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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.
Notes
1 The 7th home game for team A might be the 8th away game for team B, in which case the model fit for team B is based on 7 home and 8 away games, 15 in total.
2 Of the 329 draws that the model correctly predicted, 110 were no-score draws. Among the 1022 actual draws, 323 were no-score draws.