Fitting directed graphical Gaussian models with one hidden variable

We discuss directed acyclic graph (DAG) models to represent the independence structure of linear Gaussian systems with continuous variables: such models can be interpreted as a set of recursive univariate regressions. Then we consider Gaussian models in which one of the variables is not observed and we show how the incomplete log-likelihood of the observed data can be maximized using the EM. As the EM algorithm does not provide the matrix of the second derivatives we show how to get an explicit formula for the observed information matrix. We illustrate the utility of the models with two examples.