EM Imputation and Missing Data: Is Mean Imputation Really so Terrible?

I’m sure I don’t need to explain to you all the problems that occur as a result of missing data.  Anyone who has dealt with missing data—that means everyone who has ever worked with real data—knows about the loss of power and sample size, and the potential bias in your data that comes with listwise deletion.

Listwise deletion is the default method for dealing with missing data in most statistical software packages.  It simply means excluding from the analysis any cases with data missing on any variables involved in the analysis.

A very simple, and in many ways appealing, method devised to overcome these problems is mean imputation. Once again, I’m sure you’ve heard of it–just plug in the mean for that variable for all the missing values. The nice part is the mean isn’t affected, and you don’t lose that case from the analysis.

And it’s so easy! SPSS even has a little button to click to just impute all those means.

But there are new problems.

While it’s true the mean doesn’t change, the relationships with other variables do. And that’s usually what you’re interested in, right? Well, now they’re biased.

And while the sample size remains at its full value, the standard error of that variable will be vastly underestimated–and this underestimation gets bigger the more missing data there are. Too-small standard errors lead to too-small p-values, so now you’re reporting results that should not be there.

There are other options. Multiple Imputation and Maximum Likelihood both solve these problems. But while Multiple Imputation is not available in all the major stats packages, it is very labor-intensive to do well. And Maximum Likelihood isn’t hard or labor intensive, but usually requires using structural equation modeling software, such as AMOS or MPlus.

The good news is there are other imputation techniques that are still quite simple, and don’t cause bias in some situations. And sometimes (although rarely) it really is okay to use mean imputation. When?

If your rate of missing data is very, very small, it honestly doesn’t matter what technique you use. I’m talking very, very, very small (2-3%).

There is another, better method for imputing single values, however, that is only slightly more difficult than mean imputation. It uses the E-M Algorithm, which stands for Expectation-Maximization. It is an iterative procedure in which it uses other variables to impute a value (Expectation), then checks whether that is the value most likely (Maximization). If not, it re-imputes a more likely value. This goes on until it reaches the most likely value.

EM imputations are better than mean imputations because they preserve the relationship with other variables, which is vital if you go on to use something like Factor Analysis or Linear Regression.

EM Imputations still underestimate standard error, however. Once again, this approach is only reasonable if the standard error of individual items is not vital, like in Factor Analysis, which doesn’t have p-values.

The heavy hitters like Multiple Imputation and Maximum Likelihood are still superior methods of dealing with missing data and are in most situations the only viable approach. But you need to fit the right tool to the size of the problem.

It may be true that backhoes are better at digging holes than trowels, but trowels are just right for digging small holes. It’s better to use a small tool like EM when it fits than to ignore the problem altogether.

EM Imputation is available in SAS, Stata, R, and SPSS Missing Values Analysis module.

Tagged as: E-M Algorithm, EM algorithm, listwise deletion, maximum likelihood, mean imputation, Missing Data, Multiple Imputation, SPSS Missing Values Analysis