Generalized linear mixed model

About: Generalized linear mixed model is a research topic. Over the lifetime, 4341 publications have been published within this topic receiving 290296 citations. The topic is also known as: Generalized linear mixed model, GLMM.

Fitting Linear Mixed-Effects Models Using lme4

Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

Generalized Linear Models

Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).

Longitudinal data analysis using generalized linear models

Abstract: SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.

Fitting Linear Mixed-Effects Models using lme4

Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

Generalized Additive Models: An Introduction with R, Second Edition

Abstract: LINEAR MODELS A simple linear model Linear models in general The theory of linear models The geometry of linear modelling Practical linear models Practical modelling with factors General linear model specification in R Further linear modelling theory Exercises GENERALIZED LINEAR MODELS The theory of GLMs Geometry of GLMs GLMs with R Likelihood Exercises INTRODUCING GAMS Introduction Univariate smooth functions Additive models Generalized additive models Summary Exercises SOME GAM THEORY Smoothing bases Setting up GAMs as penalized GLMs Justifying P-IRLS Degrees of freedom and residual variance estimation Smoothing Parameter Estimation Criteria Numerical GCV/UBRE: performance iteration Numerical GCV/UBRE optimization by outer iteration Distributional results Confidence interval performance Further GAM theory Other approaches to GAMs Exercises GAMs IN PRACTICE: mgcv Cherry trees again Brain imaging example Air pollution in Chicago example Mackerel egg survey example Portuguese larks example Other packages Exercises MIXED MODELS and GAMMs Mixed models for balanced data Linear mixed models in general Linear mixed models in R Generalized linear mixed models GLMMs with R Generalized additive mixed models GAMMs with R Exercises APPENDICES A Some matrix algebra B Solutions to exercises Bibliography Index