Linear Mixed-Models with Plausible Values

Fits a linear mixed-effects model using lmer and plausible values.

Usage

lmerPV(
  formula,
  data = NULL,
  weights = NULL,
  pvs,
  relatedpvs = TRUE,
  grandmean = NULL,
  groupmean = NULL,
  group = NULL,
  nullmodel = FALSE,
  barnardrubin = TRUE,
  ...
)

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).

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.

pvs

a list indicating which variables from formula should be replaced by which plausible values variables. For more details check the examples.

relatedpvs

a logical value indicating if pvs are drawn from the same model, and have the same number of plausible values. If TRUE (default), a total of \(n\) estimations will be done, where \(n\) is the number of plausible values for each plausible value variable. If FALSE, a total of \(n_1 \times n_2 \times n_...\) estimations will be done, where \(n_i\) is the number of plausible values in each plausible value variable.

grandmean

a character vector indicating the names of columns of data to which grand-mean should be applied.

groupmean

a character vector indicating the names of columns of data to which group-mean should be applied.

group

a string specifying the variable name (within df) to be used for grouping. Categories in group are treated as independent, e.g., countries.

nullmodel

a logical value indicating if the null model should also be estimated.

barnardrubin

a logical value indicating if Barnard & Rubin adjustment should be used for estimating the degrees of freedom. Default is TRUE.

...

Arguments passed on to lme4::lmer

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.
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).

Value

a list.

Examples

# Null model - with PVs
## Named list, with element names matching formula variables
pvs = list(MATH = paste0("Math",1:5))


m1 <- lmerPV(formula = MATH ~ 1 + (1|GROUP), # Intercept varies across GROUP
      pvs = pvs, # Named list
      data = repdata, # Data frame
      weights = repdata$wt) # Weights vector
m1
#> 5 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Multilevel results with PVs:
#>  
#> Call: 
#> lmerPV(formula = MATH ~ 1 + (1 | GROUP), data = repdata, weights = repdata$wt, 
#>     pvs = pvs)
#> 
#> Random effects:
#>                    Variance
#> GROUP.(Intercept) 0.3498329
#> Residual          1.2185299
#> 
#> Fixed effects:
#>                Estimate Std. Error   t value       df Pr(>|t|)
#> (Intercept) 0.004824544   0.341747 0.0141173 4982.124 0.988737
#> --------------------------------------------------------------------------------
#> Estimated models:
#> Math1 ~ 1 + (1 | GROUP)
#> Math2 ~ 1 + (1 | GROUP)
#> Math3 ~ 1 + (1 | GROUP)
#> Math4 ~ 1 + (1 | GROUP)
#> Math5 ~ 1 + (1 | GROUP)

## Fixed effects
m1$fixef
#>                Estimate Std. Error   t value       df Pr(>|t|)
#> (Intercept) 0.004824544   0.341747 0.0141173 4982.124 0.988737

## Random effects
m1$ranef
#>                    Variance
#> GROUP.(Intercept) 0.3498329
#> Residual          1.2185299

## Models for each PV
summary(m1$models)
#>       Length Class   Mode
#> Math1 1      lmerMod S4  
#> Math2 1      lmerMod S4  
#> Math3 1      lmerMod S4  
#> Math4 1      lmerMod S4  
#> Math5 1      lmerMod S4  

# Multiple regression
## Named list, with element names matching formula variables
pvs = list(MATH = paste0("Math",1:5))


m2 <- lmerPV(formula = MATH ~ 1 + GENDER + SES + schoolSES + (1|GROUP),
             pvs = pvs, # Named list
             data = repdata, # Data frame
             weights = repdata$wt) # Weights vector
m2
#> 5 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Multilevel results with PVs:
#>  
#> Call: 
#> lmerPV(formula = MATH ~ 1 + GENDER + SES + schoolSES + (1 | GROUP), 
#>     data = repdata, weights = repdata$wt, pvs = pvs)
#> 
#> Random effects:
#>                       Variance
#> GROUP.(Intercept) 0.0002756404
#> Residual          0.8381211936
#> 
#> Fixed effects:
#>                Estimate Std. Error    t value       df     Pr(>|t|)
#> (Intercept) -64.9990035 3.90253673 -16.655578 7.010247 6.773595e-07
#> GENDER       -0.8990175 0.07564016 -11.885452 4.651592 1.173057e-04
#> SES           0.2458926 0.06342425   3.876950 4.152052 1.666901e-02
#> schoolSES     1.0641781 0.12298663   8.652795 4.979792 3.476117e-04
#> --------------------------------------------------------------------------------
#> Estimated models:
#> Math1 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math2 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math3 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math4 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math5 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)

# Multiple regression with grandmean centering
## Named list, with element names matching formula variables
pvs = list(MATH = paste0("Math",1:5))


m3 <- lmerPV(formula = MATH ~ 1 + GENDER + SES + schoolSES + (1|GROUP),
             pvs = pvs, # Named list
             data = repdata, # Data frame
             weights = repdata$wt,
             grandmean = c("SES","schoolSES"))
m3
#> 5 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Multilevel results with PVs:
#>  
#> Call: 
#> lmerPV(formula = MATH ~ 1 + GENDER + SES + schoolSES + (1 | GROUP), 
#>     data = repdata, weights = repdata$wt, pvs = pvs, grandmean = c("SES", 
#>         "schoolSES"))
#> 
#> Random effects:
#>                       Variance
#> GROUP.(Intercept) 0.0002756404
#> Residual          0.8381211936
#> 
#> Fixed effects:
#>               Estimate Std. Error    t value       df     Pr(>|t|)
#> (Intercept)  0.4589106 0.03739158  12.273100 6.660211 8.094989e-06
#> GENDER      -0.8990175 0.07564016 -11.885452 4.651592 1.173057e-04
#> SES          0.2458926 0.06342425   3.876950 4.152052 1.666901e-02
#> schoolSES    1.0641781 0.12298663   8.652795 4.979792 3.476117e-04
#> --------------------------------------------------------------------------------
#> Estimated models:
#> Math1 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math2 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math3 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math4 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math5 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)

# Multiple regression with groupmean centering
## Named list, with element names matching formula variables
pvs = list(MATH = paste0("Math",1:5))


m4 <- lmerPV(formula = MATH ~ 1 + GENDER + SES + schoolSES + (1|GROUP),
             pvs = pvs, # Named list
             data = repdata, # Data frame
             weights = repdata$wt,
             grandmean = "schoolSES",
             groupmean = "SES",
             group = repdata$GROUP)
m4
#> 5 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Multilevel results with PVs:
#>  
#> Call: 
#> lmerPV(formula = MATH ~ 1 + GENDER + SES + schoolSES + (1 | GROUP), 
#>     data = repdata, weights = repdata$wt, pvs = pvs, grandmean = "schoolSES", 
#>     groupmean = "SES", group = repdata$GROUP)
#> 
#> Random effects:
#>                     Variance
#> GROUP.(Intercept) 0.00028522
#> Residual          0.83812119
#> 
#> Fixed effects:
#>               Estimate Std. Error    t value       df     Pr(>|t|)
#> (Intercept)  0.4589091 0.03743452  12.258983 6.690742 7.869635e-06
#> GENDER      -0.8990154 0.07564056 -11.885362 4.651586 1.173108e-04
#> SES          0.2458884 0.06342472   3.876855 4.152046 1.667043e-02
#> schoolSES    1.3102965 0.07847520  16.696950 7.038119 6.399173e-07
#> --------------------------------------------------------------------------------
#> Estimated models:
#> Math1 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math2 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math3 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math4 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)
#> Math5 ~ 1 + GENDER + SES + schoolSES + (1 | GROUP)