Marginal Regression Models with Varying Coefficients for Correlated Ordinal Data.
Sonderforschungsbereich 386, Discussion Paper 177
This paper discusses marginal regression models for repeated or clustered ordinal measurements in which the coefficients of explanatory variables are allowed to vary as smooth functions of other covariates. We model the marginal response probabilities and the marginal pairwise association structure by two semiparametric regressions. To estimate the fixed parameters and varying coefficients in both models we derive an algorithm that is based on penalized generalized estimating equations. This allows to estimate the marginal model without specifying the entire distribution of the correlated categorical response variables. Our implementation of the estimation algorithm uses an orthonormal cubic spline basis that separates the estimated varying coefficients into a linear part and a smooth curvature part. By avoiding an additional backfitting step in the optimization procedure we are able to compute a robust approximation for the covariance matrix of the final estimate. We illustrate our method by an application to longitudinal data from a forest damage survey. We show how to model the dependence of damage state of beeches on non-linear trend functions and time-varying effects of age.