  This paper proposes a multiple-membership generalized linear mixed model for
ranking college football teams using only their win/loss records. The model
results in an intractable, high-dimensional integral due to the random effects
structure and nonlinear link function. We use recent data sets to explore the
effect of the choice of integral approximation and other modeling assumptions
on the rankings. Varying the modeling assumptions sometimes leads to changes in
the team rankings that could affect bowl assignments.
