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Using empirical Bayes predictors from generalized linear mixed models to test and visualize associations among longitudinal outcomes

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STATISTICAL METHODS IN MEDICAL RESEARCH 2019年第5期28卷 1399-1411页

作者： Mikulich-Gilbertson, Susan K. Wagner, Brandie D. Grunwald, Gary K. Riggs, Paula D. Zerbe, Gary O. Univ Colorado Sch Med Dept Psychiat Anschutz Med Campus Aurora CO USA Univ Colorado Sch Publ Hlth Dept Biostat & Informat Anschutz Med Campus Aurora CO USA

Medical research is often designed to investigate changes in a collection of response variables that are measured repeatedly on the same subjects. The multivariate generalized linear mixed model (MGLMM) can be used to evaluate random coefficient associations (e.g. simple correlations, partial regression coefficients) among outcomes that may be non-normal and differently distributed by specifying a multivariate normal distribution for their random effects and then evaluating the latent relationship between them. Empirical Bayes predictors are readily available for each subject from any mixed model and are observable and hence, plotable. Here, we evaluate whether second-stage association analyses of empirical Bayes predictors from a MGLMM, provide a good approximation and visual representation of these latent association analyses using medical examples and simulations. Additionally, we compare these results with association analyses of empirical Bayes predictors generated from separate mixed models for each outcome, a procedure that could circumvent computational problems that arise when the dimension of the joint covariance matrix of random effects is large and prohibits estimation of latent associations. As has been shown in other analytic contexts, the p-values for all second-stage coefficients that were determined by naively assuming normality of empirical Bayes predictors provide a good approximation to p-values determined via permutation analysis. Analyzing outcomes that are interrelated with separate models in the first stage and then associating the resulting empirical Bayes predictors in a second stage results in different mean and covariance parameter estimates from the maximum likelihood estimates generated by a MGLMM. The potential for erroneous inference from using results from these separate models increases as the magnitude of the association among the outcomes increases. Thus if computable, scatterplots of the conditionally independent empirical Bayes

关键词： Joint model multivariate model random coefficient association stochastic parameter association two-stage analysis best linear unbiased predictor empirical Bayes predictor generalized linear mixed model latent association permutation analysis

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Robust quasi-likelihood inference in generalized linear mixed models with outliers

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2011年第2期81卷 233-258页

作者： Sutradhar, Brajendra C. Bari, Wasimul Memorial Univ Dept Math & Stat St John NF Canada

It is well known that in a traditional outlier-free situation, the generalized quasi-likelihood (GQL) approach [B.C. Sutradhar, On exact quasilikelihood inference in generalized linear mixed models, Sankhya: Indian J. Statist. 66 (2004), pp. 261-289] performs very well to obtain the consistent as well as the efficient estimates for the parameters involved in the generalized linear mixed models (GLMMs). In this paper, we first examine the effect of the presence of one or more outliers on the GQL estimation for the parameters in such GLMMs, especially in two important models such as count and binary mixed models. The outliers appear to cause serious biases and hence inconsistency in the estimation. As a remedy, we then propose a robust GQL (RGQL) approach in order to obtain the consistent estimates for the parameters in the GLMMs in the presence of one or more outliers. An extensive simulation study is conducted to examine the consistency performance of the proposed RGQL approach.

关键词： consistency count and binary mixed models generalized linear mixed model generalized quasi-likelihood outliers overdispersion regression effects robust approach

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Comparison of two methods in estimating standard error of the method of simulated moments estimators for generalized linear mixed models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2018年第10期47卷 2886-2895页

作者： Lu, Yan Chen, Zhongxue Duran, Danielle Univ New Mexico Dept Math & Stat Albuquerque NM 87131 USA Indiana Univ Sch Publ Hlth Dept Epidemiol & Biostat Bloomington IN USA

The likelihood of a generalized linear mixed model (GLMM) often involves high-dimensional integrals, which in general cannot be computed explicitly. When direct computation is not available, method of simulated moments (MSM) is a fairly simple way to estimate the parameters of interest. In this research, we compared parametric bootstrap (PB) and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, the PB and NPB perform similarly;when group size is medium, NPB performs better than PB in estimating standard errors of the mean.

