Multivariate Generalized Linear Mixed Models for Joint Estimation of Sporting Outcomes

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.