  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.