关键词： generalized linear mixed model Method of simulated moments Non-parametric bootstrap Parametric bootstrap Simulations Standard errors

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Likelihood Inference for Spatial generalized linear mixed models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2015年第7期44卷 1692-1701页

作者： Torabi, Mahmoud Univ Manitoba Dept Community Hlth Sci Winnipeg MB R3E 0W3 Canada

Spatial modeling is widely used in environmental sciences, biology, and epidemiology. generalized linearmixed models are employed to account for spatial variations of point-referenced data called spatial generalized linear mixed models (SGLMMs). Frequentist analysis of these type of data is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of SGLMM computationally convenient. Recent introduction of the method of data cloning, which leads to maximum likelihood estimate, has made frequentist analysis of mixed models also equally computationally convenient. Recently, the data cloning was employed to estimate model parameters in SGLMMs, however, the prediction of spatial random effects and kriging are also very important. In this article, we propose a frequentist approach based on data cloning to predict (and provide prediction intervals) spatial random effects and kriging. We illustrate this approach using a real dataset and also by a simulation study.

关键词： Bayesian computation generalized linear mixed model Kriging Point-referenced data Spatial statistics

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Use of between-within degrees of freedom as an alternative to the Kenward-Roger method for small-sample inference in generalized linear mixed modeling of clustered count data

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第10期52卷 5099-5109页

作者： Staggs, Vincent S. Feldman, Keith Childrens Mercy Kansas City Biostat & Epidemiol Core 2400 Gillham Rd Kansas City MO 64108 USA Univ Missouri Sch Med Dept Pediat Kansas City MO 64108 USA Childrens Mercy Kansas City Hlth Serv & Outcomes Res Kansas City MO 64108 USA

Clustered count data, common in health-related research, are routinely analyzed using generalized linear mixed models. There are two well-known challenges in small-sample inference in mixed modeling: bias in the naive standard error approximation for the empirical best linear unbiased estimator, and lack of clearly defined denominator degrees of freedom. The Kenward-Roger method was designed to address these issues in linear mixed modeling, but neither it nor the simpler option of using between-within denominator degrees of freedom has been thoroughly examined in generalized linear mixed modeling. We compared the Kenward-Roger and between-within methods in two simulation studies. For simulated cluster-randomized trial data, coverage rates for both methods were generally close to the nominal 95% level and never outside 93-97%, even for 5 clusters with an average of 3 observations each. For autocorrelated longitudinal data, between-within intervals were more accurate overall, and under some conditions both the original and improved Kenward-Roger methods behaved erratically. Overall, coverage for Kenward-Roger and between-within intervals was generally adequate, if often conservative. Based on the scenarios examined here, use of between-within degrees of freedom may be a suitable or even preferable alternative to the Kenward-Roger method in some analyses of clustered count data with simple covariance structures.

关键词： generalized linear mixed model mixed model Multilevel model Hierarchical model Clustered data

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Variable selection for generalized linear mixed models by L ₁-penalized estimation

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STATISTICS AND COMPUTING 2014年第2期24卷 137-154页

作者： Groll, Andreas Tutz, Gerhard Univ Munich Dept Math D-80333 Munich Germany Univ Munich Seminar Appl Stochast Inst Stat D-80799 Munich Germany

generalized linear mixed models are a widely used tool for modeling longitudinal data. However, their use is typically restricted to few covariates, because the presence of many predictors yields unstable estimates. The presented approach to the fitting of generalized linear mixed models includes an L (1)-penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized log-likelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of potentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets.

