Class "merMod" of Fitted Mixed-Effect Models

A mixed-effects model is represented as a '>merPredD object and a response module of a class that inherits from class '>lmResp. A model with a '>lmerResp response has class lmerMod; a '>glmResp response has class glmerMod; and a '>nlsResp response has class nlmerMod.

# S3 method for merMod
anova(object, ..., refit = TRUE, model.names=NULL)
# S3 method for merMod
as.function(x, ...)
# S3 method for merMod
coef(object, ...)
# S3 method for merMod
deviance(object, REML = NULL, ...)
# S3 method for merMod
extractAIC(fit, scale = 0, k = 2, ...)
# S3 method for merMod
family(object, ...)
# S3 method for merMod
formula(x, fixed.only = FALSE, random.only = FALSE, ...)
# S3 method for merMod
fitted(object, ...)
# S3 method for merMod
logLik(object, REML = NULL, ...)
# S3 method for merMod
nobs(object, ...)
# S3 method for merMod
ngrps(object, ...)
# S3 method for merMod
terms(x, fixed.only = TRUE, random.only = FALSE, …)
# S3 method for merMod
vcov(object, correlation = TRUE, sigm = sigma(object),
     use.hessian = NULL, …)
# S3 method for merMod
model.frame(formula, fixed.only = FALSE, ...)
# S3 method for merMod
model.matrix(object, type = c("fixed", "random", "randomListRaw"), ...)
# S3 method for merMod
print(x, digits = max(3, getOption("digits") - 3),
      correlation = NULL, symbolic.cor = FALSE,
      signif.stars = getOption("show.signif.stars"), ranef.comp = "Std.Dev.", ...)

# S3 method for merMod summary(object, correlation = , use.hessian = NULL, …) # S3 method for summary.merMod print(x, digits = max(3, getOption("digits") - 3), correlation = NULL, symbolic.cor = FALSE, signif.stars = getOption("show.signif.stars"), ranef.comp = c("Variance", "Std.Dev."), show.resids = TRUE, ...) # S3 method for merMod update(object, formula., ..., evaluate = TRUE) # S3 method for merMod weights(object, type = c("prior", "working"), ...)


an R object of class '>merMod, i.e., as resulting from lmer(), or glmer(), etc.


an R object of class merMod or summary.merMod, respectively, the latter resulting from summary(<merMod>).


an R object of class '>merMod.


in the case of model.frame, a '>merMod object.


logical indicating if objects of class lmerMod should be refitted with ML before comparing models. The default is TRUE to prevent the common mistake of inappropriately comparing REML-fitted models with different fixed effects, whose likelihoods are not directly comparable.


character vectors of model names to be used in the anova table.


Not currently used (see extractAIC).


see extractAIC.


Logical. If TRUE, return the restricted log-likelihood rather than the log-likelihood. If NULL (the default), set REML to isREML(object) (see isREML).


logical indicating if only the fixed effects components (terms or formula elements) are sought. If false, all components, including random ones, are returned.


complement of fixed.only; indicates whether random components only are sought. (Trying to specify fixed.only and random.only at the same time will produce an error.)


(logical) for vcov, indicates whether the correlation matrix as well as the variance-covariance matrix is desired; for summary.merMod, indicates whether the correlation matrix should be computed and stored along with the covariance; for print.summary.merMod, indicates whether the correlation matrix of the fixed-effects parameters should be printed. In the latter case, when NULL (the default), the correlation matrix is printed when it has been computed by summary(.), and when \(p <= 20\).


(logical) indicates whether to use the finite-difference Hessian of the deviance function to compute standard errors of the fixed effects, rather estimating based on internal information about the inverse of the model matrix (see getME(.,"RX")). The default is to to use the Hessian whenever the fixed effect parameters are arguments to the deviance function (i.e. for GLMMs with nAGQ>0), and to use getME(.,"RX") whenever the fixed effect parameters are profiled out (i.e. for GLMMs with nAGQ==0 or LMMs).

use.hessian=FALSE is backward-compatible with older versions of lme4, but may give less accurate SE estimates when the estimates of the fixed-effect (see getME(.,"beta")) and random-effect (see getME(.,"theta")) parameters are correlated.


the residual standard error; by default sigma(object).


number of significant digits for printing


should a symbolic encoding of the fixed-effects correlation matrix be printed? If so, the symnum function is used.


(logical) should significance stars be used?


character vector of length one or two, indicating if random-effects parameters should be reported on the variance and/or standard deviation scale.


should the quantiles of the scaled residuals be printed?


see update.formula.


see update.


For weights, type of weights to be returned; either "prior" for the initially supplied weights or "working" for the weights at the final iteration of the penalized iteratively reweighted least squares algorithm. For model.matrix, type of model matrix to return (one of fixed giving the fixed effects model matrix, random giving the random effects model matrix, or randomListRaw giving a list of the raw random effects model matrices associated with each random effects term).

potentially further arguments passed from other methods.

