My understanding is that:
- Missing at random: Whether or not a variable's value is missing is dependent on the values of the other variables.
- Missing not at random: When the propensity for a variable's value to be missing depends on the value.
But what about when the variables are correlated, as they often are?
To make things more concrete, let us consider an experiment where we are collecting data on temperature, humidity, and CO2, and let us suppose that there relationship between these is T = H = C.
Say that we are missing all CO2 variables below 50, because the sensor freezes.
In this case, it is
Missing at random: Because the propensity of CO2 to be missing is dependant on the value of temperature and humidity. Missing not at random: Because all CO2 values below 50 are missing.
Since the variables are interlinked, missing at random => missing not at random.
Or have I made a mistake in my reasoning somewhere?