Estimating independent and simultaneous trip frequency models for all travel purposes with combined Logit/Poisson.

This paper presents an attempt to use behavioural assumptions from discrete choice models as a basis for specification of a Poisson model for count data. It consists of a theoretical part dealing with the basic assumptions. The work reported here is part of the initial testing for model specification and estimation for a new nationwide model for short trips (less than 100 kilometres one way) which also will include mode and destination choice. The approach developed in the paper was used to estimate 'trip frequency' models on a sub-sample from a national travel survey. Contrary to what is usually the case in travel demand modelling, the unit of counts is neither trips nor tours, but the number of places visited (excluding the respondent's own home) during a day. The translation of visits into tours with one or more destinations then becomes a necessary part of a complete model system, but this issue is dealt with in a separate paper. Models for 5 travel purposes are estimated. For each model specifications with 'straight' Poisson, Logit/Poisson and Gumbel/Poisson are compared both with respect to statistical fit and predictive performance. For 3 out of 5 purposes the conclusion is that both the Gumbel/Poisson and the Logit/Poisson can be accepted as the models that have generated the observations. Overall both the Gumbel/Poisson and the Logit/Poisson perform considerably better than a standard Poisson model, while the differences between the former two are marginal. Both a priori considerations and the results from independent estimation suggest that some correlation exists for the error terms between the number of visits with different purposes. This shows up when the correlation matrix for standardised residuals is calculated for the 5 purposes and indicates that independent estimation of models for different purposes might introduce bias in the separate models. To overcome the correlation problem, two methods, that do not exhaust the possibilities, are described. For the covering abstract see ITRD E126595.