Implementing factor models for unobserved heterogeneity in Stata

Abstract

We introduce a new command, heterofactor, for the maximum likelihood estimation of models with unobserved heterogeneity, including a Roy model. heterofactor fits models with up to four latent factors and allows the unobserved heterogeneity to follow general distributions. Our command differs from Stata’s sem command in that it does not rely on the linearity of the structural equations and distributional assumptions for identification of the unobserved heterogeneity. It uses the estimated distributions to numerically integrate over the unobserved factors in the outcome equations by using a mixture of normals in a Gauss-Hermite quadrature. heterofactor delivers consistent estimates, including the unobserved factor loadings, in a variety of model structures.