Regression Analysis of Multivariate Fractional Data

Abstract

The present article discusses alternative regression models and estimation methods for dealing with multivariate fractional response variables. Both conditional mean models, estimable by quasi-maximum likelihood, and fully parametric models (Dirichlet and Dirichlet-multinomial), estimable by maximum likelihood, are considered. A new parameterization is proposed for the parametric models, which accommodates the most common specifications for the conditional mean (e.g., multinomial logit, nested logit, random parameters logit, dogit). The text also discusses at some length the specification analysis of fractional regression models, proposing several tests that can be performed through artificial regressions. Finally, an extensive Monte Carlo study evaluates the finite sample properties of most of the estimators and tests considered.