lmer.RdFit 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)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.)
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).
logical scalar - Should the estimates be chosen to optimize the REML criterion (as opposed to the log-likelihood)?
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.
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".
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.
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.
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.
a function that indicates what should happen when the
data contain NAs. 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.
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.
an optional list. See the contrasts.arg of
model.matrix.default.
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).
An object of class merMod (more specifically,
an object of subclass lmerMod), for which many methods
are available (e.g. methods(class="merMod"))
In earlier version of the lme4 package, a method argument was
used. Its functionality has been replaced by the REML argument.
Also, lmer(.) allowed a family argument (to effectively
switch to glmer(.)). This has been deprecated in summer 2013,
and been disabled in spring 2019.
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.
## linear mixed models - reference values from older code
(fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy))
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#> Data: sleepstudy
#> REML criterion at convergence: 1743.628
#> Random effects:
#> Groups Name Std.Dev. Corr
#> Subject (Intercept) 24.741
#> Days 5.922 0.07
#> Residual 25.592
#> Number of obs: 180, groups: Subject, 18
#> Fixed Effects:
#> (Intercept) Days
#> 251.41 10.47
summary(fm1)# (with its own print method; see class?merMod % ./merMod-class.Rd
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#> Data: sleepstudy
#>
#> REML criterion at convergence: 1743.6
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -3.9536 -0.4634 0.0231 0.4634 5.1793
#>
#> Random effects:
#> Groups Name Variance Std.Dev. Corr
#> Subject (Intercept) 612.10 24.741
#> Days 35.07 5.922 0.07
#> Residual 654.94 25.592
#> Number of obs: 180, groups: Subject, 18
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 251.405 6.825 36.838
#> Days 10.467 1.546 6.771
#>
#> Correlation of Fixed Effects:
#> (Intr)
#> Days -0.138
str(terms(fm1))
#> Classes 'terms', 'formula' language Reaction ~ Days
#> ..- attr(*, "variables")= language list(Reaction, Days)
#> ..- attr(*, "factors")= int [1:2, 1] 0 1
#> .. ..- attr(*, "dimnames")=List of 2
#> .. .. ..$ : chr [1:2] "Reaction" "Days"
#> .. .. ..$ : chr "Days"
#> ..- attr(*, "term.labels")= chr "Days"
#> ..- attr(*, "order")= int 1
#> ..- attr(*, "intercept")= int 1
#> ..- attr(*, "response")= int 1
#> ..- attr(*, ".Environment")=<environment: 0x55a2f2ddde48>
#> ..- attr(*, "predvars")= language list(Reaction, Days)
stopifnot(identical(terms(fm1, fixed.only=FALSE),
terms(model.frame(fm1))))
attr(terms(fm1, FALSE), "dataClasses") # fixed.only=FALSE needed for dataCl.
#> Reaction Days Subject
#> "numeric" "numeric" "factor"
## Maximum Likelihood (ML), and "monitor" iterations via 'verbose':
fm1_ML <- update(fm1, REML=FALSE, verbose = 1)
#> iteration: 1
#> f(x) = 1784.642296
#> iteration: 2
#> f(x) = 1790.125637
#> iteration: 3
#> f(x) = 1798.999624
#> iteration: 4
#> f(x) = 1803.853200
#> iteration: 5
#> f(x) = 1800.613981
#> iteration: 6
#> f(x) = 1798.604631
#> iteration: 7
#> f(x) = 1752.260737
#> iteration: 8
#> f(x) = 1797.587692
#> iteration: 9
#> f(x) = 1754.954110
#> iteration: 10
#> f(x) = 1753.695682
#> iteration: 11
#> f(x) = 1754.816999
#> iteration: 12
#> f(x) = 1753.106734
#> iteration: 13
#> f(x) = 1752.939377
#> iteration: 14
#> f(x) = 1752.256879
#> iteration: 15
#> f(x) = 1752.057448
#> iteration: 16
#> f(x) = 1752.022389
#> iteration: 17
