withinBetween {mlmi}

Within between variance estimation

Description

This function implements the within-between variance estimation approach. If the imputations were generated using posterior draws, it implements the approach proposed by Barnard & Rubin (1999). If posterior draws were not used, it implements the WB approach described by von Hippel and Bartlett (2021).

Usage

withinBetween(imps, analysisFun, pd = NULL, dfComplete = NULL, ...)

Arguments

imps

A list of imputed datasets produced by one of the imputation functions in mlmi or another package.

analysisFun

A function to analyse the imputed datasets that when applied to a dataset returns a list containing a vector est and covariance matrix var.

pd

If imps was not generated by one of the imputation functions in mlmi, this argument must be specified to indicate whether the imputations were generated using posterior draws (TRUE) or not (FALSE).

dfComplete

The complete data degrees of freedom. If analysisFun returns a vector of parameter estimates, dfComplete should be a vector of the same length. If not specified, it is assumed that the complete data degrees of freedom is effectively infinite (1e+05).

...

Other parameters that are to be passed through to analysisFun.

Value

A list containing the overall parameter estimates, its corresponding covariance matrix, and degrees of freedom for each parameter.

References

Barnard J, Rubin DB. Miscellanea. Small-sample degrees of freedom with multiple imputation. Biometrika 1999; 86(4): 948-955. doi:10.1093/biomet/86.4.948

von Hippel P.T. and Bartlett J.W. Maximum likelihood multiple imputation: faster, more efficient imputation without posterior draws. Statistical Science 2021; 36(3) 400-420 doi:10.1214/20-STS793.

Examples

#simulate a partially observed dataset
set.seed(1234)
n <- 100
x <- rnorm(n)
y <- x+rnorm(n)
y[1:50] <- NA
temp <- data.frame(x,y)

#impute using normImp
imps <- normImp(temp, M=100, pd=TRUE, rseed=4423)

#define a function which analyses a dataset using our desired
#analysis model, returning the estimated parameters and their
#corresponding variance covariance matrix
analysisFun <- function(inputData) {
  mod <- lm(y~x, data=inputData)
  list(est=coef(mod), var=vcov(mod))
}
withinBetween(imps,analysisFun, dfComplete=c(n-2,n-2))