What is the difference between MAR and MCAR missing data?

by Karen Grace-Martin

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One of the important issues with missing data is the missing data mechanism.

It’s important because it affects how much the missing data bias your results, so you have to take it into account when choosing an approach to deal with the missing data.

The concepts of these mechanisms can be a bit abstract.

And to top it off, two of these mechanisms have 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.

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.

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This post is part of a series of answers about missing data that I was asked during a recent webinar.  There were nearly 300 people on the live webinar, so we didn’t get through all the questions.  So I’m answering some of the ones we missed here.

To see the full list of posts in this series, and a whole lot more, visit our Missing Data page.

tn_ircWant to learn more about how to handle Missing Data? In this 5-part workshop, you’ll learn all about two fabulous modern missing data techniques: multiple imputation and maximum likelihood.

{ 2 comments… read them below or add one }

Jeremy Taylor June 2, 2011 at 9:52 am

Great post! This is definitely something that is often confused.

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Karen June 3, 2011 at 10:28 am

Thanks, Jeremy! I know, what crazy names, huh?

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