Showing papers on "Random effects model published in 1981"

Estimation in Covariance Components Models

Abstract: Estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes. The estimation of fixed and random effects when the variances and covariances are known is presented in Bayesian terms, Point estimates of the unknown variances and covariances are computed using the EM algorithm for maximum likelihood estimation from incomplete data. The techniques are illustrated with data on law schools, field mice, and professional football teams.

Random Effects Models

Abstract: A factor is called a random effects factor if the levels of the factor represent a larger set of interest. Examples: 1. Medicine: How accurate are labs for testing for a certain disease? Do labs differ in their accuracy? Suppose we have (different) people tested at 3 different labs. Factor = Lab (i = 1, 2, 3) Unit = a person having a medical test Y ij = accuracy rating of the test for person j and lab i n i = number of people tested at Lab i Lab is a fixed effect if we care only about those labs. Lab is a random effect if the 3 labs are a random sample of all such labs. 2. Education: How well do California students learn to read by the end of first grade? Choose 6 schools in California. Then randomly choose n i students in school i to take a reading test. Factor = School (i = 1 to 6) Unit = student (j = 1 to n i) Y ij = reading score for student j in school i. School is a fixed effect if we care only about those 6 schools. School is a random effect if those schools are randomly sampled from a larger set of interest. 3. Psychology: Compare therapists for effectiveness. Factor = therapist Unit = patient Y ij = change in score on depression test after one year of therapy for patient j, therapist i. Therapist is a fixed effect if we are interested in those specific therapists Therapist is a random effect if the therapists are randomly selected from all therapists of interest.

Estimators for the One-Way Random Effects Model with Unequal Error Variances

Abstract: Using the random effects model, yij = μ + α i + ∈ ij , (i = 1, …, k; j = 1, …, ni ), where α i and ∈ ij are normal with means zero and variances σα 2 and σ i 2, this article considers eight methods of estimating σ i 2, σα 2, and thirteen corresponding procedures of estimating μ. Biases and mean squared errors (MSE's) of these procedures are examined for variations in the magnitudes of the unknown parameters, the sample sizes, and the number of groups.

Short-run residential demand for fuels: a disaggregated approach

Abstract: A disaggregated model of residential energy demand is specified and then used to examine the data and econometric techniques available to estimate such a model. Inconsistencies in the currently popular random effects model and weighted least squares generate inconsistent parameter estimates for short-run modeling. Some of the currently available pooled data is of poor quality. The principal data series of concern are the appliance-stock series, but current research is attempting to improve aggregate data. While the disaggregated elasticities reported can only be considered tentative, the approach combined with better data and econometric techniques will produce an important policy tool. The regression results are summarized in two tables in the appendix. 42 references, 5 tables.

Round robin analysis of variance via maximum likelihood

Abstract: We consider a class of linear models called round robin models which deal specifically with data arising in the interaction of a group of individuals in a round robin setting. Such models provide information not only about individual differences but also about the reciprocity behavior of the interaction partners. We provide a convergent algorithm for computing the maximum likelihood estimates of the variances and covariances associated with these models. Also, we discuss interval estimation of the linear effects, including fixed and random effects. We present a detailed data analysis on a set of speech activity data using these designs.

Explicite Formulae of Exact Tests in Mixed Balanced ANOVA-models

Abstract: As an alternative to SATTERTHWAITE's approximative test strongly unbiased tests of BARTLETT-SCHEFFE type are considered to test hypotheses about fixed and random effects in mixed and random ANOVA-models with equal cell frequencies. Explicite formulae are given to test hypotheses in the usual two- and three-way classifications and the four-way cross-classification. These formulae also can be used in the multivariate case.

Interval estimates for variance components

Abstract: The fiducial approach to the two components of variance random effects model developed by Venables and James (1978) is related to the Bayesian approach of Box and Tiao (1973). The operating characteristics, under repeated sampling, of the resulting interval estimators for the “within classes” variance component are investigated, and the behaviour of the two sets of intervals is found to be very similar, the coverage frequency of 95% probability intervals being approximately 91% when the “between classes” variance component is zero but rising rapidly to 95% as the between component increases. The probability intervals are shown to be shorter on average than a comparable confidence interval based upon the within classes sum of squares, and to be robust against nonnormality in the class means.

The power function and an approximation for testing variance components in the presence of interaction in two‐way random effects models

Abstract: In this paper we consider a two-way layout random-effects model with interaction proportional to the product of two random components and derive the distributions of the sums of squares and the F-ratio under the usual normality assumption for the random effects. Approximations to these distributions by finite series Laguerre polynomial expansions are then developed. Some numerical results are given to illustrate the applications of the theory.