Standard Errors for EM Estimates in Variance Component Models

A procedure is derived for computing standard errors in random intercept models for estimates obtained from the EM algorithm. We discuss two different approaches: a Gauss-Hermite quadrature for Gaussian random effect models and a nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is proposed which is based on an expansion of the EM estimating equation. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations