lmer with multiply imputed data

You can do this somewhat by hand if by taking advantage of the lapply functionality in R and the list-structure returned by the Amelia multiple imputation package. Here’s a quick example script.

library(Amelia)
library(lme4)
library(merTools)
library(plyr) # for collapsing estimates

Amelia is similar to mice so you can just substitute your variables in from the mice call here — this example is from a project I was working on.

 a.out <- amelia(dat[sub1, varIndex], idvars = "SCH_ID", 
            noms = varIndex[!varIndex %in% c("SCH_ID", "math12")], 
            m = 10)

a.out is the imputation object, now we need to run the model on each imputed dataset. To do this, we use the lapply function in R to repeat a function over list elements. This function applies the function — which is the model specification — to each dataset (d) in the list and returns the results in a list of models.

 mods <- lapply(a.out$imputations,
           function(d) lmer((log(wage) ~ gender + age + age_sqr + 
            occupation + degree + private_sector + overtime + 
             (1+gender|faculty), data = d)

Now we create a data.frame from that list, by simulating the values the fixed and random effects using the functions FEsim and REsim from the merTools package

imputeFEs <- ldply(mods, FEsim, nsims = 1000)
imputeREs <- ldply(mods, REsim, nsims = 1000)

The data.frames above include separate estimates for each dataset, now we need to combine them using a collapse like argument collapse

imputeREs <- ddply(imputeREs, .(X1, X2), summarize, mean = mean(mean), 
               median = mean(median), sd = mean(sd), 
               level = level[1])

imputeFEs <- ddply(imputeFEs, .(var), summarize, meanEff = mean(meanEff), 
               medEff = mean(medEff), sdEff = mean(sdEff))

Now we can also extract some statistics on the variance/covariance for the random effects across the imputed values. Here I have written two simple extractor functions to do this.

REsdExtract <- function(model){
  out <- unlist(lapply(VarCorr(model), attr, "stddev"))
  return(out)
}

REcorrExtract <- function(model){
  out <- unlist(lapply(VarCorr(model), attr, "corre"))
  return(min(unique(out)))
}

And now we can apply them to the models and store them as a vector:

modStats <- cbind(ldply(mods, REsdExtract), ldply(mods, REcorrExtract))

Update

The functions below will get you much closer to the output provided by arm::display by operating on the list of lmer or glmer objects. Hopefully this will be incorporated into the merTools package in the near future:

# Functions to extract standard deviation of random effects from model
REsdExtract <- function(model){
  out <- unlist(lapply(VarCorr(model), attr, "stddev"))
  return(out)
}

#slope intercept correlation from model
REcorrExtract <- function(model){
  out <- unlist(lapply(VarCorr(model), attr, "corre"))
  return(min(unique(out)))
}

modelRandEffStats <- function(modList){
  SDs <- ldply(modList, REsdExtract)
  corrs <- ldply(modList, REcorrExtract)
  tmp <- cbind(SDs, corrs)
  names(tmp) <- c("Imp", "Int", "Slope", "id", "Corr")
  out <- data.frame(IntSD_mean = mean(tmp$Int), 
                        SlopeSD_mean = mean(tmp$Slope), 
                    Corr_mean = mean(tmp$Corr), 
                        IntSD_sd = sd(tmp$Int),
                    SlopeSD_sd = sd(tmp$Slope), 
                        Corr_sd = sd(tmp$Corr))
  return(out)
}

modelFixedEff <- function(modList){
  require(broom)
  fixEst <- ldply(modList, tidy, effects = "fixed")
  # Collapse
  out <- ddply(fixEst, .(term), summarize,
               estimate = mean(estimate), 
               std.error = mean(std.error))
  out$statistic <- out$estimate / out$std.error
  return(out)
}

print.merModList <- function(modList, digits = 3){
  len <- length(modList)
  form <- modList[[1]]@call
  print(form)
  cat("\nFixed Effects:\n")
  fedat <- modelFixedEff(modList)
  dimnames(fedat)[[1]] <- fedat$term
  pfround(fedat[-1, -1], digits)
  cat("\nError Terms Random Effect Std. Devs\n")
  cat("and covariances:\n")
  cat("\n")
  ngrps <- length(VarCorr(modmathG[[1]]))
  errorList <- vector(mode = 'list', length = ngrps)
  corrList <- vector(mode = 'list', length = ngrps)
  for(i in 1:ngrps){
    subList <- lapply(modList, function(x) VarCorr(x)[[i]])
    subList <- apply(simplify2array(subList), 1:2, mean)
    errorList[[i]] <- subList
    subList <- lapply(modList, function(x) attr(VarCorr(x)[[i]], "corre"))
    subList <- min(unique(apply(simplify2array(subList), 1:2, function(x) mean(x))))
    corrList[[i]] <- subList
  }
  errorList <- lapply(errorList, function(x) {
    diag(x) <- sqrt(diag(x))
    return(x)
    })

  lapply(errorList, pfround, digits)
  cat("\nError Term Correlations:\n")
  lapply(corrList, pfround, digits)
  residError <- mean(unlist(lapply(modList, function(x) attr(VarCorr(x), "sc"))))
  cat("\nResidual Error =", fround(residError,
                                             digits), "\n")
  cat("\n---Groups\n")
  ngrps <- lapply(modList[[1]]@flist, function(x) length(levels(x)))
  modn <- getME(modList[[1]], "devcomp")$dims["n"]
  cat(sprintf("number of obs: %d, groups: ", modn))
  cat(paste(paste(names(ngrps), ngrps, sep = ", "),
            collapse = "; "))
  cat("\n")
  cat("\nModel Fit Stats")
  mAIC <- mean(unlist(lapply(modList, AIC)))
  cat(sprintf("\nAIC = %g", round(mAIC, 1)))
  moDsigma.hat <- mean(unlist(lapply(modmathG, sigma)))
  cat("\nOverdispersion parameter =", fround(moDsigma.hat,
                                             digits), "\n")
}