Author : James Robert Schott
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.:/5 (87 download)
Book Synopsis The Multivariate One-way Classification Model with Random Effects by : James Robert Schott
Download or read book The Multivariate One-way Classification Model with Random Effects written by James Robert Schott and published by . This book was released on 1981 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: A well-known model in univariate statistical analysis is the one-way random effects model. In this paper we investigate the multivariate generalization of this model, that is, the multivariate one-way random effects model. Two specific situations, regarding the structure of the variance-covariance matrix of the random error vectors, are considered. In the first and most general case, it is only assumed that this variance-covariance matrix is symmetric and positive definite. In the second case, it is assumed, in addition, that the variance-covariance matrix is a scalar multiple of the identity matrix. Maximum likelihood estimates are obtained and the likelihood ratio test for a hypothesis test on the rank of the variance-covariance matrix of the random effect vectors is derived. Properties of the likelihood ratio test are investigated for the general case, while for the second case an alternative test is developed and its properties are investigated. In each case a sequential procedure for determining the rank of the variance-covariance matrix of the random effect vectors is presented.