Abstract: A joint mean-correlation regression model framework was proposed for a family of generic discrete responses either balanced or unbalanced, and a Cholesky decomposition method was used for statistically meaningful reparameterization of correlation structures. To overcome computational intractability in maximizing the full likelihood function of the model, a computationally efficient Monte Carlo expectation maximization (MCEM) approach was proposed. Theoretical properties were also established for the resulting estimators. Simulation studies and a real data analysis show that the proposed approach yields highly efficient estimators for the parameters.