioral coices according to teir attitudes. On te oter and, tose wo live in transit-ric cities and tose wo are college graduates are more likely to belong to te first two segments in wic beaviors sape attitudes (notice te negative signs on tese variables associated wit te tird and fourt segments). Tose wo live close to a transit station are also more likely to belong to te first two segments; peraps teir attitudes are saped by te proximity to transit tat engenders greater level of transit use. On te oter and, iger income individuals are more likely to belong to te tird and fourt segments were attitudes sape beaviors. It is possible tat individuals wo ave reaced tis level of income ave opinions and attitudes tat ave matured, and also ave te wealt firepower to actually take teir attitudes/opinions to fruition. Tat is, tere is peraps less presence of cognitive dissonance for suc individuals tan teir lower income counterparts (lower income individuals may be less able to get out of a lesstan-desirable situation, and may cange teir attitudes as a coping mecanism). It is interesting to note tat, witin te two distinct sets of causal structures (one were beavior sapes attitudes, and te oter set were attitudes influence beavior), te causal structure tat is more dominant is te one were residential location coice affects frequency of transit use. In oter words, te longer term coice (residential location) influences te sorter term mode use decision (frequency of transit use). Tis type of relationsip is quite consistent wit tat often invoked in integrated models of transport and land use were land use coices are often considered iger in te ierarcy and assumed to influence sorter term activity-travel coices. However, it is also found tat te sizes of te segments in te causal structures were frequency of transit use influences residential location coice are not trivial. Tese segments (Segments 2 and 4) are quite sizable in teir own rigt. Individuals in tese latent segments appear to be coosing a residential location coice tat is conducive to te level of transit use tat tey undertake. Overall, it can be concluded tat tere is considerable structural eterogeneity in te sample, and any travel forecast tat assumes te same causal structure for te entire sample is likely to yield erroneous estimates of impacts of alternative transport policies and investments. Table 6 presents a detailed overview of te profile of te various latent segments in te sample. Te left alf of te table sows te percent of individuals in eac latent segment tat belong to a socio-economic group; te rigt alf of te table sows te percent of individuals in eac socio-economic group tat is assigned to eac of te latent segments. Te percent of individuals in eac socio-economic group tat belongs to a specific segment does not vary greatly. Tis is a reflection of te strong effect of te constants in Table 5 in determining segment membersip, relative to oter observed exogenous variables. Tis suggests tat tere is still room for improvement in determining te factors tat influence segment membersip, wic may be explored in future studies wit a more exaustive set of demograpic variables as well as built environment contextual variables. However, wile te latent segments may appear rater similar in profile, distinct patterns can be gleaned as one transitions across segments. For example, consider te age profile of te segments. In te first segment, 58.4 percent of individuals belong to te 35+ age group (RFA); tis percentage gradually increases from left to rigt, ending wit 63 percent of tose in te last segment (AFR) belonging to te 35+ year age group. In oter words, te segments in wic attitudes affect beaviors ave a sligtly older age profile tan te first two segments were beaviors affect attitudes. It is entirely plausible tat tere are more people in te older age groups wose attitudes ave matured and ardened, and teir coice beaviors are influenced by teir attitudes. 17