Lorelogram: A Regression Approach to Exploring Dependence in Longitudinal Categorical Responses

Abstract We propose flexible regression estimators of the marginal pairwise log-odds ratio measure of association for longitudinal categorical responses. The function that we estimate is the log-odds ratio analog of the correlogram; hence we name the function the lorelogram. Measuring the association of categorical responses on the log-odds scale allows ease of interpretation and allows pairwise association to remain unconstrained by the marginal means, a feature not shared by correlations with binary or multinomial responses. Estimation of the function is achieved through the use of standard parametric estimating equations or through an extension of generalized additive models that allows nonparametric estimation of dependence functions for fixed smoothing parameters. We apply the methodology to binary longitudinal data where scientific interest focuses on the dependence structure.