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Analytical structure of discrete choice models
Abstract In this paper a new conceptual framework of the external interventions of the active socio-economic and territorial environment in the content of the choice between the set of competitive alternatives is considered. This conceptual framework generates a new analytical procedure for the derivation of all possible mode-specific choice models, starting from the preset initial “building block” models. The analytical basis for this procedure is the description of all mappings transforming the multidimensional unit simplex of choice probabilities into other unit simplices. These mappings represent the totality of the redistributions of adopters between competitive alternatives caused by the interventions of an active environment. It is shown, for example, that the choice probabilities for the standard dogit model can be generated by the multiplication of the specific Markovian matrix by the vector of choice probabilities of the logit model. The components of this Markovian matrix are the transition probabilities of the transfer of adopters between alternatives caused by superimposition of the action of environment. Analogously, each nested model corresponds to the product of several Markovian matrices. Starting from the standard logit model, the following mappings were used for the derivation of an array of possible choice models: ratio-linear, linear, log-linear, ratio-polynomial and polynomial mappings. The result was generation of the choice models by McFadden, Gaudry, Gaudry and Dagenais, Borgers and Timmermans and Fotheringham, which are already known from the literature, together with several new choice models.
Analytical structure of discrete choice models
Abstract In this paper a new conceptual framework of the external interventions of the active socio-economic and territorial environment in the content of the choice between the set of competitive alternatives is considered. This conceptual framework generates a new analytical procedure for the derivation of all possible mode-specific choice models, starting from the preset initial “building block” models. The analytical basis for this procedure is the description of all mappings transforming the multidimensional unit simplex of choice probabilities into other unit simplices. These mappings represent the totality of the redistributions of adopters between competitive alternatives caused by the interventions of an active environment. It is shown, for example, that the choice probabilities for the standard dogit model can be generated by the multiplication of the specific Markovian matrix by the vector of choice probabilities of the logit model. The components of this Markovian matrix are the transition probabilities of the transfer of adopters between alternatives caused by superimposition of the action of environment. Analogously, each nested model corresponds to the product of several Markovian matrices. Starting from the standard logit model, the following mappings were used for the derivation of an array of possible choice models: ratio-linear, linear, log-linear, ratio-polynomial and polynomial mappings. The result was generation of the choice models by McFadden, Gaudry, Gaudry and Dagenais, Borgers and Timmermans and Fotheringham, which are already known from the literature, together with several new choice models.
Analytical structure of discrete choice models
Sonis, Michael (author)
1992
Article (Journal)
English
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