Finding the design matrix for the marginal homogeneity model

Abstract

Suppose that a homogeneous group of n subjects is observed on T occasions. Each subject has one of K levels of response at each of the T occasions. The cross-classification of the recorded responses over time forms a K T contingency table. This paper discusses the design matrix for the marginal homogeneity model, which assumes that the first-order marginal probabilities at each time are equal. The marginal homogeneity model is a linear model for the vector of cell probabilities. We obtain the design matrix by linearly transforming the parameter space of the cell probabilities; our method will work for any T and any K .