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Biometrika 1990 77(2):353-358; doi:10.1093/biomet/77.2.353
© 1990 by Biometrika Trust
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Finding the design matrix for the marginal homogeneity model

STUART R. LIPSITZ, NAN M. LAIRD and DAVID P. HARRINGTON

Department of Biostatistics, Harvard School of Public Health 677 Huntington Avenue, Boston, Massachusetts 02115, U.S.A.

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 KT 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.

Key Words: Contingency table • Linear model • Marginal homogeneity


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