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 non linear structural equations corresponding to a directed acyclic graph model; this can contain an arbitrary number of latent variables, as long as the model is identifiable. The only limitation is that the endogenous variables in the model must be discrete, with qualitative or ordered categories, while the exogenous variables may be arbitrary. The models described in this paper are defined by the list of structural equations and, for each equation, the type of link function and the linear model to be used. These models are an extended version of finite mixture models which may be suitable for causal inference when several sources of latent heterogeneity may be present. An application to the problem of education transmission, where one would like to control for the ability of the parents and that of the child, is presented as an illustration.