Simultaneous Equation Systems Involving Binary Choice Variables

In this paper a simultaneous modeling system for dichotomous endogenous variables is developed and applied empirically to longitudinal travel demand data of modal choice. The reported research is motivated by three factors. First, the analysis of discrete data has become standard practice among geographers, sociologists, and economists. In the seventies a number of new tools were developed to handle multivariate discrete data (Bishop, et al., 1975; Fienberg, 1980; Goodman, 1972). However, while these methods are invaluable in studying empirical relationships among sets of discrete variables, they have a limited ability to reveal the underlying causal structure that generated the data. Second, in travel demand analysis and housing market modeling, attention has been focused largely on single-equation models. It can be argued that this scope is too limited. Human decisions are usually not taken in isolation but in conjunction with other decisions and events. There may be complex feedback relations, recursive, sequential, and simultaneous decision structures that cannot be adequately described in a single equation. This has been a major motivation in the seventies in sociology for the development of a new modeling approach: linear structural equations with latent variables. Such models combine the classical simultaneous equation system model with a linear measurement model. Original developments, particularly the LISREL model (Joreskog, 1973, 1977), did not allow for discrete dependent variables. More recently, Muthen (1983, 1984, 1987) and others (e.g., Bentler, 1983, 1985) developed models that incorporate various types of non-normal endogenous variables, including censored/truncated polytomous and dummy variables. This paper explores the possibilities of this method for simultaneous equation models in dynamic analysis of mobility. A third motivation for the present research is the rapid growth of longitudinal data sets. In recent years many longitudinal surveys have become available for geographical, economic, and transportation analyses. In labor and housing market analysis the Panel Study of Income Dynamics (PSID, 1984) has played an important role (Heckman and Singer, 1985; Davies and Crouchley, 1984, 1985). In consumer behavior, the Cardiff Consumer Panel has been a major motivation for the development and testing of dynamic discrete choice models (Wrigley, et al., 1985; Wrigley and Dunn, 1984a, 1984b, 1984c, 1985; Dunn and Wrigley, 1985; Uncles, 1987). In the Netherlands a large general mobility panel has been conducted annually since 1984 (J. Golob, et al., 1985; van Wissen and Meurs, 1989). Here analyses have focused on discrete data on modal choice (T. Golob, et al., 1986), as well as on dynamic structural modeling (Golob and Meurs, 1987, 1988; Kitamura, 1987; Golob and van Wissen, 1988; Golob, 1988). The present paper is an extension of this line of research to incorporate dynamic structural models of modal choice, using data from the Dutch Mobility Panel. This paper is organized as follows: In Section 2 the basic methodology is developed. In Section 3 the simultaneous equation system of dummy variables is compared with the conditional logistic model, which is derived from, and equivalent to, the familiar log-linear model. In the fourth section, both models are applied to a dynamic data set of train and bus usage. Some major conclusions regarding the above are drawn in the final section.