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From what I understood:

MCAR - missingness do not depend on the values of Y (observed or missed)

MAR - missingness depends only on the components of Y that are observed, and not on the components that are missing.

Question: Is MAR more restrictive than MCAR?? since it has a conditional factor? or that comparison can't be done?

Thanks!

Djib2011
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Tiago Dias
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1 Answers1

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The way I see it MCAR and MAR do not intersect, i.e. a sample can be assumed to be missing due to either one of these mechanisms but not both. In this sense you can say that:

  • a value is MAR, if the "missingness" depends on solely on observed variables
  • a value is MCAR, if the "missingness" depends solely on unobserved variables

Try to think of it more intuitively, a value can't be missing completely at random if we can (at least partially) account for its missingness with data at our disposal.

While I don't think you can make any theoretical claim about the restrictiveness of either category, in practice it more likely that the MAR mechanism stands and not the MCAR. In fact a lot of well known imputation strategies inherently assume that all all values are MAR (e.g. MICE).

Finally, a clarification: if by $Y$ you mean just the labels, then your MAR statement is not 100% accurate. MAR essentially means that the information about the "missingness" (partially) lies in the data's features, i.e. $X$

Djib2011
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