Analysis of Variance for Multiply Imputed Data Sets (Using the \(D_2\) Statistic)

This function combines \(F\) values from analysis of variance using the \(D_2\) statistic which is based on combining \(\chi^2\) statistics (see Allison, 2001, Grund, Luedtke & Robitzsch, 2016; micombine.F, micombine.chisquare).

mi.anova(mi.res, formula, type=2)

Arguments

mi.res	Object of class mids or mids.1chain
formula	Formula for lm function. Note that this can be also a string.
type	Type for ANOVA calculations. For type=3, the car::Anova function from the car package is used.

Value

A list with the following entries:

r.squared

Explained variance \(R^2\)

anova.table

ANOVA table

References

Allison, P. D. (2002). Missing data. Newbury Park, CA: Sage.

Grund, S., Luedtke, O., & Robitzsch, A. (2016). Pooling ANOVA results from multiply imputed datasets: A simulation study. Methodology, 12(3), 75-88. doi: 10.1027/1614-2241/a000111

See also

This function uses micombine.F and micombine.chisquare.

See mice::pool.compare and mitml::testModels for model comparisons based on the \(D_1\) statistic. The \(D_2\) statistic is also included in mitml::testConstraints.

The \(D_1\), \(D_2\) and \(D_3\) statistics are also included in the mice package in functions mice::D1, mice::D2 and mice::D3.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: nhanes2 data | two-way ANOVA
#############################################################################

library(mice)
library(car)
data(nhanes2, package="mice")
set.seed(9090)

# nhanes data in one chain and 8 imputed datasets
mi.res <- miceadds::mice.1chain( nhanes2, burnin=4, iter=20, Nimp=8 )
# 2-way analysis of variance (type 2)
an2a <- miceadds::mi.anova(mi.res=mi.res, formula="bmi ~ age * chl" )

# test of interaction effects using mitml::testModels()
mod1 <- with( mi.res, stats::lm( bmi ~ age*chl ) )
mod0 <- with( mi.res, stats::lm( bmi ~ age+chl ) )

mitml::testModels(model=mod1$analyses, null.model=mod0$analyses, method="D1")
mitml::testModels(model=mod1$analyses, null.model=mod0$analyses, method="D2")

# 2-way analysis of variance (type 3)
an2b <- miceadds::mi.anova(mi.res=mi.res, formula="bmi ~ age * chl", type=3)

#****** analysis based on first imputed dataset

# extract first dataset
dat1 <- mice::complete( mi.res$mids )

# type 2 ANOVA
lm1 <- stats::lm( bmi ~ age * chl, data=dat1 )
summary( stats::aov( lm1 ) )
# type 3 ANOVA
lm2 <- stats::lm( bmi ~ age * chl, data=dat1, contrasts=list(age=contr.sum))
car::Anova(mod=lm2, type=3)
}