Let's continue with the previous example of scatter plot and extend this to a bivariate regression. Let's discuss missing data bias and error problems for the three missingness mechanisms (Nakagawa and Freckleton, 2008).

There are two input variables, X and Y, plotted on three scatter plots. The variable Y, plotted on Y-axis, has some values missing. Missingness is represented by a binary variable that captures whether data are missing for the Y variable. Here, missing values are represented by blue rings, and non-missing values are represented by orange dots. The other input variable, X, is observed completely and plotted on the X-axis. Therefore, blue rings and orange dots jointly represent the X values. In the first scatter plot, there is no significant difference between the distributions of observed and missing values. Blue rings and orange dots are spread in the same way. In the second scatter plot, the blue rings, that is, the missing values in the Y-variable, are located more often on the left side of the plot. That means missingness depends on the X-variable. When X is less than a certain value, Y values are missing, otherwise they are non-missing. In the third scatter plot, missing data in the Y-variable (missingness) depend on the Y-variable itself. When Y is less than a certain value, its values are missing, otherwise they are non-missing.

Question

It is often impossible in practice to determine whether data are MNAR, because doing so would require comparing observed Y values to missing Y values, and you do not have access to the missing Y values.

  1. True
  2. False


The answer is True. The point of delineating the three missing data mechanisms is not to determine which missing data mechanism is at work in a particular data set. Instead, the point of describing MCAR, MAR, and MNAR mechanisms is to illustrate the assumptions underlying different missing data treatments. For example, CCA is unbiased under MCAR.