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I have to choose between median or mean imputation to handle missing values. I feel median imputation will work better because it is a number that is already present in the data set and is less susceptible to outlier errors as compared to mean imputation.

What might be the disadvantages of median imputation though?

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    $\begingroup$ why not try regression, and predict the missing values based on a generalized hypothesis? $\endgroup$ – show_stopper Oct 30 '14 at 7:48
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    $\begingroup$ Putting in any one value (be it mean or median) without adding proper noise is disadvantageous anyway. $\endgroup$ – ttnphns Oct 30 '14 at 8:57
  • $\begingroup$ @nar The data is way too sparse to do any regression $\endgroup$ – web_ninja Oct 30 '14 at 9:39
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    $\begingroup$ @ttnphns In general I would have used average of the nearest neighbours from the remaining data to estimate but the sparsity of the dataset made it difficult to do that. That would have introduced some variation. So, what sort of noise is considered 'proper'? $\endgroup$ – web_ninja Oct 30 '14 at 9:42
  • $\begingroup$ It would be better if you give us a glimpse of the actual data, as currently the knowledge provided from you about the dataset is very sparse $\endgroup$ – show_stopper Oct 31 '14 at 9:52
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These are not appropriate for computing missing data - consider the case of heteroskedasticity in the data - neither of these approaches would work if their were 'weird' or idiosyncratic values in your data. In fact it would be more damaging (ie less accurate) to use mean or median replacement in this case

if youre familiar with R, you could check out the MI package (my fave) or mice. This essentially runs a series of chained (ie bayesian) regressions on the data until some convergence criteria

other options are expectation maximization (subject to overfitting problems IMO) and Hotdeck imputation

check out these resources for more explanation about why mean/median replacement is generally a bad idea

Rubin, D. B. (1996). Multiple imputation after 18+ years. Journal of the American Statistical Association, 91(434):473–489.

Schafer, J. L. (1999). Multiple imputation: a primer. Statistical Methods in Medical Research, 8:3–15.

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