merMod-class {lme4} | R Documentation

## Class "merMod" of Fitted Mixed-Effect Models

### Description

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`.

### Usage

    ## S3 method for class 'merMod'
    anova(object, ..., refit = TRUE, model.names=NULL)
    ## S3 method for class 'merMod'
    coef(object, ...)
    ## S3 method for class 'merMod'
    deviance(object, REML = NULL, ...)
    REMLcrit(object)
    ## S3 method for class 'merMod'
    extractAIC(fit, scale = 0, k = 2, ...)
    ## S3 method for class 'merMod'
    family(object, ...)
    ## S3 method for class 'merMod'
    formula(x, fixed.only = FALSE, random.only = FALSE, ...)
    ## S3 method for class 'merMod'
    fitted(object, ...)
    ## S3 method for class 'merMod'
    logLik(object, REML = NULL, ...)
    ## S3 method for class 'merMod'
    nobs(object, ...)
    ## S3 method for class 'merMod'
    ngrps(object, ...)
    ## S3 method for class 'merMod'
    terms(x, fixed.only = TRUE, random.only = FALSE, ...)
    ## S3 method for class 'merMod'
    vcov(object, correlation = TRUE, sigm = sigma(object),
    use.hessian = NULL, ...)
    ## S3 method for class 'merMod'
    model.frame(formula, fixed.only = FALSE, ...)
    ## S3 method for class 'merMod'
    model.matrix(object, type = c("fixed", "random", "randomListRaw"), ...)
    ## S3 method for class '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 class 'merMod'
    summary(object, correlation = , use.hessian = NULL, ...)
    ## S3 method for class '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 class 'merMod'
    update(object, formula., ..., evaluate = TRUE)
    ## S3 method for class 'merMod'
    weights(object, type = c("prior", "working"), ...)

### Arguments

`object` | an R object of class `merMod`, i.e., as resulting from `lmer()`, or `glmer()`, etc.
`x` | an R object of class `merMod` or `summary.merMod`, respectively, the latter resulting from `summary(<merMod>)`.
`fit` | an R object of class `merMod`.
`formula` | in the case of `model.frame`, a `merMod` object.
`refit` | 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.
`model.names` | character vectors of model names to be used in the anova table.
`scale` | Not currently used (see `extractAIC`).
`k` | see `extractAIC`.
`REML` | Logical. If `TRUE`, return the restricted log-likelihood rather than the log-likelihood. If `NULL` (the default), set `REML` to `isREML(object)` (see `isREML`).
`fixed.only` | logical indicating if only the fixed effects components (terms or formula elements) are sought. If false, all components, including random ones, are returned.
`random.only` | 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.)

`correlation`

(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.

`use.hessian`

(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.

`sigm` | the residual standard error; by default `sigma(object)`.
`digits` | number of significant digits for printing
`symbolic.cor` | should a symbolic encoding of the fixed-effects correlation matrix be printed? If so, the `symnum` function is used.
`signif.stars` | (logical) should significance stars be used?
`ranef.comp` | character vector of length one or two, indicating if random-effects parameters should be reported on the variance and/or standard deviation scale.
`show.resids` | should the quantiles of the scaled residuals be printed?
`formula.` | see `update.formula`.
`evaluate` | see `update`.

`type`

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):

`anova`:

  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 LM if fitted with `REML = TRUE`, this can be controlled via the `refit` argument. See also `anova`.

`coef`:

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

`extractAIC`:

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

`family`:

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

`fitted`:

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

`logLik`:

  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`.

`model.frame`:

  returns the `frame` slot of `merMod`.

`model.matrix`:

  returns the fixed effects model matrix.

`nobs`, `ngrps`:

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

`summary`:

  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`.

`print.summary`:

  Controls the output for the summary method.

`vcov`:

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

`update`:

  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`
absolute | `object@resp$aic()` | `-2*logLik(object)`

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.

### Slots

`resp`:

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

`Gp`:

  See `getME`.

`call`:

  The matched call.

`frame`:

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

`flist`:

  See `getME`.

`cnms`:

  See `getME`.

`lower`:

  See `getME`.

`theta`:

  Covariance parameter vector.

`beta`:

  Fixed effects coefficients.

`u`:

  Conditional model of spherical random effects coefficients.

`devcomp`:

  See `getME`.

`pp`:

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

`optinfo`:

  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`.

### Examples

    showClass("merMod")
    methods(class="merMod")## over 30  (S3) methods available

    ## -> example(lmer)  for an example of vcov.merMod()

[Package lme4 version 1.1-12 Index]