Showing papers on "Mixed model published in 1984"

Random-effects models for serial observations with binary response

Abstract: This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore (1979, Biometrics 35, 795-804), using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.

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.

A mixed-model procedure for analyzing ordered categorical data

Abstract: A mixed-model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables. This procedure resembles the best linear unbiased procedure of Henderson (1975, Biometrics 31, 423-447) for predicting the value of a quantitative response. The approach is based on a mixed-model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model. The results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf.

Alternative Approaches to Estimation of Population Pharmacokinetic Parameters: Comparison with the Nonlinear Mixed-Effect Model

Abstract: Individual pharmacokinetic parameters can be viewed as independent realizations of a random variable. The probability density function of the variable is assumed to be specified by its first two mo...

Statistical and Computational Aspects of Mixed Model Analysis

Abstract: SUMMARY Statistical and computational techniques for the analysis of data from a normal mixed model with two variances are discussed and illustrated. Two iterative algorithms for restricted maximum likelihood estimation (REML) of the variances are compared. It is shown that these algorithms are much simplified by the use of a preliminary eigenvalue-eigenvector analysis. Two numerical examples are used to illustrate the theory by showing how variance estimates are used in the estimation and testing of fixed effects in the model. Monte Carlo simulations indicate that actual alpha levels of the tests are close to the nominal levels despite the estimation of the variance components. Diagnostic techniques are employed to assess model assumptions.

An Alternative to Eisenhart's Model II and Mixed Model in the Case of Negative Variance Estimates

Abstract: An alternative model useful for addressing the problem of negative variance component estimators is proposed. Specifically, it is possible to view certain of the parameters as covariances rather than as variances. Thus, the problems of the negative variance component estimator may be resolved by using a different model. Distributional results relating to both estimation and tests of hypotheses are also given.

On Analysis of Variance in the Mixed Model

Abstract: An analysis of variance (ANOVA) is defined to be a partition of the total sum of squares into independent terms which, when suitably scaled, are chi-squared variables. A partition of less than the total sum of squares, but with these properties, will often suffice and is referred to as a partial ANOVA. Conditions for an ANOVA, and for partial ANOVAs selected to contain only specific parameters, are given. Implications for estimation of variance components from an ANOVA are also discussed. These results are largely an extension of work by Graybill and Hultquist (1961). With unbalanced data, conditions for an ANOVA and the number of terms in it both can depend on which effects in the model are fixed and which are random. This is not taken into account by those procedures for partitioning a sum of squares which distinguish between random and fixed effects only in the calculation of expected mean squares. Several examples are given.

Exact F Tests in an Anova Procedure for Dependent Observations

Abstract: Several general correlation patterns are shown in this paper which give exact F tests in an ANOVA procedure with dependent observations. This paper presents the most general correlation patterns one can assume in a one-way and two-way layout and still have the F tests be valid. Exact F tests are given for various designs. These include the unbalanced ANOVA design, analysis of covariance, random effects models, and mixed models. Bartlett's test for homogeneity of variances is shown to be exact when the independence assumption is relaxed. An example is provided to illustrate how the general correlation can occur in an experimental design.

Estimation of Covariance Matrices in Unbalanced Random and Mixed Multivariate Models

Abstract: Three HENDERSON'S Methods of estimating the variance components are generalized from one to p variables using a compact matrix notation. These results are obtained using a generalized Kronecker product of matrices, generalized trace of order p and a generalized quadratic form.

The Statistical Model

Abstract: We adopt the following formulation of the structural form of the dynamic linear simultaneous equation model: $$ XA = \tilde YB + Z\Gamma = \tilde U $$ (1.1)