Re: [amelia] Combine m datasets?

Dear Glenys, There do exist single imputation methods that people use, for example, interpolating the data, but while the best ones (such as EM) can give you a good estimate of the expected value of the missing value, they generally all fail to rigourously also provide a measure of uncertainty in that imputation. We don't want to treat the data that we didn't observe with the same confidence as the data that we were able to measure directly. With the mulitply imputed datasets you have created, the distribution across the values of any missing observation reflects the uncertainty in that imputation. If the observed predicts that observation with great confidence, then all the imputations will be very similar. If no information exists to impute the observation, the distribution of the imputations will be large (approximately with variance close to the unconditional variance of the observed values of that variable). So, collapsing your imputations into one dataset might give you good predictions for your missing values, but no measure of how confident you can be in those predictions and how much weight you should give them, or how much like the observed data you should treat them. This can trip up your analysis, including causing bias in parameters of interest. However, one of the computational benefits of multiple imputation (and perhaps the shorter answer) is that each one of these imputed datasets you have generated can be treated as if there was no missing data problem. This is why multiple imputation is sometimes described as a two step approach. You can run whatever analysis you would have run if you had the complete data in each imputed dataset (like you had hoped to run in the single imputed dataset). Generally (and in SPSS) this just requires taking whatever command you were going run, and placing it into a loop (if you are using a script). Now you have m sets of results (where m is the number of imputed datasets and 5 or 10 is in most cases plenty sufficient). To get the final answer you actually want to report to your reader, there is a simple formula to combine these results. For most quantities of interest (like regression coefficients) you just average each quantity of interest across the m datasets. The standard errors on these averaged quantities are slightly trickier, as they reflect both the average error across the models and the additional error between the models. In Stata and R we have simple functions that will do all of this seamlessly for you. I'm not sure if something similar exists in SPSS already. If anyone on the list knows of a function to combine a list of imputed results (or even to Bayesian model average) please chime in. If such a thing does not exist presently, I'm pretty sure we can whip one up for you. regards, James Honaker On Fri, 31 Aug 2007, Glenys Lafrance wrote: - Amelia mailing list served by Harvard-MIT Data Center [Un]Subscribe/View Archive: http://lists.gking.harvard.edu/?info=amelia