Showing papers on "Random effects model published in 1982"

Random-effects models for longitudinal data

Abstract: Models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit. Multivariate models with general covariance structure are often difficult to apply to highly unbalanced data, whereas two-stage random-effects models can be used easily. In two-stage models, the probability distributions for the response vectors of different individuals belong to a single family, but some random-effects parameters vary across individuals, with a distribution specified at the second stage. A general family of models is discussed, which includes both growth models and repeated-measures models as special cases. A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed. Two examples are taken from a current epidemiological study of the health effects of air pollution.

Analysis of covariance in the mixed model: higher-level, nonhomogeneous, and random regressions.

Abstract: The model generally considered in analysis of covariance has all levels of classification factors and interactions fixed, and also covariate regression coefficients fixed. Mixed models are more appropriate in most applications. A summary of estimation and hypothesis testing for analysis of covariance in the mixed model, including the case of random regression coefficients, is presented. Higher-level covariate regressions (i.e., regressions in which, for all levels of a factor or interaction, all observations on the same level have a common covariate value) are discussed. Nonestimability problems that result from defining such covariates at the levels of fixed effects are illustrated. The case of nonhomogeneous covariate regressions in the mixed model is considered in the context of interpreting predicted future differences among levels of a given factor or interaction. Nonhomogeneous regressions complicate interpretations only when they are associated with the contrast(s) of interest among fixed effects in the model. The question of whether the regressions are homogeneous is itself often of substantive interest. Different random regression coefficients associated with the levels of a random effect are also examined.

Computation of variance components using the em algorithm

Abstract: In their paper on maximum likelihood will) Incomplete data. Dempster. Laird, and Rubin (1977) noted that both maximum likelihood (ML) and restricted ML (REML) estimators of variance components in the mixed model analysis oi variance can be computed via the LM algorithm. Thi-follows from treating the random effects as missing data and using the incomplete data framework outlined in Dempster, et al. (1977). We elaborate on this idea, introducing a class of generalized ML estimates, indexed by a parameter τ, which contain REML and ordinary ML estimates as special limiting cases. This device enables us to derive a single set of iterative EM equations which yields either ML or REML estimates of the variance components, depending upon the value specified for τ.

On the Optimality of F-test on Variance Components in Mixed Linear Models

Abstract: The analysis-of-variance tests for hypotheses on random effects in regular linear models are considered. Conditions are given for these tests to be uniformly most powerful unbiased or uniformly most powerful invariant unbiased. An example shows that the difference between these conditions can be serious.

Estimating the parameters of mixed linear models with modal estimators

Abstract: This paper presents a procedure to estimate the variance components and fixed effects of mixed linear models. The mode of the joint posterior distribution of all the parameters is obtained by an iterative technique. The proposed method is illustrated with one-way and two-fold nested random models. Two numerical examples demonstrate the iterative solution.

Use of prior information for estimating the variance components

Abstract: The MINQUE and its modifications are considered for estimating the variances of the balanced one-way random effects model. The effects of the a priori values on the estimators of the variances are examined in detail. The Mean Square Errors of the estimators are compared for variations in the prior values of the unknown variances.