Let y = X[beta] + Z[alpha] + [epsilon] be a mixed linear model, where [beta] is a vector of fixed effects, [alpha] is a vector of random effects, and [epsilon] is a vector of errors. Kackar and Harville (1984) showed that the best linear unbiased estimator (BLUE) of [beta] and the best linear...

We show the best linear unbiased predictor (BLUP) can be derived as the best predictor (under normality) based on all error contrasts (i.e., transformation of data with mean 0). The result reveals an interesting connection between BLUP and REML--restricted or residual maximum likelihood--estimates.

Mixed effects models are often used in situations where responses are clustered. In this paper, we show that in the case of generalized linear mixed models where the cluster sizes are assumed to be independent random variables, whose joint distribution is unknown but does not depend on the...

Suppose that Z1, ... , ZN are iid according to a distribution F that is symmetric about [zeta]. Three widely used tests of H0: [zeta] = 0 against H1: [zeta] 0 are the t-, Wilcoxon and sign tests. Tests that reject when at least one of the above three tests exceeds the standard normal critical...

A nonlinear Gauss-Seidel type algorithm is proposed for computing the maximum posterior estimates of the random effects in a generalized linear mixed model. We show that the algorithm converges in virtually all typical situations of generalized linear mixed models. A numerical example shows the...