pool.mids.nmi: Pooling for Nested Multiple Imputation

Description

Statistical inference for scalar parameters for nested multiply imputed datasets (Rubin, 2003; Harel & Schafer, 2002, 2003; Reiter & Raghanuthan, 2007; Harel, 2007).

The NMIcombine (pool_nmi as a synonym) and NMIextract functions are extensions of mitools::MIcombine and mitools::MIextract.

Usage

pool.mids.nmi(object, method="largesample")
NMIcombine( qhat, u=NULL, se=NULL, NMI=TRUE, comp_cov=TRUE, is_list=TRUE,
       method=1)
pool_nmi( qhat, u=NULL, se=NULL, NMI=TRUE, comp_cov=TRUE, is_list=TRUE,
       method=1)
NMIextract(results, expr, fun)
# S3 method for mipo.nmi
summary(object, digits=4, ...)
# S3 method for mipo.nmi
coef(object, ...)
# S3 method for mipo.nmi
vcov(object, ...)

Value

Object of class mipo.nmi with following entries

qhat: Estimated parameters in all imputed datasets
u: Estimated covariance matrices of parameters in all imputed datasets
qbar: Estimated parameter
ubar: Average estimated variance within imputations
Tm: Total variance of parameters
df: Degrees of freedom
lambda: Total fraction of missing information
lambda_Between: Fraction of missing information of between imputed datasets (first stage imputation)
lambda_Within: Fraction of missing information of within imputed datasets (second stage imputation)

Arguments

object: Object of class mids.nmi. For summary it must be an object of class mipo.nmi.
method: For pool.mids.nmi: Method for calculating degrees of freedom. Until now, only the method "largesample" is available.
For NMIcombine and pool_nmi: Computation method of fraction of missing information. method=1 is due to Harel and Schafer (2003) or Shen (2007). method=2 is due to Harel and Schafer (2002) and is coherent to the calculation for multiply imputed datasets, while the former method is not.
qhat: List of lists of parameter estimates. In case of an ordinary imputation it can only be a list.
u: Optional list of lists of covariance matrices of parameter estimates
se: Optional vector of standard errors. This argument overwrites u if it is provided.
NMI: Optional logical indicating whether the NMIcombine function should be applied for results of nested multiply imputed datasets. It is set to FALSE if only a list results of multiply imputed datasets is available.
comp_cov: Optional logical indicating whether covariances between parameter estimates should be estimated.
is_list: Optional logical indicating whether qhat and u are provided as lists as an input. If is_list=FALSE, appropriate arrays can be used as input.
results: A list of objects
expr: An expression
fun: A function of one argument
digits: Number of digits after decimal for printing results in summary.
...: Further arguments to be passed.

References

Harel, O., & Schafer, J. (2002). Two stage multiple imputation. Joint Statistical Meetings - Biometrics Section.

Harel, O., & Schafer, J. (2003). Multiple imputation in two stages. In Proceedings of Federal Committee on Statistical Methodology 2003 Conference.

Harel, O. (2007). Inferences on missing information under multiple imputation and two-stage multiple imputation. Statistical Methodology, 4(1), 75-89. tools:::Rd_expr_doi("10.1016/j.stamet.2006.03.002")

Reiter, J. P. and Raghunathan, T. E. (2007). The multiple adaptations of multiple imputation. Journal of the American Statistical Association, 102(480), 1462-1471. tools:::Rd_expr_doi("10.1198/016214507000000932")

Rubin, D. B. (2003). Nested multiple imputation of NMES via partially incompatible MCMC. Statistica Neerlandica, 57(1), 3-18. tools:::Rd_expr_doi("10.1111/1467-9574.00217")

Examples

Run this code

if (FALSE) {
#############################################################################
# EXAMPLE 1: Nested multiple imputation and statistical inference
#############################################################################

library(BIFIEsurvey)
data(data.timss2, package="BIFIEsurvey" )
datlist <- data.timss2
# remove first four variables
M <- length(datlist)
for (ll in 1:M){
    datlist[[ll]] <- datlist[[ll]][, -c(1:4) ]
               }

#***************
# (1) nested multiple imputation using mice
imp1 <- miceadds::mice.nmi( datlist,  m=3, maxit=2 )
summary(imp1)

