Showing papers on "Mixed model published in 1978"

Alternative Formulations and Procedures for the Two-Way Mixed Model

Abstract: It is shown that various alternative formulations for the two-way mixed model can be used interchangeably in analyzing data, provided that certain relationships between the formulations with respect to the variance components and the random effiects are recognized and that certain diffierences between the parameterspaces do not come into play. The balanced two-way classification is used to illustrate how Henderson's (1963, 1975) mixed-model procedures for estimating linear functions of fixed and random effiects diffier from procedures that treat all effiects asfixed. Explicit expressions are obtained, for the balanced two-way model, for variance-component estimators yielded by each of three procedures. maximum likelihood (ML), restricted maximum likelihood (REML), and a pseudo-Bayesian modification of-REML. Mean squared error comparisons among these three procedures tend to favor the pseudo-Bayesian procedure.

Analysis Of Repeated Measures Data: A Simulation Study.

Abstract: This paper examines three statistical analysis procedures appropriate to repeated measures data -- classical mixed model analysis of variance, multivariate analysis of repeated measures, and analysis of covariance structures. These procedures differ in their assumptions concerning the covariances between the latent random variables in the model underlying the repeated measures. Simulated data were employed to investigate the effect that violating the assumptions of each model had on the following: Type I error rates; power of the test; degree of bias in the parameter estimates; and the relative efficiency of the estimates. The data indicate that with respect to Type I error rates and estimates of repeated measures effects, violations of assumptions for all three procedures produce similar results. Depending on the size of the repeated measures effects, there are differences between procedures concerning power. The estimates produced by analysis of covariance structures techniques tend to have smaller standard errors.

Analysis of Variance: Selection of a Model and Summary Statistics

Abstract: : The topics of this paper are models for the analysis of variance (ANOVA) (fixed, random, or mixed models) and the subsequent summary statistics (F ratio, quasi-F ratio, and magnitude of treatment effect) that may be computed following the ANOVA. ANOVA is a useful method for assessing the statistical significance of treatment effects. But the significance of an effect is a function of two decisions. The first decision is the selection of a model and an appropriate sampling plan for elements within each of the treatment factors. The second decision is the choice of summary statistics that indicate the extent of significance achieved. In this paper, comparisons will be made between models and between summary statistics. Specific issues will be clarified concerning the interpretation of results when various models and summary statistics are used on the same set of data.