Showing papers on "Mixed model published in 1994"
TL;DR: This article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by Laird and Ware (1982, Biometrics 38, 963-974).
Abstract: This article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by Laird and Ware (1982, Biometrics 38, 963-974). Our discussion of the large-sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by Self and Liang (1987, Journal of the American Statistical Association 82, 605-610).
972 citations
TL;DR: An efficient and straightforward procedure is described for specifying and estimating parameters of general mixed models which contain both hierarchical and crossed random factors.
Abstract: An efficient and straightforward procedure is described for specifying and estimating parameters of general mixed models which contain both hierarchical and crossed random factors. This is done using a model formulated for purely hierarchically structured data and generalizes the results of Raudenbush (1993) . The exposition is for the continuous response linear model with natural extensions to generalized linear, nonlinear, and multivariate models.
235 citations
TL;DR: Several statistical guidelines that should be followed are suggested, including the inclusion of explicit consideration of effects as fixed or random and clear descriptions of F tests of interest would provide the reader with confidence that the author has performed the analysis correctly.
Abstract: Analysis of variance is one of the most commonly used statistical techniques among ecologists and evolutionary biologists. Because many ecological experiments involve random as well as fixed effects, the most appropriate analysis of variance model to use is often the mixed model. Consideration of effects in an analysis of variance as fixed or random is critical if correct tests are to be made and if correct inferences are to be drawn from these tests. A literature review was conducted to determine whether authors are generally aware of the differences between fixed and random effects and whether they are performing analyses consistent with their consideration. All articles (excluding Notes and Comments) in Ecology and Evolution for the years 1990 and 1991 were reviewed. In general, authors that stated that their model contained both fixed and random effects correctly analyzed it as a mixed model. There were two cases, however, where authors attempted to define fixed effects as random in order to justify broader generalizations about the effects. Most commonly (63% of articles using two—way or greater ANOVA), authors neglected to mention whether they were dealing with a completely fixed, random, or mixed model. In such instances, it was not clear if the author was aware of the distinction between fixed and random effects, and it was often difficult to ascertain from the article whether their analysis was consistent with their experimental methods. These findings suggest several statistical guidelines that should be followed. In particular, the inclusion of explicit consideration of effects as fixed or random and clear descriptions of F tests of interest would provide the reader with confidence that the author has performed the analysis correctly. In addition, such an explicit statement would clarify the limits of the inferences about significant effects.
234 citations
TL;DR: The conclusions are: 1) the Gibbs sampler converged to the true posterior distributions, as suggested by CASE I; 2) it provides a richer description of uncertainty about genetic
Abstract: Summary - The Gibbs sampling is a Monte-Carlo procedure for generating random samples from joint distributions through sampling from and updating conditional distributions. Inferences about unknown parameters are made by: 1) computing directly summary statistics from the samples; or 2) estimating the marginal density of an unknown, and then obtaining summary statistics from the density. All conditional distributions needed to implement the Gibbs sampling in a univariate Gaussian mixed linear model are presented in scalar algebra, so no matrix inversion is needed in the computations. For location parameters, all conditional distributions are univariate normal, whereas those for variance components are scaled inverted chi-squares. The procedure was applied to solve a Gaussian animal model for litter size in the Gamito strain of Iberian pigs. Data were 1 213 records from 426 dams. The model had farrowing season (72 levels) and parity (4) as fixed effects; breeding values (597), permanent environmental effects (426) and residuals were random. In CASE I, variances were assumed known, with REML (restricted maximum likelihood) estimates used as true parameter values. Here, means and variances of the posterior distributions of all effects were obtained, by inversion, from the mixed model equations. These exact solutions were used to check the Monte-Carlo estimates given by Gibbs, using 120 000 samples. Linear regression slopes of true posterior means on Gibbs means were almost exactly 1 for fixed, additive genetic and permanent environmental effects. Regression slopes of true posterior variances on Gibbs variances were 1.00, 1.01 and 0.96, respectively. In CASE II, variances were treated as unknown, with a flat prior assigned to these. Posterior densities of selected location parameters, variance components, heritability and repeatability were estimated. Marginal posterior distributions of dispersion parameters were skewed, save the residual variance; the means, modes and medians of these distributions differed from the REML estimates, as expected from theory. The conclusions are: 1) the Gibbs sampler converged to the true posterior distributions, as suggested by CASE I; 2) it provides a richer description of uncertainty about genetic
227 citations
TL;DR: This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models that is closest to the profiles for the usual mixed model with exact calculations.
