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Large crossed data sets, described by generalized linear mixed models, havebecome increasingly common and provide challenges for statistical analysis. Atvery large sizes it becomes desirable to have the computational costs ofestimation, inference and prediction (both space and time) grow at mostlinearly with sample size. Both traditional maximum likelihood estimation andnumerous Markov chain Monte Carlo Bayesian algorithms take superlinear time inorder to obtain good parameter estimates. We propose moment based algorithmsthat, with at most linear cost, estimate variance components, measure theuncertainties of those estimates, and generate shrinkage based predictions formissing observations. When run on simulated normally distributed data, ouralgorithm performs competitively with maximum likelihood methods.

Efficient moment calculations for variance components in large unbalanced crossed random effects models