## A Dynamic Analysis of Activity and Travel Patterns

### Authors

GOULIAS K G, Pennsylvania State University, USA

### Description

Travel behavior research has turned to panel surveys for information on the dynamic properties of human behavior that may be characterized by stages in its evolution. For example, when households change residence they may follow a variety of stages of cog

### Abstract

Travel behavior research has turned to panel surveys for information on the dynamic properties of human behavior that may be characterized by stages in its evolution. For example, when households change residence they may follow a variety of stages of cognitive disengagement from their ÒoldÓ place of residence to a subsequent cognitive engagement with their new place of residence. Similar stages that are not directly observed (and for this called latent) may be the source generating the data we collect on car ownership, mode choice, time use and trip making, and so forth. This nature of dynamic behavior is one of the issues to consider in activity-based travel demand forecasting as we move to a more explicit treatment of time in modeling. In fact, many activity-travel models use the concept of a latent variable to account for observed and unobserved human heterogeneity. The latter may be due to lack of specific questions in the reporting instrument andor from entities that cannot be measured such as prejudice, moral commitments, obligations, affect, propensity to do something, and so forth. Two distinct groups of methods to quantify unobserved heterogeneity have been the structural equations pollen, 1989) and the econometric models (Heckman, 1981). In both groups, however, the heterogeneity description via latent variables has been done using a static continuous latent variable. In contrast, heterogeneity may be better depicted as a latent dynamic variable that for each person in a population evolves k0.m one stage to another. In fact, identifying and describing heterogeneous paths of change using the latent discrete dynamic variable idea may capture heterogeneity in a more holistic and informative way.

The focus of this paper is on the dynamic properties of day-to-day and year-to-year changes in activity participation and travel using data from different years (called waves) of the Puget Sound Transportation Panel (PSTP). This is done in the context of three different but related behavioral aspects that are:

a) Daily activity patterns that are described using cluster group membership. Each person is classified into a cluster based on the frequency of activities and the amount of time the person spends in activities in a day. Then, each cluster is a category of a variable, X. Change from one behavioral cluster to another over time is studied assuming the existence of another variable, Y, that is latent and represents the true unobserved daily schedule of activity and travel.

b) Daily travel patterns that are described also using cluster group membership. Each person is classified into a cluster based on the frequency of trips by mode and the amount of travel time in a day. Then, each cluster is a category of a variable, X. Change from one behavioral cluster to another over time is studied assuming the existence of another variable that is latent and represents the true unobserved trip schedule.

c) Daily travel patterns that are described using a few activity-travel sequence types within a day. The sequence types are defined based on the daily sequence of activity content and complexity of activity-travel patterns used by each person in a day. Similarly to the other two aspects, change from one category (type of sequencing) to another is studied.

For each group of models discussed here the evolution of membership among the categories of each variable, X, over time is assumed to emerge from an unknown underlying stochastic process that is a combination of multiple paths of change. These paths are the result of switching behavior among categories of a latent variable representing different sequential stages in a personÕs unobserved willingness to use a given activity-travel schedule. The existence of many qualitatively different paths of change, which we need to identify to understand and describe behavior, is a component of heterogeneity. The statistical tool used to accomplish identification and measurement of latent paths of change is the Mixed Markov Latent Class (MMLC) model.

MMLC models use the concept of a dynamic discrete latent variable and they are a non-parametric case of the family of models presented and discussed in Heckman, 1981. In MMLC, transitions from one point in time to anolher are investigated assuming and testing for the existence of multiple paths of change. The data are assumed to emerge from different Markov chains operating at the level of latent variables with each chain having its own dynamics. Other methods to do this are provided in the time series literature where the time point is the unit of analysis. However, time series modeling requires many time points to describe the underlying stochastic process generating the data. In the social sciences literature, the closest ÒrelativeÓ to the approach here are the structural equations as defined in Bollen, 1989. The first important distinction between the MMLC and structural equations regards the nature of the latent variable, Y, which is assumed to be continuous in structural equations and categorical in MMLC. The second distinction is the set of strong parametric assumptions needed in structural equations to estimate parameters. No such assumptions are needed in the MMLC models as explained in later sections.

In the next section, the problem addressed and the general MMLC model are defined first. Then a summary of the data used is provided. This is followed by models for activity-travel and their interpretation. The paper concludes with a summary.

#### Publisher

Association for European Transport