I need a single imputed dataset (e.g. to create a country group dummy from the imputed country per capita income data). R offers packages package for creating multiple imputed data (e.g. Amelia) and combining results from multiple datasets (as in MItools). My concern is if I can average all the imputed data to obtain a single dataset. If so, how can I do it in R?
You can't average the data. Since the variables will be same across the imputed data, you have to append each imputed data. For example, if you have 6 variables with 1000 observations and your imputation frequency is 5 , then you will have the final data of 6 variables with 5000 observations. You use the
rbind function to append the data in R. For example, if you have five imputed data (assuming that you have already these data in hand), your final data will be obtained as
finaldata <- rbind(data1,data2,data3,data4,data5)
For details, see here.
The regression coefficient from each imputed data will be usually different; so the coefficient is obtained as average of coefficients of all imputed data. But, there is additional rule for standard error. See here for details.
Multiple imputation models for missing data are rarely employed in practice as simulation studies suggest that the chances of the true underlying parameters lying within the cover intervals are not always accurately depicted. I would strongly recommend a testing of the process based on simulated data (with parameters known precisely), based on real data in the area of investigation. A simulation study reference https://www.google.com/url?sa=t&source=web&rct=j&ei=Ua4BVJgD5MiwBMKggKgP&url=http://www.ssc.upenn.edu/~allison/MultInt99.pdf&cd=13&ved=0CCEQFjACOAo&usg=AFQjCNF1Rg6SbFPwLv5n3jYIVNA_iTMPCg&sig2=d2VORWbqTNygdM6Z51TZEg
I suspect employing say five simple/naive models for the missing data may be better in producing less bias and cover intervals that accurately include the true underlying parameters. Rather than pooling of the parmeter estimates, one may do better by employing Bayesian techniques (see work with imputation models in this light at https://www.google.com/url?sa=t&source=web&rct=j&ei=mqcAVP7RA5HoggSop4LoDw&url=http://gking.harvard.edu/files/gking/files/measure.pdf&cd=5&ved=0CCUQFjAE&usg=AFQjCNFCZQwfWJDrrjzu4_5syV44vGOncA&sig2=XZUM14OMq_A01FyN4r61Zw ).
Yes, not much of a ringing endorsement of standard missing data imputation models and to quote a source, for example, http://m.circoutcomes.ahajournals.org/content/3/1/98.short?rss=1&ssource=mfr :"We describe some background of missing data analysis and criticize ad hoc methods that are prone to serious problems. We then focus on multiple imputation, in which missing cases are first filled in by several sets of plausible values to create multiple completed datasets,..." where I would insert "(?)" after plausible as naive models, for one, are not generally best described as producing plausible predictions. However, models incorporating the dependent variable y, itself, as an independent variable (so called calibration regression) may better meet this characterization.