Homogeneous matrix equations and multivariate linear models

AbstractThe growth curve model (Potthoff and Roy, 1964) and an extension (von Rosen, 1989) are considered. The mean structures for the models are given by ABC and ∑i AiBiCi, respectively, where the A and C matrices are known and the B matrices unknown. The purpose is to discuss homogeneous matrix equations DBE=0, DiBEi =0, i = 1,2,…, s and D1B1E1+D2B2E2=0 regarded as restrictions on the parameter space 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 to obtain interpretable maximum likelihood estimators