#***************
# (2) first linear regression: ASMMAT ~ migrant + female
res1 <- with( imp1, stats::lm( ASMMAT ~ migrant + female ) ) # fit
pres1 <- miceadds::pool.mids.nmi( res1 )  # pooling
summary(pres1)  # summary
coef(pres1)
vcov(pres1)

#***************
# (3) second linear regression: likesc ~ migrant + books
res2 <- with( imp1, stats::lm( likesc ~ migrant + books  ) )
pres2 <- miceadds::pool.mids.nmi( res2 )
summary(pres2)

#***************
# (4) some descriptive statistics using the mids.nmi object
res3 <- with( imp1, c( "M_lsc"=mean(likesc), "SD_lsc"=stats::sd(likesc) ) )
pres3 <- miceadds::NMIcombine( qhat=res3$analyses )
summary(pres3)

#*************
# (5) apply linear regression based on imputation list

# convert mids object to datlist
datlist2 <- miceadds::mids2datlist( imp1 )
str(datlist2, max.level=1)

# double application of lapply to the list of list of nested imputed datasets
res4 <- lapply( datlist2, FUN=function(dl){
    lapply( dl, FUN=function(data){
            stats::lm( ASMMAT ~ migrant + books, data=data )
                                } )
                }  )

# extract coefficients
qhat <- lapply( res4, FUN=function(bb){
            lapply( bb, FUN=function(ww){
                    coef(ww)
                        } )
                } )
# shorter function
NMIextract( results=res4, fun=coef )

# extract covariance matrices
u <- lapply( res4, FUN=function(bb){
            lapply( bb, FUN=function(ww){
                    vcov(ww)
                        } )
                } )
# shorter function
NMIextract( results=res4, fun=vcov )

# apply statistical inference using the NMIcombine function
pres4 <- miceadds::NMIcombine( qhat=qhat, u=u )
summary(pres4)

#--- statistical inference if only standard errors are available
# extract standard errors
se <- lapply( res4, FUN=function(bb){
            lapply( bb, FUN=function(ww){
                # ww <- res4[[1]][[1]]
                sww <- summary(ww)
                sww$coef[,"Std. Error"]
                        } )
                } )
se
# apply NMIcombine function
pres4b <- miceadds::NMIcombine( qhat=qhat, se=se )
# compare results
summary(pres4b)
summary(pres4)

#############################################################################
# EXAMPLE 2: Some comparisons for a multiply imputed dataset
#############################################################################

library(mitools)
data(data.ma02)

# save dataset as imputation list
imp <- mitools::imputationList( data.ma02 )
print(imp)
# save dataset as an mids object
imp1 <- miceadds::datlist2mids( imp )

# apply linear model based on imputationList
mod <- with( imp, stats::lm( read ~ hisei + female ) )
# same linear model based on mids object
mod1 <- with( imp1, stats::lm( read ~ hisei + female ) )

# extract coefficients
cmod <- mitools::MIextract( mod, fun=coef)
# extract standard errors
semod <- lapply( mod, FUN=function(mm){
                smm <- summary(mm)
                smm$coef[,"Std. Error"]
                        } )
# extract covariance matrix
vmod <- mitools::MIextract( mod, fun=vcov)

#*** pooling with NMIcombine with se (1a) and vcov (1b) as input
pmod1a <- miceadds::NMIcombine( qhat=cmod, se=semod, NMI=FALSE )
pmod1b <- miceadds::NMIcombine( qhat=cmod, u=vmod, NMI=FALSE )
# use method 2 which should conform to MI inference of mice::pool
pmod1c <- miceadds::NMIcombine( qhat=cmod, u=vmod, NMI=FALSE, method=2)

#*** pooling with mitools::MIcombine function
pmod2 <- mitools::MIcombine( results=cmod, variances=vmod )
#*** pooling with mice::pool function
pmod3a <- mice::pool( mod1 )
pmod3b <- mice::pool( mod1, method="Rubin")

#--- compare results
summary(pmod1a)   # method=1  (the default)
summary(pmod1b)   # method=1  (the default)
summary(pmod1c)   # method=2
summary(pmod2)
summary(pmod3a)
summary(pmod3b)
}