Computation of variance components using the em algorithm

Abstract

In their paper on maximum likelihood will) Incomplete data. Dempster. Laird, and Rubin (1977) noted that both maximum likelihood (ML) and restricted ML (REML) estimators of variance components in the mixed model analysis oi variance can be computed via the LM algorithm. Thi-follows from treating the random effects as missing data and using the incomplete data framework outlined in Dempster, et al. (1977). We elaborate on this idea, introducing a class of generalized ML estimates, indexed by a parameter τ, which contain REML and ordinary ML estimates as special limiting cases. This device enables us to derive a single set of iterative EM equations which yields either ML or REML estimates of the variance components, depending upon the value specified for τ.