Multilevel Factor analysis models for continuous and discrete data

A very general class of multilevel factor analysis and structural equation models is proposed which are derived from considering the concatenation of a series of building blocks that use sets of factor structures defined within the levels of a multilevel model. An MCMC estimation algorithm is proposed for this structure to produce parameter chains for point and interval estimates. We show how traditional models for binary response factor analysis can be extended to fit multiple factors within a multilevel data structure. It is shown how a probit link function has useful interpretations and in particular that this allows the joint modeling of binary, ordered and continuous response variables. The model is applied to the study of country differences in a large scale study of Mathematics achievement in schools.