This article presents a random-effects model for multivariate and grou
ped univariate ordered categorical data. The assumed family of distrib
utions for the random effects adopts a wide variety of forms and shape
s. The model's likelihood has a closed expression and can be computed
without recourse to numerical integration or Gaussian quadrature. A bi
variate and a grouped univariate example are used to illustrate the pr
oposed model.