Showing papers on "Mixed model published in 1973"

A Discussion of the Two-Way Mixed Model

Abstract: In his text on the analysis of variance, Sheffe (1959) presents a detailed development of the mixed model for two factors. The model, as initially described, appears to be quite general and is capable of accomodating a wide variety of experimental situations in which one factor is assumed fixed and the other random. Other authors have proposed different models which appear to differ from Scheff6's model in various ways. These models have been the subject of considerable discussion, with much of the controversy focusing on the expressions for the expected value of the mean square associated with the random factor. The purpose of this paper is to relate some of the existing models to the Scheffe model in an attempt to provide the user with some guidance in the choice of an appropriate model. The question of the correct expressions for the expected mean squares is also resolved. Although primary consideration is given to the relations between contending, infinite population models, one relation to the limiting form of the finite model is also noted. For ease of reference, the models are formally stated in Section 2. These statements also contain the basic relations between the models. These relations are then discussed in Section 3, and in Section 4, the correct expressions for the expected means squares are given.

Asymptotic Properties and Computation of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance

Abstract: : The problem considered is the estimation of the parameters in the mixed model of the analysis of variance, assuming normality of the random effects and errors. Both asymptotic properties of such estimates as the size of the design increases and numerical procedures for their calculation are discussed. Estimation is carried out by the method of maximum likelihood. It is shown that there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal and asymptotically efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix as the size of the design increases. This is accomplished using a Taylor series expansion of the log-likelihood.

A Study of Life-Testing Models and Statistical Analyses for the Logistic Distribution.

Abstract: : Section I summarizes several methods for obtaining various useful types of models, particularly ones with U-shaped hazard functions. These models include mixed models, composite models, components in series, nonhomogeneous Poisson Processes, polynomial models and models obtained by transformations from other well-known models. Some point estimation and hypothesis testing results are given for linear and quadratic hazard function models in Section 2. In Section 3 point and interval estimation procedures based on the maximum likelihood estimators for the location and scale parameters of the logistic distribution are considered. (Author Modified Abstract)

Estimating the Covariance Matrix of the Random Components in the Mixed Model Appropriate to Single Sample Repeated Measures Data

Abstract: A method for estimating the variances and covariances of the random components of the mixed model, appropriate to single sample repeated measures data, is discussed. To illustrate its use, an example is presented which is concerned with the effect of syntactic and semantic violations of linguistic rules on the free recall of verbal materials. The procedures are based on the structural analysis of the covariance matrix of the repeated measures.