miceadds (version 2.2-0)

NMIwaldtest: Wald Test for Nested Multiply Imputed Datasets

Description

Performs a Wald test for nested multiply imputed datasets (NMIwaldtest) and ordinary multiply imputed datasets (MIwaldtest), see Reiter and Raghanuthan (2007). The correspondent statistic is also called the $D_1$ statistic.

The function create.designMatrices.waldtest is a helper function for the creation of design matrices.

Usage

NMIwaldtest(qhat, u, Cdes = NULL, rdes = NULL, testnull = NULL)
MIwaldtest(qhat, u, Cdes = NULL, rdes = NULL, testnull = NULL)
"summary"(object,digits=4,...)
"summary"(object,digits=4,...)
create.designMatrices.waldtest( pars , k )

Arguments

qhat

List or array of estimated parameters

u

List or array of estimated covariance matrices of parameters

Cdes

Design matrix $C$ for parameter test (see Details)

rdes

Constant vector $r$ (see Details)

testnull

Vector containing names of parameters which should be tested for a parameter value of zero.

object

Object of class NMIwaldtest

digits

Number of digits after decimal for print

...

Further arguments to be passed

pars

Vector of parameter names

k

Number of linear hypotheses which should be tested

Value

List with following entries

Details

The Wald test is performed for a linear hypothesis $C \bold{\theta} = r$ for a parameter vector $\bold{\theta}$.

References

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

See Also

NMIcombine

Examples

## Not run: 
# #############################################################################
# # EXAMPLE 1: Nested multiple imputation and Wald test | TIMSS data
# #############################################################################
# 
# 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)
# 
# #**** Model 1: Linear regression with interaction effects
# res1 <- with( imp1 , stats::lm( likesc ~ female*migrant + female*books  ) )
# pres1 <- pool.mids.nmi( res1 )
# summary(pres1)
# 
# # test whether both interaction effects equals zero
# pars <- dimnames(pres1$qhat)[[3]]
# des <- create.designMatrices.waldtest( pars = pars , k=2)
# Cdes <- des$Cdes
# rdes <- des$rdes
# Cdes[1, "female:migrant"] <- 1
# Cdes[2, "female:books"] <- 1
# wres1 <- NMIwaldtest( qhat=pres1$qhat , u=pres1$u , Cdes=Cdes , rdes=rdes )
# summary(wres1)
# 
# # a simpler specification is the use of "testnull"
# testnull <- c("female:migrant" , "female:books")
# wres1b <- NMIwaldtest( qhat=qhat , u=u , testnull=testnull )
# summary(wres1b)
# 
# #**** Model 2: Multivariate linear regression
# res2 <- with( imp1 , stats::lm( cbind( ASMMAT , ASSSCI ) ~ 
#                            0 + I(1*(female==1)) + I(1*(female==0))   ) )
# pres2 <- pool.mids.nmi( res2 )
# summary(pres2)
# 
# # test whether both gender differences equals -10 points
# pars <- dimnames(pres2$qhat)[[3]]
#   ##  > pars
#   ##  [1] "ASMMAT:I(1 * (female == 1))" "ASMMAT:I(1 * (female == 0))"
#   ##  [3] "ASSSCI:I(1 * (female == 1))" "ASSSCI:I(1 * (female == 0))"
# 
# des <- create.designMatrices.waldtest( pars = pars , k=2)
# Cdes <- des$Cdes
# rdes <- c(-10,-10)
# Cdes[1, "ASMMAT:I(1*(female == 1))"] <- 1
# Cdes[1, "ASMMAT:I(1*(female == 0))"] <- -1
# Cdes[2, "ASSSCI:I(1*(female == 1))"] <- 1
# Cdes[2, "ASSSCI:I(1*(female == 0))"] <- -1
# 
# wres2 <- NMIwaldtest( qhat=pres2$qhat , u=pres2$u , Cdes=Cdes , rdes=rdes )
# summary(wres2)
# 
# # test only first hypothesis
# wres2b <- NMIwaldtest( qhat=pres2$qhat , u=pres2$u , Cdes=Cdes[1,,drop=FALSE] ,
#                          rdes=rdes[1] )
# summary(wres2b)
# 
# #############################################################################
# # EXAMPLE 2: Multiple imputation and Wald test | TIMSS data
# #############################################################################
# 
# library(BIFIEsurvey)
# data(data.timss2 , package="BIFIEsurvey" )
# dat <- data.timss2[[1]]
# dat <- dat[ , - c(1:4) ]
# 
# # perform multiple imputation
# imp <- mice::mice( dat , m=6 , maxit=3 )
# 
# # define analysis model
# res1 <- with( imp , lm( likesc ~ female*migrant + female*books  ) )
# pres1 <- mice::pool( res1 )
# summary(pres1)
# 
# # Wald test for zero interaction effects
# qhat <- pres1$qhat
# u <- pres1$u
# pars <- dimnames(pres1$qhat)[[2]]
# des <- create.designMatrices.waldtest( pars = pars , k=2)
# Cdes <- des$Cdes
# rdes <- des$rdes
# Cdes[1, "female:migrant"] <- 1
# Cdes[2, "female:books"] <- 1
# 
# # apply MIwaldtest function
# wres1 <- MIwaldtest( qhat , u , Cdes , rdes )
# summary(wres1)
# 
# # use again "testnull"
# testnull <- c("female:migrant" , "female:books")
# wres1b <- MIwaldtest( qhat=qhat , u=u , testnull=testnull )
# summary(wres1b)
# 
# #***** linear regression with cluster robust standard errors
# 
# # convert object of class mids into a list object
# datlist_imp <- mids2datlist( imp )
# # define cluster
# idschool <- as.numeric( substring( data.timss2[[1]]$IDSTUD , 1 , 5 ) )
# # linear regression
# res2 <- lapply( datlist_imp , FUN = function(data){
#            lm.cluster( data=data , formula=likesc ~ female*migrant + female*books ,
#                             cluster= idschool ) } )
# # extract parameters and covariance matrix
# qhat <- lapply( res2 , FUN = function(rr){ coef(rr) } )
# u <- lapply( res2 , FUN = function(rr){ vcov(rr) } )
# # perform Wald test
# wres2 <- MIwaldtest( qhat , u , Cdes , rdes )
# summary(wres2)
# ## End(Not run)