Multilevel Factor Models for Ordinal Variables

This article tackles several issues involved in specifying, fitting, and interpreting the results of multilevel factor models for ordinal variables. First, the problem of model specification and identification is addressed, outlining parameter interpretation. Special attention is devoted to the consequences on interpretation stemming from the usual choice of not decomposing the specificities into hierarchical components. Then a general strategy of analysis is outlined, highlighting the role of the exploratory steps. The theoretical topics are illustrated through an application to graduates' job satisfaction, where estimation is based on maximum likelihood via an Expectation-Maximization algorithm with adaptive quadrature.