scholarly journals Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models

2013 ◽  
Vol 20 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Keunbaik Lee
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Bayesian Modeling ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models

Modeling the random effects covariance matrix for generalized linear mixed models

2012 ◽  
Vol 56 (6) ◽  
pp. 1545-1551 ◽  
Author(s):  
Keunbaik Lee ◽  
JungBok Lee ◽  
Joseph Hagan ◽  
Jae Keun Yoo
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models

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 Within- and Between-cluster Effects in Generalized Linear Mixed Models: A Discussion of Approaches and the Xthybrid command

2017 ◽  
Vol 17 (1) ◽  
pp. 89-115 ◽  
Author(s):  
Reinhard Schunck ◽  
Francisco Perales
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Negative Binomial ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Consistent Estimation ◽  
Random Effects Models ◽  
Fixed Effects Models ◽  
Correlated Random Effects

One typically analyzes clustered data using random- or fixed-effects models. Fixed-effects models allow consistent estimation of the effects of level-one variables, even if there is unobserved heterogeneity at level two. However, these models cannot estimate the effects of level-two variables. Hybrid and correlated random-effects models are flexible modeling specifications that separate within-and between-cluster effects and allow for both consistent estimation of level-one effects and inclusion of level-two variables. In this article, we elaborate on the separation of within- and between-cluster effects in generalized linear mixed models. These models present a unifying framework for an entire class of models whose response variables follow a distribution from the exponential family (for example, linear, logit, probit, ordered probit and logit, Poisson, and negative binomial models). We introduce the user-written command xthybrid, a shell for the meglm command. xthybrid can fit a variety of hybrid and correlated random-effects models.

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