Multivariate Generalized Linear Mixed Models for Joint Estimation of Sporting Outcomes

TL;DR

This paper introduces multivariate generalized linear mixed models that account for correlations in team effects across multiple sports outcomes, improving prediction and inference, implemented in the R package mvglmmRank.

Contribution

It develops and applies multivariate GLMMs with correlated random effects for sports outcome prediction, filling a gap in joint modeling approaches.

Findings

Enhanced prediction accuracy demonstrated on college football and basketball data.

Models successfully capture correlations between different game outcomes.

Implementation in R package mvglmmRank facilitates practical application.

Abstract

This paper explores improvements in prediction accuracy and inference capability when allowing for potential correlation in team-level random effects across multiple game-level responses from different assumed distributions. First-order and fully exponential Laplace approximations are used to fit normal-binary and Poisson-binary multivariate generalized linear mixed models with non-nested random effects structures. We have built these models into the R package mvglmmRank, which is used to explore several seasons of American college football and basketball data.