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This paper describes an efficient EM algorithm for maximum likelihoodestimation of a system of nonlinear structural equations corresponding to adirected acyclic graph model that can contain an arbitrary number of latentvariables. The endogenous variables in the model must be categorical, while theexogenous variables may be arbitrary. The models discussed in this paper are anextended version of finite mixture models suitable for causal inference. Anapplication to the problem of education transmission is presented as anillustration.

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