HOMOGENEOUS MATRIX EQUATIONS AND MULTIVARIATE LINEAR-MODELS

The growth curve model (Potthoff and Roy, 1964) and an extension (von Rosen, 1989) are considered. The mean structures for the models are gi ven by ABC and SIGMA(i) A(i)B(i)C(i), respectively, where the A and C matrices are known and the B matrices unknown. The purpose is to discu ss homogeneous matrix equations DBE = 0, D(i)BE(i) = 0, i = 1, 2, ..., s and D1B1E1 + D2B2E2 = 0 regarded as restrictions on the parameter s pace in statistical models. Among other results, we will see what kind of restrictions have to be imposed on the D and E matrices in order t o obtain interpretable maximum likelihood estimators.