Some developments on the cross-nested logit model

In this paper the cross-nested logit (CNL) model is reformulated as a generalization of the two levels hierarchical logit model. The proposed analytical formulation is derived from the GEV model. Moreover, a general expression of the covariance matrix of the CNL model presenting interesting empirical evidence is proposed. It will be also demonstrated that it is generally possible to specify the model so that this general expression reproduces any given hypothetical homoscedastic covariance matrix. Hence, from the latter, not just probit or mixed multinomial logit choice probabilities (through some simulation methods, e.g. Montecarlo) but also CNL choice probabilities (with a closed analytical form) could be derived. Moreover, comparisons among CNL and probit choice probabilities are presented and the resulting similarity indicates that the CNL is a very interesting closed form alternative to the more flexible non-closed form models.