Solved – MCAR test for large number variables and small sample size

data preprocessingmcarmissing datamultiple-imputationr

I have a dataset with 101 observations and 402 columns (those columns comprise several multiple-item questionnaires). Among those 402 columns, 10 of them are categorical and the remaining are continuous. There are 82 observations without missing values, which means 18% of the entire sample (N=101) has one or more missing values. There are 14 missing patterns with 10 of them containing only one observation.

I would like to examine if the missing data mechanism is MCAR in this dataset. I have tried LittleMCAR ("BaylorEdPsych" package) and TestMCARNormality ("MissMech" package) to test for MCAR using RStudio (version 1.1.442). However, LittleMCAR only allows a maximum of 50 variables; TestMCARNormality did not work out either. The code for TestMCARNormality is shown as below:

## df[1:10] were excluded due to their class of categorical variables; del.lesscases was set to 1 because default for this parameter was 6, and if set to default it would have no missing pattern in the test.

TestMCARNormality(df[11:402], del.lesscases = 1)

After I ran this code, it showed the following error:

Error in solve.default(sigoo) :
system is computationally singular: reciprocal condition number = 1.37693e-17

I wasn't sure why this happen and what it meant. I was wondering if anyone knows how I can address this issue and how I can test MCAR for my dataset. Thank you in advance for your time; sincerely appreciated!!

Best Answer

MissMech imputes missing data in order to do its MCAR test. Having more variables (columns) than observations (rows) can cause problems for data imputation, which I would guess is what is happening here.

Also, when you do an MCAR test, you are assuming that the missing data mechanism is random, i.e. you're assuming MCAR, and the p-value tells you how consistent the missing data pattern is with that assumption.

You have to use your knowledge about the subject at hand to justify that assumption. I.e. you could have theoretical reasons to believe the missing data is MCAR, MAR or MNAR.

In the absence of any strong theoretical reasons, you could take a more exploratory approach to missing data mechanisms, see Tierney et al. (2014).

Related Solutions

Solved – How to impute an ordinal variable with MICE but prevent it from taking one value

The following code defines and calls a dedicated imputation function that separates imputation of cases with tumor_size == 0 from tumor_size > 0.

## How to impute an ordinal variable with MICE but prevent it from taking one value?

df <- data.frame(age = c(24,37,58,65,70,84),
                 overall_tumor_grade = c(1,1,2,3,'X',NA),
                 tumor_size = c(1.5,2.0,4.2,5.6,0,0.1))

mice.impute.tumor <- function(y, ry, x, ...){
    ymis <- y[!ry]
    tmis <- x$tumor_size[!ry] > 0
        t  <- x$tumor_size > 0
    y[!ry] <- NA
    ymis[!tmis] <- "X"
    ymis[tmis] <- mice.impute.polyreg(y[t, drop = TRUE], ry[t], x[t,], ...)
    ymis
}

ini <- mice(df, maxit = 0)
meth <- ini$meth
meth["overall_tumor_grade"] <- "tumor"
imp <- mice(df, meth = meth, maxit = 1, m = 2)

Solved – Questions on multiple imputation with MICE for a multigroup-SEM-analysis? (including survey weights)

(I'm the creator of lavaan.survey)

As Stas already indicated, the combination (multiple imputation * complex sampling) can be tricky business. The main papers are Kott (1995) and Kim, Brick & Fuller (2006).

Here are some considerations:

As mentioned by Stas, all the usual best practices of MI apply. Considering the below, I would probably not use quickpred() initially. There is a risk it will discard things that you actually need. It might help to make some reasonable subselection though.
If you have weights, these need to be included in the imputation model as a covariate (Kim et al. 2006, p. 518). Since you are doing multiple group analysis ("domain estimation"), you also need to include the interaction between the group dummies and the weights in the imputation model (p. 519).
If you have strata and clusters, things become more complicated. The imputation model needs to account for the resulting correlation between the observations. If not you will get the wrong standard errors (Kim et al. 2006: p. 514). A model-based way of doing this might be to include strata as fixed effects and clusters as random effects in a Bayesian imputation model. A more survey-like approach would be to follow Stas' suggestion and use a resampling procedure that respects the strata and clusters. For example, in bootstrapping and with just the clusters, you would sample a random cluster (PSU) with replacement and then individuals (2SUS) with replacement within the sampled clusters.

Another advantage of Stas' resampling suggestion, even without strata and clusters, is that you will account for the uncertainty about the parameters of the imputation model including that caused by the weights. I am not sure if mice does this accurately by default. This is usually a relatively small additional term in the variance but it might make a difference.

Once you have the multiply imputed datasets, you can just pass these as an imputationList to lavaan.survey (see the JSS lavaan.survey paper). lavaan.survey will then do all the usual MI pooling calculations for you. So you don't need to manually fit a model separately for each imputation!

Hope this helps,

All the best, Daniel

P.S. Thanks to Stas and @Gaming_dude who brought this post to my attention. I would be happy to continue the conversation (here, lavaan Google discussion group, twitter, email..)!