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Showing papers on "Random effects model published in 1974"


Journal ArticleDOI
TL;DR: In this paper, two simple estimators are derived for the means of the random effect model by means of predictive sample reuse, which are applied to two sets of data in the literature and compared with several other procedures.
Abstract: SUMMARY Two simple estimators are derived here for the means of the random effect model by means of predictive sample reuse. They are applied to two sets of data in the literature and compared with several other procedures. The mixed model is also discussed.

1,859 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the conventional F-test does not have the expected null distribution, and the expected mean squares are not in general equal under HA, whereas the Satterthwaite test does.
Abstract: SUMMARY In the three stage nested design with random effects, let ?A2 be the variance of factor A (the top stage). It is often desirable to test the hypothesis HA: GA2 = 0. In the unbalanced case, the conventional F-test for HA does not in general have the expected null distribution, and the expected mean squares are not in general equal under HA . Tietjen and Moore [1968] proposed that a Satterthwaite-like procedur-e be used to construct a denominator (and D.F.) which would have, under HA , the same expected mean square as the numerator. It was pointed out by W. H. Kruskal, however, that such a procedure had no justification since the mean squares were not independent and did not have chi-square distributions. This paper is an attempt to revisit the question by investigatiing the properties of this approximation and those of the conventional F-test. It is shown that the conventional F-test does considerably better as an approximation under imbalance than does the Satterthwaite test.

28 citations


Journal ArticleDOI
TL;DR: In this paper, necessary and sufficient conditions for admissibility are given for test procedures based on a preliminary test of significance, which is equivalent to the intuitive and practical condition that acceptance regions of the procedures have convex sections in certain variables, while other variables are fixed.
Abstract: Necessary and sufficient conditions for admissibility are given for test procedures based on a preliminary test of significance. Three types of problems are studied—testing the normal mean, fixed effects models of the analysis of variance and random effects models. Admissibility in this instance is equivalent to the intuitive and practical condition that acceptance regions of the procedures have convex sections in certain variables, while other variables are fixed. It is easy to check when the conditions hold. A discussion of optimality properties of these and other types of pooling procedures is given.

12 citations


Journal ArticleDOI
TL;DR: It is shown here for a wide class of -models that Henderson's Method 2, despite being one of the methods collectively called Generalized method 2, does not suffer from limitation (ii), and is a generalization of limitation (i) that nullifies (ii).
Abstract: Three methods of estimating variance components from unbalanced data are given in Henderson [1953]. Method 2, designed to circumvent biasedness that results from using MIethod 1 on mixed models, is characterized more generally in Searle [1968] as a special way of executing what is described there as a simplified form of a Generalized Method 2. In that description 2 limitations are discussed: (i) It is proven that the simplified form of the Generalized M\l[ethod 2 can be used only when there are no interactions between fixed and random factors. (ii) It is suggested that the Generalized Method 2 is not uniquely specified. There is no doubt about limitation (i): Henderson's Method 2 can be used only when the model has no interactions between fixed and random effects. However, we show here for a wide class of -models that Henderson's Method 2, despite being one of the methods collectively called Generalized Method 2, does not suffer from limitation (ii). Indeed, it is a generalization of limitation (i) that nullifies (ii); i.e., for a wide class of models, Method 2 is well defined. One comment on limitation (i) is appropriate. Models that include any nesting of fixed and random factors within each other are also excluded from Method 2, because such models are tantamount to having interactions between fixed aind random factors.

10 citations


Journal ArticleDOI
TL;DR: In this article, the problem of estimating variance components in the three-stage nested randomeffects model from a Bayesian viewpoint is considered and some Bayes estimators of the variance components are developed using appropriate loss functions and adopting a non-informative reference prior distribution.
Abstract: The problem of estimation of the variance components in the three-stage nested randomeffects model is considered from a Bayesian viewpoint.Under the usual assumptions of normality and independence of random effects some Bayes estimators of the variance components are developed using appropriate loss functions and adopting a non-informative reference prior distribution.

10 citations


Journal ArticleDOI
TL;DR: In this paper, level-α: tests obtainable from the analysis of variance table are given for testing these effects, and tables are provided to illustrate the size function and the power function of the tests.
Abstract: It is known that in the random effect model, exact F-tests are not obtainable from the analysis of variance table for testing the main effects in a three-way layout. Similarly exact F-tests are not obtainable for the main effects and certain interactions in higher-way layouts. In this paper level-α: tests obtainable from the analysis of variance table are given for testing these effects. Tables are provided to illustrate the size function and the power function of the tests.

9 citations


Journal ArticleDOI
Paul I. Feder1
TL;DR: The analysis of variance is a technique for comparing treatment means or for estimating components of variation as mentioned in this paper, which can be classified into two types: fixed effects analysis of the variance and random effects analysis.
Abstract: The analysis of variance is a technique for comparing treatment means or for estimating components of variation. The former is called fixed effects analysis of variance and the latter is called random effects analysis of variance. Many nonstatisticians ..

4 citations


Journal ArticleDOI
TL;DR: In this paper, the standard one-way analysis of variance model with random effects (variance components model) is considered and the customary assumptions of zero means, zero correlations, and equal variances are made for the random terms of this balanced model.
Abstract: Consider the standard one-way analysis of variance model with random effects (variance components model). The customary assumptions of zero means, zero correlations, and equal variances are made for the random terms of this balanced model. The customary normality assumptions are also made when other than point estimates are desired. This standard model is generalized, in several ways, by addition of one or two types of “error” terms. The extended models are applicable to much more general situations than the standard model. However, exact results are developed for investigating the mean and both variance components (of the standard model) and for investigating subsets of these parameters. The generality level for an extended model depends on which parameters are investigated. Customary procedures for the standard model remain usable for some investigations and extensions, but more general models are applicable when use of customary results is not required. A method for rejection of outliers by use of the standard model is described and shown to be applicable for some of the extensions.

Journal ArticleDOI
TL;DR: In this paper, Barakowski et al. proposed a method to generate nested randomeffects by considering all possible combinations of levels for a given sample size and fixed number of random factors.
Abstract: BARCIKOWSKI (1972, 1973) described procedures for selecting optimum sample size and number of levels in a one-way randomeffects analysis of variance. In this paper the latter procedures were expanded upon to include nested random-effects designs. That is, given the number of random factors, level of significance (oJ, total sample size (N), estimates of the population effects (6o’s), and a decision on the effects one desires to detect (B’s), power values can be calculated for each factor in a nested random-effects design (Scheffe, 1959, pp. 248-255). The computer program described herein generates nested randomeffects designs by considering all possible (Options 1 and 2) or specific (Options 3-6) combinations of levels for a given sample size and fixed number of random factors (maximum five factors). Power values for each of the factors in these designs are then calculated using additional given information, i.e., 90’s, ~’s, and a. A researcher may then select the design which offers the highest probability of detecting significant differences, that is, the nested random-effects design which has optimum sample size and number of levels.