Generalized linear mixed models a pseudo-likelihood approach

Wolfinger, Russ; O’Connell, Michael

doi:10.1080/00949659308811554

Cited by 1,105 publications

(764 citation statements)

References 21 publications

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“…Consider a generalized linear mixed model represented as follows: (5) where α is a vector of fixed effects, δ is a vector of random effects normally distributed with mean 0 and variance matrix G, and g(.) is a differentiable monotonic link function with inverse g −1 (in our case, the logit link).…”

Section: Pseudo-likelihood Methodsmentioning

confidence: 99%

“…These methods require initial estimates for all of the first-stage model parameters. When the data are sparse one must use techniques that do not have this requirement, such as the pseudo-likelihood approach [ 5,6 ] or Markov chain Monte Carlo methods such as Gibbs sampling [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

“…The pseudo-likelihood approach of Wolfinger and O'Connell [ 5 ] uses Taylor expansions to approximate a generalized linear mixed model (GLLM) with a linear mixed pseudo-model, and the parameters can be estimated using restricted maximum likelihood estimation. The penalized quasi-likelihood (PQL) approach of Breslow and Clayton [ 6 ] is a special case of the pseudo-likelihood technique and involves approximations based on Laplace's method.…”

Section: Introductionmentioning

confidence: 99%

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The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

Capanu

Orlow

Berwick

et al. 2008

Statistics in Medicine

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For major genes known to influence the risk of cancer, an important task is to determine the risks conferred by individual variants, so that one can appropriately counsel carriers of these mutations. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little empirical evidence available about each individual mutation. Hierarchical modeling offers a natural strategy to leverage the collective evidence from these rare variants with sparse data. This can be accomplished when there are available higher level covariates that characterize the variants in terms of attributes that could distinguish their association with disease. In this article we explore the use of hierarchical modeling for this purpose using data from a large population-based study of the risks of melanoma conferred by variants in the CDKN2A gene. We employ both a pseudolikelihood approach and a Bayesian approach using Gibbs sampling. The results indicate that relative risk estimates tend to be primarily influenced by the individual case-control frequencies when several cases and/or controls are observed with the variant under study, but that relative risk estimates for variants with very sparse data are more influenced by the higher level covariate values, as one would expect. The analysis offers encouragement that we can draw strength from the aggregating power of hierarchical models to provide guidance to medical geneticists when they offer counseling to patients with rare or even hitherto unobserved variants. However, further research is needed to validate the application of asymptotic methods to such sparse data.

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Section: Pseudo-likelihood Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

Capanu

Orlow

Berwick

et al. 2008

Statistics in Medicine

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“…In order to estimate fixed and random effects as well as variance components, the GLMM (3) is transformed into a pseudo-LMM by applying a Taylor expansion of first order to S 2 (Wolfinger and O'Connell, 1993). If D ¼ ðqm=qZÞ Z¼Ẑ denotes the matrix of partial derivates at the estimated parameters, then a new response variable is obtained as Y*ED 21 (S 2 2m) 1 h. This pseudo-response is modelled by the LMM…”

Section: Datamentioning

confidence: 99%

Comparison of statistical models to analyse the genetic effect on within-litter variance in pigs

Wittenburg

Guiard

Teuscher

et al. 2008

Animal

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Genetics affects not only the weight of piglets at birth but also the variability of birth weight within litter. Previous studies on this topic assigned the sample standard deviation of piglet birth weights within litter as an observation to the sow. However, the contribution of the difference in mean birth weight per sex on the within-litter variance has been neglected so far. This work deals with the genetic effect on within-litter variance when different statistical models with different distributional assumptions are used and considers the sex effect and appropriate weights per trait. Traits were formed from the pooled sample variance of male and female birth weights within litter. A linear model approach was fitted to the logarithmized within-litter variance and the sample standard deviation. A generalized linear model with gamma-distributed residuals and log-link function was applied to the untransformed sample variance. Models were compared by analysing data from 9439 litters from Landrace and Large White of a commercial breeding programme. The estimates of heritability for different traits ranged from 7% to 11%. Although the generalized linear mixed model is preferred from a mathematical view, the rank correlations between breeding values of the linear mixed models and the generalized linear mixed model were relatively high, i.e. 94% to 98%. By residual diagnostics, a linear mixed model using the weighted and pooled within-litter standard deviation was identified as most suitable.

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“…Formal testing of whether the random effects are required in a model will depend on whether the best-fitting model is a generalized linear model, or a generalized additive model. For the former, we compared the fit using a generalized linear mixed-effects model (Breslow and Clayton, 1993;Wolfinger and O'Connell, 1993) while the latter, when there are significant nonlinear predictors, should be compared using a generalized additive mixed mode (Wang, 1998;Wood, 2004).…”

Section: Generalized Additive Mixed Model For Binary Outcomesmentioning

confidence: 99%

Methods for testing theory and evaluating impact in randomized field trials: Intent-to-treat analyses for integrating the perspectives of person, place, and time

Brown¹,

Wang²,

Kellam³

et al. 2008

Drug and Alcohol Dependence

152

139

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Randomized field trials provide unique opportunities to examine the effectiveness of an intervention in real world settings and to test and extend both theory of etiology and theory of intervention. These trials are designed not only to test for overall intervention impact but also to examine how impact varies as a function of individual level characteristics, context, and across time. Examination of such variation in impact requires analytical methods that take into account the trial's multiple nested structure and the evolving changes in outcomes over time. The models that we describe here merge multilevel modeling with growth modeling, allowing for variation in impact to be represented through discrete mixtures-growth mixture models-and nonparametric smooth functions-generalized additive mixed models. These methods are part of an emerging class of multilevel growth mixture models, and we illustrate these with models that examine overall impact and variation in impact. In this paper, we define intent-to-treat analyses in group-randomized multilevel field trials and discuss appropriate ways to identify, examine, and test for variation in impact without inflating the Type I error rate. We describe how to make causal inferences more robust to misspecification of covariates * Corresponding author. Tel.: +1 813 974 6672. E-mail address: hbrown@health.usf.edu (C.H. Brown). Conflict of InterestAuthor Muthén is a co-developer of Mplus, which is discussed in this paper. There are no conflicts of interest. in such analyses and how to summarize and present these interactive intervention effects clearly. Practical strategies for reducing model complexity, checking model fit, and handling missing data are discussed using six randomized field trials to show how these methods may be used across trials randomized at different levels. NIH Public Access

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Generalized linear mixed models a pseudo-likelihood approach

Cited by 1,105 publications

References 21 publications

The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

The use of hierarchical models for estimating relative risks of individual genetic variants: An application to a study of melanoma

Comparison of statistical models to analyse the genetic effect on within-litter variance in pigs

Methods for testing theory and evaluating impact in randomized field trials: Intent-to-treat analyses for integrating the perspectives of person, place, and time

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