Statistical inference on some mixed MANOVA-GMANOVA models with random effects
This paper consists of two parts. Part I is concerned with a multivariate parallel profile model with random effects. In Section 1 a multivariate parallel profile model, which is useful in analyzing multiple-response parallel growth curves of several groups, is described in detail and is reduced to a canonical form. In Section 2, the likelihood ratio (= LR) statistic for a hypothesis concerning the adequacy of a random-effects covariance structure is obtained. However, since the exact LR criterion is complicated and impractical, it is suggested to use a modified LR statistic, which is the LR criterion for a modified hypothesis. An asymptotic expansion of the null distribution of the statistic is derived. The LR criterion for the hypothesis is also discussed. In Section 3 the maximum likelihood estimators (= MLE's) of unknown mean parameters are obtained under the random-effects covariance structure, and one of the MLE's is compared with the MLE in the case when the covariance matrix has no structures. Further, two testing problems are considered. Modified LR statistics and their asymptotic null distributions are obtained. In Section 4 we discuss the single-response case. Part II is concerned with a growth curve model with covariates and random effects. In Section 5, a growth curve model with covariates is outlined and is reduced to a canonical form. The model is a mixed MANOVA-GMANOVA model which has random-effects covariance structures based on a single response variable. In Section 6, test statistics for a general hypothesis concerning the adequacy of a family of random-effects covariance structures are proposed. A modified LR statistic and its asymptotic null distribution are obtained. The LR criterion for the hypothesis is also discussed. In Section 7 the MLE's of unknown mean parameters are obtained under one of these covariance structures, and the efficiency of one of the MLE's is discussed. Finally, in Section 8 the results of Section 6 are exemplified by a data set of repeated measurements.
multiple-response parallel growth curves
scientific article; zbMATH DE number 863643