On estimation and testing arising from order restricted balanced mixed model

• Published in: Journal of statistical planning and inference Vol. 77; no. 2; pp. 281 - 292
• Main Authors: Pan, Guohua, Khattree, Ravindra
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.03.1999; New York,NY Elsevier Science; Amsterdam
• Subjects: Compound symmetry; Exact sciences and technology; Experimental design; Intraclass correlation structure; Likelihood ratio test; Mathematics; Maximum likelihood estimation; Mixed effects model; Probability and statistics; Randomized complete block design; Sciences and techniques of general use; Statistics; Maximum likelihood estimation; Randomized complete block design; Intraclass correlation structure; Mixed effects model; Compound symmetry; Likelihood ratio test; Statistical method; Prior information; Tree(graph); Error estimation; Block design; Randomized design; Experimental design; Maximum likelihood; Variance analysis
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(98)00191-8

The randomized complete block design is one of the most widely used experimental designs to systematically control the variability arising from known nuisance sources. The balanced mixed effects model is usually appropriate for such an experiment when the blocks used in the experiment are randomly chosen. In applications with k increasing or decreasing treatment levels, there is sometimes prior knowledge about the ordering of the treatment effects. The most commonly seen orderings include simple ordering, simple tree ordering and umbrella orderings with known or unknown peaks. A natural question is how to incorporate the prior ordering information in estimating the parameters in a balanced mixed effects model so that the estimated treatment effects are consistent with the prior information and the estimated variances of the block effects and experiment errors are nonnegative. In this paper we derive the maximum likelihood estimators of the parameters in a balanced mixed model subject to any partial ordering of the treatment effects, which includes the usual maximum likelihood estimators as a special case. An example is provided to illustrate the results.