For statisticians or researchers, when you come across data that has MAR and MNAR missing values, which is the most preferred methods to produce accurate estimates? Would you go the Complete Case Analysis or do some imputations? Why?
@Ramanjaneyulu..I have gone through the article. Don't you think imputation affects the estimates obtained, since the sample size will be larger
A standard book on missing data is Little and Rubin (2002). It is very easy to provide examples where complete-case analysis gets substantially different answers than MAR (i.e., complete-case is likely wrong).
Generally, MNAR is nonignorable nonresponse where you need a model or certain other extra information because the nonrespondents have different characteristics from the respondents.
MAR, when properly performed, is an extension of hot-deck in a manner that is somewhat mathematically sound. In some situations, when the deviations from MAR are not too extreme, it is possible to perform certain adjustments so that the outputs from the 'adjusted' MAR are more reasonable in the sense the certain aggregates from the outputs are closer to certain benchmark totals where the benchmark totals are likely to be closer to the 'truith'.
You replied "Don't you think imputation affects the estimates obtained, since the sample size will be larger." Put simply: Not in practice.
Each imputed data set is of the same size as the original data set but with missing values replaced by predictions from the imputation model. Adding the estimates does effectively inflate n within that imputed data set, but this is handled in three steps. First, noise is added to each prediction added to the model to take into account the uncertainty in estimating the imputed data. Second, multiple data sets are imputed so that on average the noise cancels out and the estimates are unbiased. Third when the estimates are combined from the imputed data sets the uncertainty inherent in the imputation process can be assessed by the variability between the imputed data sets and this between-imputation variance is used to adjust the combined inferences (effectively adding to the standard errors).
So you add in data to complete the data set and adjust the standard errors to account for the uncertainty in estimation individual data points and the overall imputation process. Provided you impute sufficient numbers of data sets (40 or 50 is better than say 4 or 5) the resulting inferences can be accurate for MAR data and may well help increase power and reduce bias even if the data are MNAR.
The following paper is very advanced and intended for experienced 'imputers'.
Bayesian Simultaneous Edit and Imputation for Multivariate Categorical Data
Link for JASA paper by Manrique-Vallier, D. and Reiter, J.P. May not appear until 2017.
http://www.tandfonline.com/doi/full/10.1080/01621459.2016.1231612
The methods also deal with 'edit' restraints (i.e., a child under 16 cannot be married).
There is an earlier paper for continuous-type data.
Kim, H., Cox, L. H., Karr, A. F., Reiter, J. P., Wang, Q. (2014), Simultaneous Edit-Imputation for Continuous Microdata,, JASA, 110, 987-999..
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