Inference for Correlations and Covariances for Multiply Imputed Datasets

Statistical inference for correlations and covariances for multiply imputed datasets

micombine.cor(mi.res, variables=NULL, conf.level=0.95,
     method="pearson", nested=FALSE, partial=NULL )

micombine.cov(mi.res, variables=NULL, conf.level=0.95,
     nested=FALSE )

Arguments

mi.res

Object of class mids or mids.1chain

variables

Indices of variables for selection

conf.level

Confidence level

method

Method for calculating correlations. Must be one of "pearson" or "spearman". The default is the calculation of the Pearson correlation.

nested

Logical indicating whether the input dataset stems from a nested multiple imputation.

partial

Formula object for computing partial correlations. The terms which should be residualized are written in the formula object partial. Alternatively, it can be a vector of variables.

Value

A data frame containing the coefficients (r, cov) and its corresponding standard error (rse, cov_se), fraction of missing information (fmi) and a \(t\) value (t).

The corresponding coefficients can also be obtained as matrices by requesting attr(result,"r_matrix").

See also

See stats::cor.test for testing correlation coefficients.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: nhanes data | combination of correlation coefficients
#############################################################################

library(mice)
data(nhanes, package="mice")
set.seed(9090)

# nhanes data in one chain
imp.mi <- miceadds::mice.1chain( nhanes, burnin=5, iter=20, Nimp=4,
                  method=rep("norm", 4) )

# correlation coefficients of variables 4, 2 and 3 (indexed in nhanes data)
res <- miceadds::micombine.cor(mi.res=imp.mi, variables=c(4,2,3) )
  ##     variable1 variable2       r    rse fisher_r fisher_rse    fmi       t      p
  ##   1       chl       bmi  0.2458 0.2236   0.2510     0.2540 0.3246  0.9879 0.3232
  ##   2       chl       hyp  0.2286 0.2152   0.2327     0.2413 0.2377  0.9643 0.3349
  ##   3       bmi       hyp -0.0084 0.2198  -0.0084     0.2351 0.1904 -0.0358 0.9714
  ##     lower95 upper95
  ##   1 -0.2421  0.6345
  ##   2 -0.2358  0.6080
  ##   3 -0.4376  0.4239

# extract matrix with correlations and its standard errors
attr(res, "r_matrix")
attr(res, "rse_matrix")

# inference for covariance
res2 <- miceadds::micombine.cov(mi.res=imp.mi, variables=c(4,2,3) )

# inference can also be conducted for non-imputed data
res3 <- miceadds::micombine.cov(mi.res=nhanes, variables=c(4,2,3) )

# partial correlation residualizing bmi and chl
res4 <- miceadds::micombine.cor(mi.res=imp.mi, variables=c("age","hyp" ),
                  partial=~bmi+chl )
res4
# alternatively, 'partial' can also be defined as c('age','hyp')

#############################################################################
# EXAMPLE 2: nhanes data | comparing different correlation coefficients
#############################################################################

library(psych)
library(mitools)

# imputing data
imp1 <- mice::mice( nhanes,  method=rep("norm", 4 ) )
summary(imp1)

#*** Pearson correlation
res1 <- miceadds::micombine.cor(mi.res=imp1, variables=c(4,2) )

#*** Spearman rank correlation
res2 <- miceadds::micombine.cor(mi.res=imp1, variables=c(4,2),  method="spearman")

#*** Kendalls tau
# test of computation of tau for first imputed dataset
dat1 <- mice::complete(imp1, action=1)
tau1 <- psych::corr.test(x=dat1[,c(4,2)], method="kendall")
tau1$r[1,2]    # estimate
tau1$se     # standard error

# results of Kendalls tau for all imputed datasets
res3 <- with( data=imp1,
        expr=psych::corr.test( x=cbind( chl, bmi ), method="kendall") )
# extract estimates
betas <- lapply( res3$analyses, FUN=function(ll){ ll$r[1,2] } )
# extract variances
vars <- lapply( res3$analyses, FUN=function(ll){ (ll$se[1,2])^2 } )
# Rubin inference
tau_comb <- mitools::MIcombine( results=betas, variances=vars )
summary(tau_comb)

#############################################################################
# EXAMPLE 3: Inference for correlations for nested multiply imputed datasets
#############################################################################

library(BIFIEsurvey)
data(data.timss4, package="BIFIEsurvey" )
datlist <- data.timss4

# object of class nested.datlist
datlist <- miceadds::nested.datlist_create(datlist)
# inference for correlations
res2 <- miceadds::micombine.cor(mi.res=datlist, variables=c("lang", "migrant", "ASMMAT"))
}