#> f(x) = 1752.022728
#> iteration: 18
#> f(x) = 1751.971687
#> iteration: 19
#> f(x) = 1751.952603
#> iteration: 20
#> f(x) = 1751.948524
#> iteration: 21
#> f(x) = 1751.987176
#> iteration: 22
#> f(x) = 1751.983213
#> iteration: 23
#> f(x) = 1751.951971
#> iteration: 24
#> f(x) = 1751.946276
#> iteration: 25
#> f(x) = 1751.946698
#> iteration: 26
#> f(x) = 1751.947568
#> iteration: 27
#> f(x) = 1751.945312
#> iteration: 28
#> f(x) = 1751.944180
#> iteration: 29
#> f(x) = 1751.943533
#> iteration: 30
#> f(x) = 1751.942441
#> iteration: 31
#> f(x) = 1751.942170
#> iteration: 32
#> f(x) = 1751.942370
#> iteration: 33
#> f(x) = 1751.942278
#> iteration: 34
#> f(x) = 1751.942204
#> iteration: 35
#> f(x) = 1751.941309
#> iteration: 36
#> f(x) = 1751.940931
#> iteration: 37
#> f(x) = 1751.940567
#> iteration: 38
#> f(x) = 1751.940179
#> iteration: 39
#> f(x) = 1751.940082
#> iteration: 40
#> f(x) = 1751.940270
#> iteration: 41
#> f(x) = 1751.941501
#> iteration: 42
#> f(x) = 1751.939489
#> iteration: 43
#> f(x) = 1751.939392
#> iteration: 44
#> f(x) = 1751.939398
#> iteration: 45
#> f(x) = 1751.939425
#> iteration: 46
#> f(x) = 1751.939355
#> iteration: 47
#> f(x) = 1751.939490
#> iteration: 48
#> f(x) = 1751.939363
#> iteration: 49
#> f(x) = 1751.939345
#> iteration: 50
#> f(x) = 1751.939344
#> iteration: 51
#> f(x) = 1751.939345
#> iteration: 52
#> f(x) = 1751.939348
#> iteration: 53
#> f(x) = 1751.939344
(fm2 <- lmer(Reaction ~ Days + (Days || Subject), sleepstudy))
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + ((1 | Subject) + (0 + Days | Subject))
#> Data: sleepstudy
#> REML criterion at convergence: 1743.669
#> Random effects:
#> Groups Name Std.Dev.
#> Subject (Intercept) 25.051
#> Subject.1 Days 5.988
#> Residual 25.565
#> Number of obs: 180, groups: Subject, 18
#> Fixed Effects:
#> (Intercept) Days
#> 251.41 10.47
anova(fm1, fm2)
#> refitting model(s) with ML (instead of REML)
#> Data: sleepstudy
#> Models:
#> fm2: Reaction ~ Days + ((1 | Subject) + (0 + Days | Subject))
#> fm1: Reaction ~ Days + (Days | Subject)
#> npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
#> fm2 5 1762.0 1778.0 -876.00 1752.0
#> fm1 6 1763.9 1783.1 -875.97 1751.9 0.0639 1 0.8004
sm2 <- summary(fm2)
print(fm2, digits=7, ranef.comp="Var") # the print.merMod() method
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + ((1 | Subject) + (0 + Days | Subject))
#> Data: sleepstudy
#> REML criterion at convergence: 1743.669
#> Random effects:
#> Groups Name Variance
#> Subject (Intercept) 627.56905
#> Subject.1 Days 35.85838
#> Residual 653.58350
#> Number of obs: 180, groups: Subject, 18
#> Fixed Effects:
#> (Intercept) Days
#> 251.40510 10.46729
print(sm2, digits=3, corr=FALSE) # the print.summary.merMod() method
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + ((1 | Subject) + (0 + Days | Subject))
#> Data: sleepstudy
#>
#> REML criterion at convergence: 1743.7
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -3.963 -0.463 0.020 0.465 5.186
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> Subject (Intercept) 627.6 25.05
#> Subject.1 Days 35.9 5.99
#> Residual 653.6 25.57
#> Number of obs: 180, groups: Subject, 18
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 251.41 6.89 36.51
#> Days 10.47 1.56 6.71
## 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)
#> boundary (singular) fit: see help('isSingular')
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: distance ~ age + (age | Subject) + (0 + nsex | Subject) + (0 +
#> nsexage | Subject)
#> Data: Orthodont
#> REML criterion at convergence: 442.6367
#> Random effects:
#> Groups Name Std.Dev. Corr
#> Subject (Intercept) 2.3268096
#> age 0.2264158 -0.61
#> Subject.1 nsex 0.0001559
#> Subject.2 nsexage 0.0000000
#> Residual 1.3100560
#> Number of obs: 108, groups: Subject, 27
#> Fixed Effects:
#> (Intercept) age
#> 16.7611 0.6602
#> optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings