Statistical inference on some mixed MANOVA-GMANOVA models with random effects
type: Item
instance of: scholarly article
title: Statistical inference on some mixed MANOVA-GMANOVA models with random effects
zbMATH Open document ID: 0844.62046
author: Takahisa Yokoyama
published in: Hiroshima Mathematical Journal
publication date: 1996-09-01T00:00:00Z
review text: 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 d…
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62J10
zbMATH DE Number: 863643
zbMATH Keywords: multivariate parallel profile model
zbMATH Keywords: multiple-response parallel growth curves
zbMATH Keywords: likelihood ratio
zbMATH Keywords: random-effects covariance structure
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: maximum likelihood estimators
zbMATH Keywords: unknown mean
zbMATH Keywords: single-response case
zbMATH Keywords: covariates
zbMATH Keywords: mixed MANOVA-GMANOVA model
zbMATH Keywords: asymptotic null distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206127624
OpenAlex ID: W1600473370
DOI: 10.32917/HMJ/1206127624
description: scientific article; zbMATH DE number 863643