scholarly journals Restricted likelihood ratio testing in linear mixed models with general error covariance structure

2011 ◽  
Vol 5 (0) ◽  
pp. 1718-1734 ◽  
Author(s):  
Andrea Wiencierz ◽  
Sonja Greven ◽  
Helmut Küchenhoff
Keyword(s):  
Likelihood Ratio ◽  
Mixed Models ◽  
Linear Mixed Models ◽  
Covariance Structure ◽  
Error Covariance ◽  
Restricted Likelihood ◽  
Likelihood Ratio Testing ◽  
Error Covariance Structure ◽  
General Error

Restricted Likelihood Ratio Testing for Zero Variance Components in Linear Mixed Models

2008 ◽  
Vol 17 (4) ◽  
pp. 870-891 ◽  
Author(s):  
Sonja Greven ◽  
Ciprian M Crainiceanu ◽  
Helmut Küchenhoff ◽  
Annette Peters
Keyword(s):  
Likelihood Ratio ◽  
Mixed Models ◽  
Variance Components ◽  
Linear Mixed Models ◽  
Restricted Likelihood ◽  
Likelihood Ratio Testing

On estimating and testing associations between random coefficients from multivariate generalized linear mixed models of longitudinal outcomes

2015 ◽  
Vol 26 (3) ◽  
pp. 1130-1145 ◽  
Author(s):  
Susan K Mikulich-Gilbertson ◽  
Brandie D Wagner ◽  
Paula D Riggs ◽  
Gary O Zerbe
Keyword(s):  
Likelihood Ratio ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Mathematical Proof ◽  
Linear Mixed Models ◽  
Delta Method ◽  
Standard Errors ◽  
Ratio Test ◽  
Type I ◽  
Time Lags

Different types of outcomes (e.g. binary, count, continuous) can be simultaneously modeled with multivariate generalized linear mixed models by assuming: (1) same or different link functions, (2) same or different conditional distributions, and (3) conditional independence given random subject effects. Others have used this approach for determining simple associations between subject-specific parameters (e.g. correlations between slopes). We demonstrate how more complex associations (e.g. partial regression coefficients between slopes adjusting for intercepts, time lags of maximum correlation) can be estimated. Reparameterizing the model to directly estimate coefficients allows us to compare standard errors based on the inverse of the Hessian matrix with more usual standard errors approximated by the delta method; a mathematical proof demonstrates their equivalence when the gradient vector approaches zero. Reparameterization also allows us to evaluate significance of coefficients with likelihood ratio tests and to compare this approach with more usual Wald-type t-tests and Fisher’s z transformations. Simulations indicate that the delta method and inverse Hessian standard errors are nearly equivalent and consistently overestimate the true standard error. Only the likelihood ratio test based on the reparameterized model has an acceptable type I error rate and is therefore recommended for testing associations between stochastic parameters. Online supplementary materials include our medical data example, annotated code, and simulation details.

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.

scholarly journals Effects of error covariance structure on estimation of model averaging weights and predictive performance

2013 ◽  
Vol 49 (9) ◽  
pp. 6029-6047 ◽  
Author(s):  
Dan Lu ◽  
Ming Ye ◽  
Philip D. Meyer ◽  
Gary P. Curtis ◽  
Xiaoqing Shi ◽  
...  
Keyword(s):  
Model Averaging ◽  
Covariance Structure ◽  
Predictive Performance ◽  
Error Covariance ◽  
Error Covariance Structure

Likelihood ratio tests for variance components in linear mixed models

2009 ◽  
Vol 139 (4) ◽  
pp. 1435-1448 ◽  
Author(s):  
Viviana Giampaoli ◽  
Julio M. Singer
Keyword(s):  
Likelihood Ratio ◽  
Mixed Models ◽  
Variance Components ◽  
Linear Mixed Models ◽  
Likelihood Ratio Tests

A systematic approach for identifying level-1 error covariance structures in latent growth modeling

2016 ◽  
Vol 41 (3) ◽  
pp. 444-455 ◽  
Author(s):  
Cherng G. Ding ◽  
Ten-Der Jane ◽  
Chiu-Hui Wu ◽  
Hang-Rung Lin ◽  
Chih-Kang Shen
Keyword(s):  
Systematic Approach ◽  
Growth Modeling ◽  
Covariance Structure ◽  
Latent Growth Modeling ◽  
Covariance Structures ◽  
Latent Growth ◽  
Error Covariance ◽  
Nested Relations ◽  
Level 1 ◽  
Error Covariance Structure

It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which, however, is not systematically addressed in the literature. In this study, we first discuss characteristics of various covariance structures and their nested relations, based on which we then propose a systematic approach to facilitate identifying a plausible covariance structure. A test for stationarity of an error process and the sequential chi-square difference test are conducted in the approach. Preliminary simulation results indicate that the approach performs well when sample size is large enough. The approach is illustrated with empirical data. We recommend that the approach be used in LGM empirical studies to improve the quality of the specification of the error covariance structure.

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