Abstract: This paper presents a mixed model of inheritance with a finite number of polygenic loci. This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, likelihood profiles were obtained for the finite polygenic mixed model, the usual mixed model, with exact and approximate calculations, and for a class D regressive model. The profiles for the finite polygenic mixed model were closest to the profiles for the usual mixed model with exact calculations.
68 citations
TL;DR: In this article, subject-specific and population-averaged continuation ratio logit models for multivariate discrete time survival data are presented for a psychological experiment using a quadratic polynomial relationship across time that depends on a time independent condition.
Abstract: SUMMARY Subject-specific and population-averaged continuation ratio logit models are presented for multivariate discrete time survival data. The models characterize data from a psychological experiment by using a quadratic polynomial relationship across time that depends on a time-independent condition. A multivariate normal random effects distribution is imposed on intercept, linear and quadratic terms in the subject-specific model, which is fitted by using a combination of Gibbs sampling and buffered stochastic substitution. Variance components that tend towards 0 are addressed in this context. In addition, generalized estimating equations estimates of the parameters in the population-averaged model are compared with analogous estimates for the mixed effects model.
31 citations
TL;DR: In this article, the performance of the variance estimators is compared by simulating their mean squared errors and biases using some one-way models with unbalanced data, and specific recommendations are made on the choice of the nonnegative estimator to be used in practical applications.
Abstract: Mixed models involving two variance components are considered when the data are unbalanced, one variance component corresponding to a random effect and a second variance component corresponding to experimental error. For estimating the random-effect variance component, several nonnegative estimators are derived. The estimators have explicit expressions and are easily computable. The performances of the various estimators are studied by simulating their mean squared errors and biases using some one-way models with unbalanced data, and specific recommendations are made on the choice of the nonnegative estimator to be used in practical applications. Some generalizations are obtained for estimating a randomeffect variance component in a more general model with unbalanced data. The analysis of variance (ANOVA) estimator and the proposed estimators are computed using real data for two examples. The ANOVA estimator has a value that is substantially different from the other estimators in the two examples. The sim...
19 citations
01 Jan 1994
TL;DR: In this article, a general multivariate mixed effect linear model is introduced and a procedure for testing certain class of hypotheses concerning the random effect structure is developed, based on a statistic in a readily computable form, facilitating the use at model building stage.
Abstract: A general multivariate mixed effect linear model is introduced Special cases of the model include the multivariate nested error covariance component regression and the random coefficient repeated measure model Discussion is given on modeling the random effect structure and its effect on statistical inference A procedure for testing certain class of hypotheses concerning the random effect structure is developed The procedure is based on a statistic in a readily computable form, facilitating the use at the model building stage 1 The Model This paper is concerned with introducing a general multivariate mixed effect model, and with developing a procedure for testing hypotheses concerning the random effect structure in such a model For simplicity we concentrate here on mixed models with the one-way random effect structure, ie, with the random effect (other than the error term) involving one unknown covariance matrix To introduce our general model, first consider the most widely used univariate mixed effect model with the one-way classification random effect or with the nested error structure The response yij and the k ? 1 explanatory variable Xij for the j-th individual in the z-th group are assumed to satisfy
13 citations
TL;DR: Equ equations to predict the power of detection of a QTL are described, based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed.
Abstract: Analysis of variance can be used to detect the linkage of segregating quantitative trait loci (QTLs) to molecular markers in outbred populations. Using independent full-sib families and assuming linkage equilibrium, equations to predict the power of detection of a QTL are described. These equations are based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed. A simple prediction of power from the mean squares is used that assumes a random model so that in the mixed-model situation this is an approximation. Simulation is used to illustrate the failure of the random model to predict mean squares and, hence, the power. The mixed model is shown to provide accurate prediction of the mean squares and, using the approximation, of power.
