Fitting directed acyclic graphs with latent nodes as finite mixtures models, with application to education transmission

This paper describes an efficient EM algorithm for maximum likelihood estimation of a system of nonlinear structural equations corresponding to a directed acyclic graph model that can contain an arbitrary number of latent variables. The endogenous variables in the model must be categorical, while the exogenous variables may be arbitrary. The models discussed in this paper are an extended version of finite mixture models suitable for causal inference. An application to the problem of education transmission is presented as an illustration.