  Copulas, generalized estimating equations, and generalized linear mixed
models promote the analysis of grouped data where non-normal responses are
correlated. Unfortunately, parameter estimation remains challenging in these
three frameworks. Based on prior work of Tonda, we derive a new class of
probability density functions that allow explicit calculation of moments,
marginal and conditional distributions, and the score and observed information
needed in maximum likelihood estimation. Unlike true copulas, our quasi-copula
model only approximately preserves marginal distributions. Simulation studies
with Poisson, negative binomial, Bernoulli, and Gaussian bases demonstrate the
computational and statistical virtues of the quasi-copula model and its
limitations.
