Multidimensional Analysis for the definition of the choice set in Discrete Choice Models

The dissertation is organized as follows: • Chapter 2 focuses the attention on the Random Utility Model and the derivation of the different discrete choice models. We will show the properties and characteristics of the most used methods: Binary Logit, Multinomial Logit, Nested and Cross-Nested Logit. At the end of the chapter we show how all these models are derivable considering a general model, the Generalized Extreme Value Models. • in Chapter 3 we describe what kind of problems can arise when we consider a discrete choice model in which the alternative to be chosen has spatial implication. We introduce some contiguity measurement that will be useful for the proceeding of the dissertation and then we consider some modifications to the classical logit models that allow to introduce spatial component in the analysis (Spatial Multinomial Logit, Mixture of Logit models, etc.). However, these models don’t consider that in some kind of analysis, i.e. destination and residential choice analysis, the number of alternatives is huge and in this case a computational burden for the estimation could be. To solve this problem technique to aggregate alternatives or to sample them and apply the model on a reduced choice-set are introduced, underlining advantages and drawbacks. • Chapter 4 intends to show how multidimensional analysis could be a tool to solve some problems related to the spatial dimension and to the size of the choice set. We introduce briefly Principal Component Analysis and therefore we describe the Constrained Principal Component Analysis (CPCA), showing that considering a particular matrix rather than the scalar product matrix, it’s possible to carry out a new method to aggregate the alternatives. The CPCA will be showed to be useful also to propose an innovative way to conduce a stratified sampling. • in Chapter 5 we shows the usefulness of the two techniques applying them on a data-set relative to the choice of residential location in Zurich area. First of all we build a model on the full choice-set of alternatives and we estimate the parameters; afterwards, we carry out the aggregation and the sampling of the possible chooses, following the approach we introduce previously; furthermore a simple random sampling has been applied and then the model built for the full choice set has been applied for the samples obtained in the different way. At the end of the chapter we compare the results obtained with the different techniques showing the improvements that we can have with the innovative methodology. The analysis has been carried out combining the use of S-Plus, in which we wrote the code to implement the Multidimensional Analysis, and of BIOGEME (Bierlaire 2003), (Bierlaire 2005), a software that allows the estimation of different Generalized Extreme Value models.