Hi guys,
I would appreciate if anyone could share your knowledge of the missing data mechanism MAR,MCAR and MNAR in the simplest analogy, description and example and how these terms are relate or effect to the biased result. My highest respect for those could explain your knowledge with your own words or recommend me the good online resources. Thanks in advance
Have you read any of John Graham's stuff on missing data? His Annual Review of Psychology chapter (see link below) is pretty readable, I think. If the first link doesn't work, try the second. HTH.
http://www.annualreviews.org/doi/pdf/10.1146/annurev.psych.58.110405.085530
http://www.stats.ox.ac.uk/~snijders/Graham2009.pdf
Let's think about an example where you want to estimate the mean income within a certain population, which you obtain via questionnaires. Suppose some income measures are missing. When missingness is MCAR, then the missingness is completely random, as if some questionnaires were lost by chance. When missingness is MAR, than the missingness is random within subgroups of other observed variables, for instance, suppose that you also collect data on the profession of subject and that say mangers are more likely not the share their income, than, within subgroups of the profession, missing is random. Missingness is MNAR when n the reason for missingness depends on the missing values themselves/ For instance, suppose people don't want to share their income when it is below 1000 euros per month because they are ashamed of it. I hope this enhances your understanding concerning these definitions.
Hi guys,
I think i'm the only one confused with the missing mechanism theory, after having revision on some journals, i could feel myself sharing the same story and the same boat with other researchers puzzled in term of its mechanisme theory names as reported in :
http://www.stats.ox.ac.uk/~snijders/Graham2009.pdf
I spent about a week to understand on this topic but it still confusing.I want to study about the imputation process in missing data. Shall i put these three concept aside and proceed to study the imputation process without considering MAR,MCAR and MNAR theories? How far these theories significant in the imputation process in missing data?
Dear Aisyah mat jasin,
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.
The terminology describing missingness mechanisms is confusing. In particular the meaning of 'missing at random' is often misunderstood, leading researchers faced with missing data problems away from multiple imputation, a method with considerable advantages.
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.
it 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.
MNAR: none of the methods above will necessarily work and assumptions need to be made about what is happening with the missing data.
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