lmer
Fit Linear Mixed-Effects Models
Fit a linear mixed-effects model (LMM) to data, via REML or maximum likelihood.
- Keywords
- models
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. (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, seedummy
or thelmer_alt
function from theafex
package.)- data
an optional data frame containing the variables named in
formula
. By default the variables are taken from the environment from whichlmer
is called. Whiledata
is optional, the package authors strongly recommend its use, especially when later applying methods such asupdate
anddrop1
to the fitted model (such methods are not guaranteed to work properly ifdata
is omitted). Ifdata
is omitted, variables will be taken from the environment offormula
(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()
orglmerControl()
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. Forlmer
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. Priorweights
are not normalized or standardized in any way. In particular, the diagonal of the residual covariance matrix is the squared residual standard deviation parametersigma
times the vector of inverseweights
. Therefore, if theweights
have relatively large magnitudes, then in order to compensate, thesigma
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 ofgetOption("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 moreoffset
terms can be included in the formula instead or as well, and if more than one is specified their sum is used. Seemodel.offset
.- contrasts
an optional list. See the
contrasts.arg
ofmodel.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 theREML
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 useas.formula
orreformulate
); model fits will work but subsequent methods such asdrop1
,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 aslm
andglm
. While it does automatically drop collinear variables (with a message rather than a warning), it does not automatically fill inNA
values for the dropped coefficients; these can be added viafixef(fitted.model,add.dropped=TRUE)
. This information can also be retrieved viaattr(getME(fitted.model,"X"),"col.dropped")
.the deviance function returned when
devFunOnly
isTRUE
takes a single numeric vector argument, representing thetheta
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, runninggetME(.,"theta")
to retrieve thetheta
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 thetheta
vector and elements of the lower triangles of the Cholesky factors of the random effects.
Value
An object of class merMod
(more specifically,
an object of subclass lmerMod
), 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
# 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)
# }