Mixed Models and Shrinkage Estimation for Balanced and Unbalanced Designs

TL;DR

This paper explores the relationship between shrinkage estimation, empirical Bayes, and mixed effects models, applying these concepts to both balanced and unbalanced correlated response designs, including sports outcome prediction.

Contribution

It introduces a mixed model for predicting English Premier League game outcomes that incorporates team effects and compares empirical and Bayesian predictors.

Findings

Empirical best linear unbiased predictors outperform Bayesian predictors in certain scenarios.

The mixed model effectively accounts for team effects in sports outcome prediction.

Comparison shows advantages of different estimation methods in unbalanced designs.

Abstract

The known connection between shrinkage estimation, empirical Bayes, and mixed effects models is explored and applied to balanced and unbalanced designs in which the responses are correlated. As an illustration, a mixed model is proposed for predicting the outcome of English Premier League games that takes into account both home and away team effects. Results based on empirical best linear unbiased predictors obtained from fitting mixed linear models are compared with fully Bayesian predictors that utilize prior information from the previous season.