关键词： generalized linear mixed model Lasso Gradient ascent Penalty linear models Variable selection

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Misspecification of the covariance structure in generalized linear mixed models

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STATISTICAL METHODS IN MEDICAL RESEARCH 2016年第2期25卷 630-643页

作者： Chavance, M. Escolano, S. Ctr Rech Epidemiol & Sante Populat INSERM CESP Villejuif France

When fitting marginal models to correlated outcomes, the so-called sandwich variance is commonly used. However, this is not the case when fitting mixed models. Using two data sets, we illustrate the problems that can be encountered. We show that the differences or the ratios between the naive and sandwich standard deviations of the fixed effects estimators provide convenient means of assessing the fit of the model, as both are consistent when the covariance structure is correctly specified, but only the latter is when that structure is misspecified. When the number of statistical units is not too small, the sandwich formula correctly estimates the variance of the fixed effects estimator even if the random effects are misspecified, and it can be used in a diagnostic tool for assessing the misspecification of the random effects. A simple comparison with the naive variance is sufficient and we propose considering a ratio of the naive and sandwich standard deviation out of the [3/4;4/3] interval as signaling a risk of erroneous inference due to a model misspecification. We strongly advocate broader use of the sandwich variance for statistical inference about the fixed effects in mixed models.

关键词： Correlated outcomes covariance structure diagnostic tool generalized linear mixed model

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Monte Carlo approximation through Gibbs output in generalized linear mixed models

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JOURNAL OF MULTIVARIATE ANALYSIS 2005年第2期94卷 300-312页

作者： Chan, JSK Kuk, AYC Yam, CHK Univ Hong Kong Dept Stat & Actuarial Sci Pokfulam Rd Hong Kong Hong Kong Peoples R China Natl Univ Singapore Dept Stat & Appl Probabil Singapore 117543 Singapore Univ Hong Kong Dept Community Med Hong Kong Hong Kong Peoples R China

Geyer (J. Roy. Statist. Soc. 56 (1994) 291) proposed Monte Carlo method to approximate the whole likelihood function. His method is limited to choosing a proper reference point. We attempt to improve the method by assigning some prior information to the parameters and using the Gibbs output to evaluate the marginal likelihood and its derivatives through a Monte Carlo approximation. Vague priors are assigned to the parameters as well as the random effects within the Bayesian framework to represent a non-informative setting. Then the maximum likelihood estimates are obtained through the Newton Raphson method. Thus, out method serves as a bridge between Bayesian and classical approaches. The method is illustrated by analyzing the famous salamander mating data by generalized linear mixed models. (c) 2004 Elsevier Inc. All rights reserved.

关键词： generalized linear mixed model Monte Carlo Newton Raphsom Monte Carlo relative likelihood Gibbs sampler Metropolis-Hastings algorithm

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Spatial generalized linear mixed models in small area estimation

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2019年第3期47卷 426-437页

作者： Torabi, Mahmoud Univ Manitoba Dept Community Hlth Sci S113 Med Serv Bldg750 Bannatyne Ave Winnipeg MB R3K 0W3 Canada

In survey sampling, policy decisions regarding the allocation of resources to sub-groups of a population depend on reliable predictors of their underlying parameters. However, in some sub-groups, called small areas due to small sample sizes relative to the population, the information needed for reliable estimation is typically not available. Consequently, data on a coarser scale are used to predict the characteristics of small areas. mixed models are the primary tools in small area estimation (SAE) and also borrow information from alternative sources (e.g., previous surveys and administrative and census data sets). In many circumstances, small area predictors are associated with location. For instance, in the case of chronic disease or cancer, it is important for policy makers to understand spatial patterns of disease in order to determine small areas with high risk of disease and establish prevention strategies. The literature considering SAE with spatial random effects is sparse and mostly in the context of spatial linear mixed models. In this article, small area models are proposed for the class of spatial generalized linear mixed models to obtain small area predictors and corresponding second-order unbiased mean squared prediction errors via Taylor expansion and a parametric bootstrap approach. The performance of the proposed approach is evaluated through simulation studies and application of the models to a real esophageal cancer data set from Minnesota, U.S.A. The Canadian Journal of Statistics 47: 426-437;2019 (c) 2019 Statistical Society of Canada

关键词： generalized linear mixed model maximum likelihood estimation parametric bootstrap small area estimation spatial model Taylor expansion

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A simulation-based goodness-of-fit test for random effects in generalized linear mixed models

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SCANDINAVIAN JOURNAL OF STATISTICS 2006年第4期33卷 721-731页

作者： Waagepetersen, Rasmus Univ Aalborg Inst Math Sci DK-9220 Aalborg Denmark

The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.

关键词： conditional simulation empirical distribution function generalized linear mixed model goodness-of-fit random effects

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