Ibirénoyé H. R. Sodjahin

Spare time activities

The EM algorithm for estimating parameters of normal mixed effects models

I lay out here the steps I went through when trying to understand the mechanic of the EM algorithm. I’m interested in situations where closed-form solution exists for the parameters of interest. Situations involving simulation of the conditional distribution are beyond the scope of this paper. I start by deriving the explicit solutions for estimating linear mixed effects models by maximum likelihood through the EM algorithm, and provide formula for computing the information matrix (and thus, the standard errors) of obtained estimates. Finally, numerical examples using simulated data are also provided and estimated in each case.