Jacob Felson writes,

Here is a question I was hoping you might address (on your blog?) It has to do with the distribution of missing data in a dataset. What is the relationship between the total percentage missing observations, and the number of observations left after listwise deletion? Given the percentage of missing observations in the data matrix, what is the expected number of observations after listwise deletion?

To take an arbitrary example, say you have 10 variables and 100 cases, 1000 total observations. 20% of the observations are missing. What is the expected number of observations after listwise deletion?

I was wondering whether any one does research on this kind of thing. For example, what would a specific pattern of missing data (say, measured as the number of listwise deleted cases relative to the number of expectation of such cases, given total missing observations) say about the administration of a dataset, and what would it say about the probability that the data are missing at random?

My reply: I wasn’t familiar with the term “listwise deletion,” but it seems to be the same thing as “complete-case analysis” (a more descriptive term, I think). Anyway, I’m not quite sure why the question arises since I’d think you could answer it directly with any particular dataset. For your example, if you have 100 units with 10 observations each and 20% missing, one extreme is that the same 20 units are missing all the observations (in which case you’d lose 20% with listwise deletion); in another extreme, everybody is missing at least one variable, in which case you can’t do listwise deletion at all! It depends on the pattern of what’s missing.

If you want a more quantitative answer, one approach would be to trawl the internet for a few thousand datasets, and, for each, count the number of units, number of observations, number of completely observed units, and number of missing observations–and see what patterns arise empirically. It could make for an intersesting paper.