University of California Transportation Center

This research has two objectives. The first objective is to explore the use of the modeling tool called "latent structural equations" (structural equations with latent variables) in the general field of travel behavior analysis and the more specific field of dynamic analysis of travel behavior. The second objective is to apply a latent structural equation model in order to determine the causal relationships between income, car ownership, and mobility.

Many transportation researchers might be unfamiliar with latent structural equation modeling, which is also known as "latent structural analysis," "causal analysis," and "soft modeling." However, most researchers will be quite familiar with techniques that are special cases of latent structural equations: e.g., conventional multiple regression and simultaneous equations, path analysis, and (confirmatory) factor analysis. Furthermore, recent advances in estimation techniques have made it possible to incorporate discrete choice variables and other non-normal variables in structural equations models. Thus, probit choice models (binomial, ordered, and multinomial) can be incorporated within the general model framework.

The empirical analysis reported here involves dynamic travel demand data from the Dutch National Mobility Panel for the three years 1984 through 1986. All variables in the model, with the exception of income level in the first year, are endogenous: income is treated as an ordinal (four category) variable; car ownership is treated as either an ordinal (ordered probit) or a categorical (multinomial probit) choice variable; and mobility, in terms of car trips and public transport trips, is treated as two censored (tobit) continuous variables. The model fits the data well, but only scratches the surface of the potential of latent structural equation modeling with panel data. Some possible extensions are outlined.

The methodological discussion is not intended as a comprehensive overview of structural equation modeling with latent variables. Rather, the aim is to explore the technique in comparison to conventional methods of travel behavior analysis. Many extensive overviews are available, due to the popularity of the technique in the fields of sociology and psychology, and more recently in marketing research. The technique as described here has been in use since the early 1970s, but, because of recent rapid developments, current overviews are more relevant to transportation researchers. Such overviews are provided by Bentler (1980), Bentler and Weeks (1985), Fornell and Larcker (1981), Hayduk (1987), and Joreskog and Wold (1982), among others. In particular, Hayduk (1897) provides an extensive bibliography. Historical developments are reviewed in Bentler (1986) and Bielby and Hauser (1977).

The author is aware of three computer programs for latent structural equation modeling: LISREL (Joreskog and Sorbom, 1984; 1987), EQS (Bentler, 1985), and LISCOMP (Muthen, 1987). Each program is based on a different approach to estimation and testing and each has its advantages and disadvantages. The three approaches are briefly reviewed in Section 6 on estimation methods. The application results presented here were obtained using the LISCOMP program. It is also possible to replicate the approaches of these programs by implementing several separate estimation procedures (e.g., maximum likelihood estimations of probit models and tobit models, and generalized least square and maximum likelihood estimations of siumultaneous equations) in sequential and recursive order, but this is inefficient in view of the available comprehensive packages.