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.

Avoiding Bias Due to Nonrandom Scheduling When Modeling Trends in Home-Field Advantage

“…• Besides the statistical tests reported here, many others were performed during research for this paper. For example, an early draft only considered full season results from the Phase I mixed model, and also explored trends in the estimated home and away mean scores and conditional home and away error variances from a joint model for home and away scores (Broatch & Karl 2017b, Section 2.1). These were abandoned for the sake of providing a tighter narrative; however, these fitted values remain in the full season Phase I results of the supplementary data and may be further explored by the reader.…”