David A. Harville

Bio: David A. Harville is an academic researcher from Iowa State University. The author has contributed to research in topics: Best linear unbiased prediction & Linear model. The author has an hindex of 19, co-authored 30 publications receiving 4457 citations.

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

Abstract: Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.

Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models

Abstract: Best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known. If the true values are replaced by estimated values, the mean squared errors of the estimators of the fixed and random effects increase in size. The magnitude of this increase is investigated, and a general approximation is proposed. The performance of this approximation is investigated in the context of (a) the estimation of the effects of the balanced one-way random model and (b) the estimation of treatment contrasts for balanced incomplete block designs.

Mean Squared Error of Estimation or Prediction under a General Linear Model

Abstract: The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predictor depends on parameters which generally are unknown. Various exact or approximate expressions are given for the mean squared error (MSE) of the predictor obtained by replacing the unknown parameters with estimates. Several estimators of the MSE are investigated.

Unbiasedness of two-stage estimation and prediction procedures for mixed linear models

Abstract: The traditional method for estimating or predicting linear combinations of the fixed effects and realized values of the random effects in mixed linear models is first to estimate the variance components and then to proceed as if the estimated values of the variance components were the true values. This two-stage procedure gives unbiased estimators or predictors of the linear combinations provided the data vector is symmetrically distributed about its expected value and provided the variance component estimators are translation-invariant and are even functions of the data vector. The standard procedures for estimating the variance components yield even, translation-invariant estimators.

Hierarchical Linear Models: Applications and Data Analysis Methods

Abstract: Introduction The Logic of Hierarchical Linear Models Principles of Estimation and Hypothesis Testing for Hierarchical Linear Models An Illustration Applications in Organizational Research Applications in the Study of Individual Change Applications in Meta-Analysis and Other Cases Where Level-1 Variances are Known Three-Level Models Assessing the Adequacy of Hierarchical Models Technical Appendix

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Conducting Meta-Analyses in R with the metafor Package

Abstract: The metafor package provides functions for conducting meta-analyses in R. The package includes functions for fitting the meta-analytic fixed- and random-effects models and allows for the inclusion of moderators variables (study-level covariates) in these models. Meta-regression analyses with continuous and categorical moderators can be conducted in this way. Functions for the Mantel-Haenszel and Peto's one-step method for meta-analyses of 2 x 2 table data are also available. Finally, the package provides various plot functions (for example, for forest, funnel, and radial plots) and functions for assessing the model fit, for obtaining case diagnostics, and for tests of publication bias.