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

TL;DR

This paper introduces a moment-based algorithm for efficiently estimating variance components in large unbalanced crossed random effects models, achieving linear computational costs and competitive accuracy.

Contribution

It presents a novel moment-based approach that reduces computational complexity to linear time, enabling scalable analysis of large generalized linear mixed models.

Findings

Performs competitively with maximum likelihood methods on simulated data.

Achieves linear computational cost for estimation, inference, and prediction.

Provides uncertainty measures and shrinkage predictions efficiently.

Abstract

Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation, inference and prediction (both space and time) grow at most linearly with sample size. Both traditional maximum likelihood estimation and numerous Markov chain Monte Carlo Bayesian algorithms take superlinear time in order to obtain good parameter estimates. We propose moment based algorithms that, with at most linear cost, estimate variance components, measure the uncertainties of those estimates, and generate shrinkage based predictions for missing observations. When run on simulated normally distributed data, our algorithm performs competitively with maximum likelihood methods.