Objects from the Class

Objects of class merMod are created by calls to lmer, glmer or nlmer.

S3 methods

The following S3 methods with arguments given above exist (this list is currently not complete):

%% TODO: document differences between update and update.merMod

returns the sequential decomposition of the contributions of fixed-effects terms or, for multiple arguments, model comparison statistics. For objects of class lmerMod the default behavior is to refit the models with ML if fitted with REML = TRUE, this can be controlled via the refit argument. See also anova.


returns the deviance function, the same as lmer(*, devFunOnly=TRUE), and mkLmerDevfun() or mkGlmerDevfun(), respectively.


Computes the sum of the random and fixed effects coefficients for each explanatory variable for each level of each grouping factor.


Computes the (generalized) Akaike An Information Criterion. If isREML(fit), then fit is refitted using maximum likelihood.


family of fitted GLMM. (Warning: this accessor may not work properly with customized families/link functions.)


Fitted values, given the conditional modes of the random effects. For more flexible access to fitted values, use predict.merMod.


Log-likelihood at the fitted value of the parameters. Note that for GLMMs, the returned value is only proportional to the log probability density (or distribution) of the response variable. See logLik.


returns the frame slot of '>merMod.


returns the fixed effects model matrix.

nobs, ngrps:

Number of observations and vector of the numbers of levels in each grouping factor. See ngrps.


Computes and returns a list of summary statistics of the fitted model, the amount of output can be controlled via the print method, see also summary.


Controls the output for the summary method.


Calculate variance-covariance matrix of the fixed effect terms, see also vcov.


See update.

Deviance and log-likelihood of GLMMs

One must be careful when defining the deviance of a GLM. For example, should the deviance be defined as minus twice the log-likelihood or does it involve subtracting the deviance for a saturated model? To distinguish these two possibilities we refer to absolute deviance (minus twice the log-likelihood) and relative deviance (relative to a saturated model, e.g. Section 2.3.1 in McCullagh and Nelder 1989). With GLMMs however, there is an additional complication involving the distinction between the likelihood and the conditional likelihood. The latter is the likelihood obtained by conditioning on the estimates of the conditional modes of the spherical random effects coefficients, whereas the likelihood itself (i.e. the unconditional likelihood) involves integrating out these coefficients. The following table summarizes how to extract the various types of deviance for a glmerMod object:

conditional unconditional
relative deviance(object) NA in lme4

This table requires two caveats:

  • If the link function involves a scale parameter (e.g. Gamma) then object@resp$aic() - 2 * getME(object, "devcomp")$dims["useSc"] is required for the absolute-conditional case.

  • If adaptive Gauss-Hermite quadrature is used, then logLik(object) is currently only proportional to the absolute-unconditional log-likelihood.

For more information about this topic see the misc/logLikGLMM directory in the package source.



A reference class object for an lme4 response module (lmResp-class).


See getME.


The matched call.


The model frame containing all of the variables required to parse the model formula.


See getME.


See getME.


See getME.


Covariance parameter vector.


Fixed effects coefficients.


Conditional model of spherical random effects coefficients.


See getME.


A reference class object for an lme4 predictor module (merPredD-class).


List containing information about the nonlinear optimization.

See Also

lmer, glmer, nlmer, '>merPredD, '>lmerResp, '>glmResp, '>nlsResp

Other methods for merMod objects documented elsewhere include: fortify.merMod, drop1.merMod, isLMM.merMod, isGLMM.merMod, isNLMM.merMod, isREML.merMod, plot.merMod, predict.merMod, profile.merMod, ranef.merMod, refit.merMod, refitML.merMod, residuals.merMod, sigma.merMod, simulate.merMod, summary.merMod.

  • anova.merMod
  • as.function.merMod
  • coef.merMod
  • deviance.merMod
  • df.residual.merMod
  • extractAIC.merMod
  • family.merMod
  • fitted.merMod
  • formula.merMod
  • glmerMod-class
  • lmerMod-class
  • logLik.merMod
  • merMod
  • merMod-class
  • model.frame.merMod
  • model.matrix.merMod
  • ngrps.merMod
  • nobs.merMod
  • nobs
  • nlmerMod-class
  • print.merMod
  • print.summary.merMod
  • show,merMod-method
  • show.merMod
  • show.summary.merMod
  • summary.merMod
  • summary.summary.merMod
  • terms.merMod
  • update.merMod
  • vcov.merMod
  • vcov.summary.merMod
  • weights.merMod
  • REMLcrit
methods(class="merMod")## over 30  (S3) methods available

## -> example(lmer)  for an example of vcov.merMod()
# }
Documentation reproduced from package lme4, version 1.1-21, License: GPL (>= 2)

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