## Probit Sequential Models for Users? Choices

### Authors

F Russo, G ChilĂ , Department of Computer Science, Mathematics, Electronics and Transportation, Mediterranea University of Reggio Calabria, IT

### Description

A probit sequential model is proposed, to simulate the permanence or the transition of the actual system state of a general decision maker, considering decisions taken in the previous period and events that affect user and network characteristics.

### Abstract

In a behavioural approach, demand models generally simulate user?s choices through discrete choice models. The consolidated approach is unable to explicitly simulate the variation in choice probability, due to a variety of events that affect the system characteristics of user and of transportation network. A model able to simulate explicitly choices taken in the present time in relation to choices taken in the previous time is necessary in order to simulate, for example: path choice for high frequency service; evacuation, when a population have to evacuate due to a forthcoming disaster; vehicle ownership, when socio-economic properties of families and technical characteristics of vehicles change in the time.

In this note demand models are classified as:

- not dynamic, if they give the choice probability not considering system evolution;

- dynamic, if they give the choice probability considering system evolution.

Dynamic models are named sequential models if they give the choice probability according to the current and the previous system condition, thus considering system evolution and earlier decisions.

Sequential models result from sequential analysis, which arose as science applied to the observation of social behaviour in psychology. Sequential analysis of sequential recorded data can provided an additional level of information about whatever behaviour in comparison with non-sequential analysis. In the sequential analysis, data are analyzed in respect of transitional probabilities. These probabilities are one kind of conditional probabilities. Conditional probabilities are defined as probabilities with which a particular target event occur, relative to another given event. Transition probabilities are distinguished from other conditional probabilities in that the target and given events occur at different times. Transitional probabilities can be arranged in transition matrix. Each cell of transition matrix indicates the number of times a particular transition occurred.

In this work, the transition matrix represents the choice process of a generic decision maker, related to previous decisions. Each row of the transition matrix indicates the transition probabilities for a set of users which have taken a given choice in the previous period. In the present period, the choice set is defined as maintenance or modification of choice set defined in the previous period. For the first time, a probit sequential model for each row of the transition matrix is proposed, to simulate the permanence or the transition of the actual system state. The probit model allows for any arbitrary variance-covariance structure of the disturbance term, as regards alternatives in present time and/or previous choices in previous time. Also, the model allows to evaluate whether or not specific transition frequencies from an antecedent to a consequent state differ than what one would expect if the two states were independent.

In the literature, some example of sequential models are applied to path choice, to evacuation simulation and to ownership of vehicles. The first two models are characterized by a behavioural approach, but they allow to simulate the user?s choice process considering only two alternatives (binary sequential model). The last model allows to consider a general choice set, but it is characterized by a logit specification, which doesn?t allow to represent any correlation among choice alternatives. We highlight that in the literature there exist other examples of models applied to vehicle ownership simulation, which can be classified as pseudo-dynamics, because they consider the effects of the past choices, but are based on static (not dynamic) structures.

At first, the proposed probit sequential model has been applied to the ownership of vehicles, in order to compare the results obtained with the experimentation of models used in literature.

The model has been specified, calibrated and validated using a database relative to the socio-economic evolution of a sample family and also using two databases relative to the technical-performances characteristics of vehicles.

An analysis of recorded data related to order, significance and stationarity of sequential structure is presented. Several hypothesis related to lag-analysis of recorded data are tested, in order to decide if current decisions are directly influenced by the most recent previous decisions or not.

The results obtained by the experimentation of the model are presented in the paper.

#### Publisher

Association for European Transport