A Monte-Carlo algorithm for maximum likelihood estimation of variance components

A new algorithm for finding maximum likelihood (ML) solutions to variance components is introduced. This algorithm first treats random effects as fixed, then expresses the pseudo-fixed effects as linear transformations of a set of standard normal deviates which eventually are integrated out numerically through Monte-Carlo simulation. An iterative algorithm is employed to estimate the standard deviation (rather than the variance) of the random effects. This method is conceptually simple and easy to program because repeated updating and inverting the variance-covariance matrix of data is not required. It is potentially useful for handling large data sets and data that are not normally distributed.