Means of determining monotonicity of missing pattern other than eyeballing? And how monotone is monotone for the purpose of multiple imputation?

Question

I have a large dataset with a large number of variables. Missingness as high as ~25% in some variables, many vars with no missing.

Judgment of the monotonicity of the missing pattern is important for the selection of a multiple imputation method. I have seen some sources talk about "monotone or near-monotone" patterns. But how monotone is monotone, and how do you know, other than by looking?

Every text I have seen recommends eyeballing the patterns. But is there not some means of statistically summarizing monotonicity (e.g., sum of belongingness the main missing pattern controlling for belongingness to other patterns)?

I have not seen anything like this in any text, but maybe I'm just missing it.

If I organize the data matrix to maximize the number of missing measurements clustered in a monotone pattern, I have about 35% of measurements in the pattern. (Other measurements display something of a "fan" pattern similar to that seen here. How would I decide whether this were monotonic "enough" to assume it for the purpose of MI?

I know that I could also do MI in two steps in order to isolated the monotonic pattern, then run MI again with a monotone method. As fun as this sounds, I'm trying to determine whether it's reasonable to do it in one fell swoop.

Answer 1

Rico, with today's chained equations algorithms, you typically do not need to worry about monotonicity, though exploiting it may make convergence more rapid and stable.

Section 4.1 of my book Flexible Imputation of Missing Data proposes two new measures to summarize the missing data pattern: influx and outflux. This pair can be used to diagnose monotonicity quickly.