A Parametric Model for Cluster Correlated Categorical Data

A fully parametric copula model for symmetric dependent clustered categorical data is discussed. The model accommodates any marginal regression models of interest and admits a broad range of within cluster association. The form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes. The model contains an association parameter which is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence. Two examples are given to illustrate the methods.