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

TL;DR

This paper introduces an efficient EM algorithm for estimating complex directed acyclic graph models with latent variables, extending finite mixture models for causal inference, demonstrated through an education transmission case study.

Contribution

It presents a novel EM algorithm for maximum likelihood estimation in DAG models with latent variables, applicable to categorical endogenous variables and arbitrary exogenous variables.

Findings

Efficient EM algorithm for complex DAG models with latent variables

Extension of finite mixture models for causal inference

Application to education transmission demonstrates practical utility

Abstract

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.