11 citations
24 Apr 1994
TL;DR: The purpose of this presentation is to present an overview of the methodology for generalized mixed linear models, a general framework for generalized linear models with random effects, which has been developed recently.
Abstract: Generalized linear models provide a methodology for doing regression and ANOV A-type analysis with data whose errors are not necessarily normally-distributed. Common applications in agriculture include categorical data, survival analysis, bioassay, etc. Most of the literature and most of the available computing software for generalized linear models applies to cases in which all model effects are fixed. However, many agricultural research applications lead to mixed or random effects models: split-plot experiments, animaland plant-breeding studies, multi-location studies, etc. Recently, through a variety of efforts in a number of contexts, a general framework for generalized linear models with random effects, the "generalized linear mixed model," has been developed. The purpose of this presentation is to present an overview of the methodology for generalized mixed linear models. Relevant background, estimating equations, and general approaches to interval estimation and hypothesis testing will be presented. Methods will be illustrated via a small data set involving binary data.
8 citations
TL;DR: In this article, a simple procedure is presented to estimate skewness and kurtosis of the distributions of the random effects of the model, for the model II of a one-way classification.
Abstract: Generalising the ANOVA method of estimating variance components in mixed linear models a simple procedure is presented to estimate skewness and kurtosis of the distributions of the random effects of the model. For the model II of a one-way classification this procedure is demonstrated explicitly.
TL;DR: The potential of mixed models in finite element analysis is critically reviewed to serve as an aid for researchers in this article, together with a comparison with displacement and equilibrium models and the variational principles adopted.
Journal Article•
TL;DR: In this article, two usual procedures to fit multivariate repeated measures design, the multivariate mixed model approach (MMM) and doubly multivariate model approach, as a generalization of techniques used in univariate design are reviewed.
Abstract: Analytical procedures to fitting multivariate repeated measures designs. In this work we review two usual procedures to fit multivariate repeated measures design, the multivariate mixed model approach (MMM) and doubly multivariate model approach (DMM), as a generalization of techniques used in univariate design. We offer a detailed comment of statistical packages using this design (SPSS and BMDP) and we review the analytical procedures of the two methods. We conclude that SPSS provides very detailed results and different sphericity multisampling criteria. Users of BMDP must be then extremely careful interpreting the results of statistical analysis of multivariate repeated measures designs.
TL;DR: In this paper, the authors give likelihood ratio tests for testing some special structures on the dispersion matrix, which is a special model associated with the random effects of which the conventional model is not justified in practice.
Abstract: Exact and approximate methods are available in the literature to compare the fixed effect levels in an unbalanced two-way mixed model under the conventional distributional assumptions for random effects. However, as suggested by SHEFFE (1959) the conventional assumptions may not be justified in practice. Recently, KHATRI and PATEL (1992) have studied a model with an unstructured dispersion matrix associated with the random effects of which the conventional model is a special model. In this note we give likelihood ratio tests for testing some special structures on the dispersion matrix.
TL;DR: In this article, it is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value.
Abstract: The traditional method for estimating the linear function of fixed parameters in mixed linear model is a two-stage procedure. In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance components to estimating the linear function of fixed parameters according to generalized least squares method.
In this paper the general mixed linear model is considered in which a matrix related to fixed parameters and or/a dispersion matrix of observation vector may be deficient in rank. It is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value and the estimators of variance components from first stage are translation-invariant and are even functions of the observation vector.
01 Jan 1994
TL;DR: In this article, a usual block design with treatment effects fixed and block effects random is considered, and a comparison of experiments is based on the asymptotic covariance matrix of a robust estimator both for shift and scale parameters given by Fisher consistent and Frechet differentiable functional.
Abstract: In the paper a usual block design with treatment effects fixed and block effects random is considered. Comparison of experiments is based on the asymptotic covariance matrix of a robust estimator both for shift and scale parameters given by Fisher consistent and Frechet differentiable functional (recently proposed by Bednarski and Zontek, 1994). In the class of equiblock-sized designs A- and D-optimality are discussed.