# lmer {lme4}

Fit Linear Mixed-Effects Models

### Description

Fit a linear mixed-effects model (LMM) to data, via REML or maximum likelihood.

### Usage

lmer(formula, data = NULL, REML = TRUE, control = lmerControl(), start = NULL, verbose = 0L, subset, weights, na.action, offset, contrasts = NULL, devFunOnly = FALSE, ...)

### Arguments

- formula
- a two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a
`~`

operator and the terms, separated by`+`

operators, on the right. Random-effects terms are distinguished by vertical bars (`"|"`

) separating expressions for design matrices from grouping factors. Two vertical bars (`"||"`

) can be used to specify multiple uncorrelated random effects for the same grouping variable. - data
- an optional data frame containing the variables named in
`formula`

. By default the variables are taken from the environment from which`lmer`

is called. While`data`

is optional, the package authors*strongly*recommend its use, especially when later applying methods such as`update`

and`drop1`

to the fitted model (*such methods are not guaranteed to work properly if*). If`data`

is omitted`data`

is omitted, variables will be taken from the environment of`formula`

(if specified as a formula) or from the parent frame (if specified as a character vector). - REML
- logical scalar - Should the estimates be chosen to optimize the REML criterion (as opposed to the log-likelihood)?
- control
- a list (of correct class, resulting from
`lmerControl()`

or`glmerControl()`

respectively) containing control parameters, including the nonlinear optimizer to be used and parameters to be passed through to the nonlinear optimizer, see the`*lmerControl`

documentation for details. - start
- a named
`list`

of starting values for the parameters in the model. For`lmer`

this can be a numeric vector or a list with one component named`"theta"`

. - verbose
- integer scalar. If
`> 0`

verbose output is generated during the optimization of the parameter estimates. If`> 1`

verbose output is generated during the individual PIRLS steps. - subset
- an optional expression indicating the subset of the rows of
`data`

that should be used in the fit. This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default. - weights
- an optional vector of ‘prior weights’ to be used in the fitting process. Should be
`NULL`

or a numeric vector. Prior`weights`

are*not*normalized or standardized in any way. In particular, the diagonal of the residual covariance matrix is the squared residual standard deviation parameter`sigma`

times the vector of inverse`weights`

. Therefore, if the`weights`

have relatively large magnitudes, then in order to compensate, the`sigma`

parameter will also need to have a relatively large magnitude. - na.action
- a function that indicates what should happen when the data contain
`NA`

s. The default action (`na.omit`

, inherited from the 'factory fresh' value of`getOption("na.action")`

) strips any observations with any missing values in any variables. - offset
- this can be used to specify an
*a priori*known component to be included in the linear predictor during fitting. This should be`NULL`

or a numeric vector of length equal to the number of cases. One or more`offset`

terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See`model.offset`

. - contrasts
- an optional list. See the
`contrasts.arg`

of`model.matrix.default`

. - devFunOnly
- logical - return only the deviance evaluation function. Note that because the deviance function operates on variables stored in its environment, it may not return
*exactly*the same values on subsequent calls (but the results should always be within machine tolerance). - ...
- other potential arguments. A
`method`

argument was used in earlier versions of the package. Its functionality has been replaced by the`REML`

argument.

### Details

- If the
`formula`

argument is specified as a character vector, the function will attempt to coerce it to a formula. However, this is not recommended (users who want to construct formulas by pasting together components are advised to use`as.formula`

or`reformulate`

); model fits will work but subsequent methods such as`drop1`

,`update`

may fail. - Unlike some simpler modeling frameworks such as
`lm`

and`glm`

which automatically detect perfectly collinear predictor variables,`[gn]lmer`

cannot handle design matrices of less than full rank. For example, in cases of models with interactions that have unobserved combinations of levels, it is up to the user to define a new variable (for example creating`ab`

within the data from the results of`interaction(a,b,drop=TRUE)`

). - the deviance function returned when
`devFunOnly`

is`TRUE`

takes a single numeric vector argument, representing the`theta`

vector. This vector defines the scaled variance-covariance matrices of the random effects, in the Cholesky parameterization. For models with only simple (intercept-only) random effects,`theta`

is a vector of the standard deviations of the random effects. For more complex or multiple random effects, running`getME(.,"theta")`

to retrieve the`theta`

vector for a fitted model and examining the names of the vector is probably the easiest way to determine the correspondence between the elements of the`theta`

vector and elements of the lower triangles of the Cholesky factors of the random effects.

### Values

An object of class `merMod`

, for which many methods are available (e.g. `methods(class="merMod")`

)

### See Also

`lm`

for linear models; `glmer`

for generalized linear and `nlmer`

for nonlinear mixed models.

### Examples

## linear mixed models - reference values from older code (fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)) summary(fm1)# (with its own print method; see class?merMod % ./merMod-class.Rd str(terms(fm1)) stopifnot(identical(terms(fm1, fixed.only=FALSE), terms(model.frame(fm1)))) attr(terms(fm1, FALSE), "dataClasses") # fixed.only=FALSE needed for dataCl. fm1_ML <- update(fm1,REML=FALSE) (fm2 <- lmer(Reaction ~ Days + (Days || Subject), sleepstudy)) anova(fm1, fm2) sm2 <- summary(fm2) print(fm2, digits=7, ranef.comp="Var") # the print.merMod() method print(sm2, digits=3, corr=FALSE) # the print.summary.merMod() method (vv <- vcov.merMod(fm2, corr=TRUE)) as(vv, "corMatrix")# extracts the ("hidden") 'correlation' entry in @factors ## Fit sex-specific variances by constructing numeric dummy variables ## for sex and sex:age; in this case the estimated variance differences ## between groups in both intercept and slope are zero ... data(Orthodont,package="nlme") Orthodont$nsex <- as.numeric(Orthodont$Sex=="Male") Orthodont$nsexage <- with(Orthodont, nsex*age) lmer(distance ~ age + (age|Subject) + (0+nsex|Subject) + (0 + nsexage|Subject), data=Orthodont)

Documentation reproduced from package lme4, version 1.1-10. License: GPL (>= 2)