miceadds (version 2.2-0)

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)
"summary"(object, digits=4, ...)
"coef"(object, ...)
"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

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 <- 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 <- 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 <- 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 <- NMIcombine( qhat = res3$analyses )
# summary(pres3)
# 
# #*************
# # (5) apply linear regression based on imputation list
# 
# # convert mids object to datlist
# datlist2 <- mids2datlist( imp1 )
# str(datlist2, max.level=1)
# 
# # double application of lapply to the list of list of nested imputed datasets
# res4 <- lapply( datlist2 , FUN = function(dl){
#     lapply( dl , FUN = function(data){ 
#             stats::lm( ASMMAT ~ migrant + books  , data = data )
#                                 } )
#                 }  )
#                 
# # extract coefficients
# qhat <- lapply( res4 , FUN = function(bb){
#             lapply( bb , FUN = function(ww){
#                     coef(ww)
#                         } )
#                 } )
# # shorter function
# NMIextract( results=res4 , fun=coef )                
# 
# # extract covariance matrices
# u <- lapply( res4 , FUN = function(bb){
#             lapply( bb , FUN = function(ww){
#                     vcov(ww)
#                         } )
#                 } )        
# # shorter function
# NMIextract( results=res4 , fun=vcov )                               
# 
# # apply statistical inference using the NMIcombine function
# pres4 <- NMIcombine( qhat=qhat , u=u )                
# summary(pres4)
# 
# #--- statistical inference if only standard errors are available     
# # extract standard errors
# se <- lapply( res4 , FUN = function(bb){
#             lapply( bb , FUN = function(ww){
#                 # ww <- res4[[1]][[1]]
#                 sww <- summary(ww)
#                 sww$coef[,"Std. Error"]
#                         } )
#                 } )        
# se
# # apply NMIcombine function
# pres4b <- 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 <- 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 <- NMIcombine( qhat = cmod , se = semod , NMI = FALSE )
# pmod1b <- NMIcombine( qhat = cmod , u = vmod , NMI = FALSE )
# # use method 2 which should conform to MI inference of mice::pool
# pmod1c <- 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)
# ## End(Not run)