lmer: Fit Linear Mixed-Effects Models

Description Usage Arguments Details Value See Also Examples

View source: R/lmer.R

Description

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

Usage

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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, 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 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.

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

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

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## 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)

Example output

Loading required package: Matrix
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) 24.740       
          Days         5.922   0.07
 Residual             25.592       
Number of obs: 180, groups:  Subject, 18
Fixed Effects:
(Intercept)         Days  
     251.41        10.47  
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) 612.09   24.740       
          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   36.84
Days          10.467      1.546    6.77

Correlation of Fixed Effects:
     (Intr)
Days -0.138
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: R_GlobalEnv> 
  ..- attr(*, "predvars")= language list(Reaction, Days)
 Reaction      Days   Subject 
"numeric" "numeric"  "factor" 
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  
refitting model(s) with ML (instead of REML)
Data: sleepstudy
Models:
fm2: Reaction ~ Days + ((1 | Subject) + (0 + Days | Subject))
fm1: Reaction ~ Days + (Days | Subject)
    Df    AIC    BIC  logLik deviance  Chisq Chi 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
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) 627.5691
 Subject.1 Days         35.8582
 Residual              653.5838
Number of obs: 180, groups:  Subject, 18
Fixed Effects:
(Intercept)         Days  
  251.40510     10.46729  
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    36.5
Days           10.47       1.56     6.7
2 x 2 Matrix of class "dpoMatrix"
            (Intercept)      Days
(Intercept)   47.408479 -1.980557
Days          -1.980557  2.432246
2 x 2 Matrix of class "corMatrix"
            (Intercept)       Days
(Intercept)   1.0000000 -0.1844402
Days         -0.1844402  1.0000000
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) 2.3270        
           age         0.2264   -0.61
 Subject.1 nsex        0.0000        
 Subject.2 nsexage     0.0000        
 Residual              1.3100        
Number of obs: 108, groups:  Subject, 27
Fixed Effects:
(Intercept)          age  
    16.7611       0.6602  

lme4 documentation built on May 1, 2019, 8:02 p.m.