One of the important issues with missing data is the missing data mechanism. You may have heard of these: MCAR, MAR, and MNAR.
The mechanism is important because it affects how much the missing data bias your results. This has a big impact on what is a reasonable approach to dealing with the missing data. So you have to take it into account in choosing an approach.
The concepts of these mechanisms can be a bit abstract.
And to top it off, two of these mechanisms have really confusing names: Missing Completely at Random and Missing at Random.
Missing Completely at Random (MCAR)
Missing Completely at Random is pretty straightforward. What it means is what is says: the propensity for a data point to be missing is completely random.
There’s no relationship between whether a data point is missing and any values in the data set, missing or observed.
The missing data are just a random subset of the data.
Missing at Random (MAR)
This is where the unfortunate names come in.
Missing at Random means the propensity for a data point to be missing is not related to the missing data, but it is related to some of the observed data.
Whether or not someone answered #13 on your survey has nothing to do with the missing values, but it does have to do with the values of some other variable.
So for example if older people are more likely to skip survey question #13 than younger people, the missingness mechanism is based on age, a different variable.
A better name would actually be Missing Conditionally at Random, because the missingness is conditional on another variable. But that’s not what Rubin originally picked, and it would really mess up the acronyms at this point.
The idea is, if we can control for this conditional variable, we can get a random subset.
You can imagine that good techniques for data that is missing at random need to incorporate variables that are related to the missingness.