scholarly journals Estimation of the covariance matrix of random effects in longitudinal studies

2007 ◽  
Vol 35 (6) ◽  
pp. 2795-2814 ◽  
Author(s):  
Yan Sun ◽  
Wenyang Zhang ◽  
Howell Tong
Keyword(s):  
Longitudinal Studies ◽  
Covariance Matrix ◽  
Random Effects

scholarly journals Basic Features of the Analysis of Germination Data with Generalized Linear Mixed Models

Data ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 6 ◽  
Author(s):  
Alberto Gianinetti
Keyword(s):  
Boundary Conditions ◽  
Longitudinal Studies ◽  
Random Effects ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Covariance Structure ◽  
Conditional Models ◽  
Error Terms ◽  
Germination Indices

Germination data are discrete and binomial. Although analysis of variance (ANOVA) has long been used for the statistical analysis of these data, generalized linear mixed models (GzLMMs) provide a more consistent theoretical framework. GzLMMs are suitable for final germination percentages (FGP) as well as longitudinal studies of germination time-courses. Germination indices (i.e., single-value parameters summarizing the results of a germination assay by combining the level and rapidity of germination) and other data with a Gaussian error distribution can be analyzed too. There are, however, different kinds of GzLMMs: Conditional (i.e., random effects are modeled as deviations from the general intercept with a specific covariance structure), marginal (i.e., random effects are modeled solely as a variance/covariance structure of the error terms), and quasi-marginal (some random effects are modeled as deviations from the intercept and some are modeled as a covariance structure of the error terms) models can be applied to the same data. It is shown that: (a) For germination data, conditional, marginal, and quasi-marginal GzLMMs tend to converge to a similar inference; (b) conditional models are the first choice for FGP; (c) marginal or quasi-marginal models are more suited for longitudinal studies, although conditional models lead to a congruent inference; (d) in general, common random factors are better dealt with as random intercepts, whereas serial correlation is easier to model in terms of the covariance structure of the error terms; (e) germination indices are not binomial and can be easier to analyze with a marginal model; (f) in boundary conditions (when some means approach 0% or 100%), conditional models with an integral approximation of true likelihood are more appropriate; in non-boundary conditions, (g) germination data can be fitted with default pseudo-likelihood estimation techniques, on the basis of the SAS-based code templates provided here; (h) GzLMMs are remarkably good for the analysis of germination data except if some means are 0% or 100%. In this case, alternative statistical approaches may be used, such as survival analysis or linear mixed models (LMMs) with transformed data, unless an ad hoc data adjustment in estimates of limit means is considered, either experimentally or computationally. This review is intended as a basic tutorial for the application of GzLMMs, and is, therefore, of interest primarily to researchers in the agricultural sciences.

ANOVA models with random effects: an approach via symmetry

1986 ◽  
Vol 23 (A) ◽  
pp. 355-368 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Spectral Decomposition ◽  
Linear Models ◽  
Random Variables ◽  
Components Of Variance

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

scholarly journals Computationally Stable Estimation Procedure for the Multivariate Linear Mixed-Effect Model and Application to Malaria Public Health Problem

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Eric Houngla Adjakossa ◽  
Norbert Mahouton Hounkonnou ◽  
Grégory Nuel
Keyword(s):  
Em Algorithm ◽  
Covariance Matrix ◽  
Random Effects ◽  
Estimation Procedure ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Consistent Estimate ◽  
Linear Mixed Effects Models ◽  
Linear Mixed Effects ◽  
The Em Algorithm

Abstract In this paper, we provide the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effects models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance matrix, we provide an explicit expression of the profiled deviance through a reparameterization of the model. This strategy can be viewed as the generalization of the estimation procedure used by Douglas Bates and his co-authors in the context of the fitting of one-dimensional linear mixed-effects models. Beside its robustness regarding the starting points, the approach enables a numerically consistent estimate of the random effects covariance matrix while classical alternatives such as the EM algorithm are usually non-consistent. In a simulation study, we compare the estimates obtained from the present method with the EM algorithm-based estimates. We finally apply the method to a study of an immune response to Malaria in Benin.

Flexible Modelling of the Covariance Matrix in a Linear Random Effects Model

2000 ◽  
Vol 42 (7) ◽  
pp. 807-822 ◽  
Author(s):  
Emmanuel Lesaffre ◽  
David Todem ◽  
Geert Verbeke ◽  
Mike Kenward
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Random Effects Model

scholarly journals Modelling the random effects covariance matrix in longitudinal data

2003 ◽  
Vol 22 (10) ◽  
pp. 1631-1647 ◽  
Author(s):  
Michael J. Daniels ◽  
Yan D. Zhao
Keyword(s):  
Longitudinal Data ◽  
Covariance Matrix ◽  
Random Effects
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