Fitting Linear Mixed-Effects Models using lme4
نویسندگان
چکیده
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 fixedand 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.
منابع مشابه
amer: Using lme4 to fit Generalized Additive Mixed Models
The lme4 package uses sparse matrix technology and clever decompositions of the likelihood to fit linear, generalized, and nonlinear mixed-effects models. The amer package extends lme4’s scope to include generalized additive mixed models (GAMM). This vignette summarizes the main ideas behind additive models and their representation in the form of a mixed model, describes the modifications to lm...
متن کاملA tutorial on fitting Bayesian linear mixed models using Stan
With the arrival of the R packages nlme and lme4, linear mixed models (LMMs) have come to be widely used in psychology, cognitive science, and related areas. In this tutorial, we provide a practical introduction to fitting LMMs in a Bayesian framework using the probabilistic programming language Stan. Although the Bayesian framework has several important advantages, specifying a Bayesian model ...
متن کاملChanges to the Mixed Effects Models chapters in ELM
The book “Extending the Linear Model with R” (ELM) [5] first appeared in 2005 and was based on R version 2.2.0. R is updated regularly and so it is natural that some incompatibilities with the current version have been introduced. For most of the chapters, these changes have been minor and have been addressed in the errata and/or subsequent reprintings of the text. However, for chapter 8 and 9,...
متن کاملLinear mixed model implementation in lme4
We describe the form of the linear mixed-effects and generalized linear mixed-effects models fit by lmer and give details of the representation and the computational techniques used to fit such models. These techniques are illustrated on several examples.
متن کاملPenalized least squares versus generalized least squares representations of linear mixed models
The methods in the lme4 package for R for fitting linear mixed models are based on sparse matrix methods, especially the Cholesky decomposition of sparse positive-semidefinite matrices, in a penalized least squares representation of the conditional model for the response given the random effects. The representation is similar to that in Henderson’s mixed-model equations. An alternative represen...
متن کامل