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

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

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. (Because of the way it is
implemented, the `||`

-syntax *works
only for design matrices containing
numeric (continuous) predictors*; to fit models with independent
categorical effects, see `dummy`

or the `lmer_alt`

function from the `afex`

package.)

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 data is omitted*). If

`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
penalized iteratively reweighted least squares (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.

An object of class `merMod`

(more specifically,
an object of *subclass* `lmerMod`

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

)

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.When handling perfectly collinear predictor variables (i.e. design matrices of less than full rank),

`[gn]lmer`

is not quite as sophisticated as some simpler modeling frameworks such as`lm`

and`glm`

. While it does automatically drop collinear variables (with a message rather than a warning), it does not automatically fill in`NA`

values for the dropped coefficients; these can be added via`fixef(fitted.model,add.dropped=TRUE)`

. This information can also be retrieved via`attr(getME(fitted.model,"X"),"col.dropped")`

.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.

`lm`

for linear models;
`glmer`

for generalized linear; and
`nlmer`

for nonlinear mixed models.

# NOT RUN { ## 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) # }