Transformation-based flexible error structures for choice modeling

In this paper, we propose a reverse Yeo-Johnson (YJ) transformation to accommodate flexible skewed and fat-tailed specifications of stochastic terms in multivariate choice models. Essentially, we specify a YJ transformation of the univariate error terms to a univariate symmetric distribution, and then tie the resulting transformed univariate symmetric terms into a convenient symmetric multivariate distribution. In this paper, we use a normal distribution for the transformed univariate symmetric terms and bring these together using a multivariate normal distribution. In this way, the original non-normal error terms become reverse YJ-transformed. The use of such a flexible parametric distribution lends additional robustness to the maximum likelihood (ML) estimator. The proposed approach can be applied to a number of different univariate and multivariate mixed modeling choice structures. In a demonstration application, in the current paper, the proposed model is applied to investigate the effect of urban living on walking frequency, considering the choice of urban living as being endogenous to walking frequency.