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On the variability of hybrid discrete choice models

It is well-known that not all the variables affecting decisions in a discrete choice situation are objective characteristics of the alternatives. Some of them are associated with difficult to measure attributes which may be represented as latent variables. Since this type of variables cannot be directly observed by the analyst, they must be estimated through a special model (typically a MIMIC model), but this includes an error term. We have found no discussion about the fact that if one estimates a hybrid discrete choice model (i.e. incorporating latent variables) one should find that the variability of its utility function increases in relation to that of a classic discrete choice model without latent variables. To analyse the effects of this induced variability we conducted a theoretical analysis of the problem and complemented it with misspecification and response analysis tests using artificial data. We found that the extra variability has no major effects over the model estimates except when alternatives are correlated, a far too often occurrence in practice.