How to test for multivariate normality with missing values?

Question

When applying missMech:TestMCARNormality on a data frame (see below) in which three columns consist of NAs for the same 6 rows:

summary(TestMCARNormality(data = mvn.BN))

I am getting an error message:

Warning: More than one missing data pattern should be present.
Error in TestMCARNormality(data = mvn.BN) : 

My intention is to test the multivariate normality assumption of SEM with this data. My suspicion was that because these three columns have missing values for the very same subjects, the missing mechanism cannot be considered arbitrary. Because these three vectors reflect the same phenomena, I tried collapsing them into one latent variable like this:

sndPre <- 'sndPre  =~ r + rlct + int'

summary(fit <- cfa(sndPre, data = mvn.BN, missing="fiml"))

df$sndPre <- lavPredict(fit)

However, testing for multi-normality with the new data consisting of the latent variable instead of the three original vectors resulted in the same error message as before.

Help would be highly appreciated!

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Answer 1

Just some small hints, hope I am able to help at little bit. (unfortunately I still have not completely understood what you are trying to archive.

I took a look at your data - the missing data always occurs in the same pattern. This means - if there are missing data it is always this pattern:

non-NA, NA, NA, NA, non-NA, non-NA, non-NA

This is also what your error message is about.

Warning: More than one missing data pattern should be present.

When you do the transformation you described (combining the variables to one variable) this still does not change. The new pattern is:

non-NA, NA, non-NA, non-NA, non-NA

But still it is the same pattern all over the dataset.

My suspicion was that because these three columns have missing values for the very same subjects, the missing mechanism cannot be considered arbitrary.

Yes - this is probably the most obvious case of non-MCAR data you can have. Actually so obvious, that MissMech can't even calculate something.

From the wikipedia definition of MCAR

if the events that lead to any particular data-item being NA are independent both of observable variables and of unobservable parameters of interest

This is clearly not the case for your data. Because the NAs were independent they would be somehow distributed equally over all variables. The fact that the NAs occur only for 3 variables shows this. Because you can say: If a values is NA depends on, it being of variable v2,v3,v4 - because only for these variables NAs occur.

Normally the MCAR test would test this assumption "independent both of observable variables and of unobservable parameters". It would somehow look if all possible patterns occur equally often. Because only then the data is MCAR. If there is from the start only 1 pattern - you can't even start calculating the frequency of patterns.

Hope I could help a little bit - this is the rather simplified explanation to keep it understandable.

About the multivariate normality test:

library("MVN")
library("mice")

#imputation with mice
imp <- mice(mvn, m=5)
imp_data <- complete(imp, action = 1)

# mvn test with MVN package
mvn(imp_data, univariatePlot = "qqplot")

That would be using mice in a non-multiple imputation way. You could also do multiple imputation, but then you would have to pool the imputation results. Both ways it might be possible you introduce bias, since your data is not MCAR. But you could also introduce bias if you do a complete case analysis. So probably no way to 100% avoid bias.