miceadds (version 3.2-48)

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, ...)

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.

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)

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.

Reiter, J. P., & Raghunathan, T. E. (2007). The multiple adaptations of multiple imputation. Journal of the American Statistical Association, 102(480), 1462-1471.

Rubin, D. B. (2003). Nested multiple imputation of NMES via partially incompatible MCMC. Statistica Neerlandica, 57(1), 3-18.

See Also

mice::pool, mitools::MIcombine, mitools::MIextract

mice.nmi, MIcombine.NestedImputationResultList

Examples

# NOT RUN {
#############################################################################
# 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)
# }