Re: [amelia] Using Amelia and the Central Limit Theorem

Hello Amelia list, nearly one year ago I've posted a question in this list (it can be seen here [1]) about a dataset I was making imputations using Amelia. The objective of such imputations is only to complete missing data and stop there. No further analysis should be made. Now I have a similar dataset which I'm trying to impute, with the same objective. In summary I'm using Amelia to impute, say m = 15, and using the mean and variance of these 15 imputations as my final result (more specifically, the mean is the variable of interest). However I've noticed that when I make two or more Amelia runs with m = 15, I can have very different final results (the means), most possibly due to the high variability of the data itself. I understand this is normal, since Amelia uses bootstrapped data to generate each imputation, so the results are expected to differ. However the high discrepancy I'm getting with different Amelia runs is a problem since I'm using only the mean of m imputations as the final result. So, if I use one Amelia run, my result is totally dependent of what happened in this unique run. What I'm trying to do now is to get more "consistent" results, in the sense that my final result is not dependent of only one Amelia run. To achieve this, I thought in using the Central Limit Theorem (CLT) to get my final mean, as follows: 1) Run the same Amelia model 1000 times, with m = 15 2) Within each of the 1000 runs I extract the mean of the m imputations, so I have 1000 means (assuming that each Amelia run is independent from each other, so I treat the means as iid random variables) 3) Calculate the mean from the distribution of these 1000 means, which should be normally distributed by the CLT (and that E(\bar{X}) = \mu and Var(\bar{X}) = \sigma^2/n). I've made a few runs of 1000 Amelia runs following this pseudo-code, and the final result is very similar among them (i.e. they have almost identical normal distributions and very similar final means). For me this sounds more reasonable to use than one only Amelia run to extract a mean, but I would like to hear yours opinion about this, and in particular if this is a valid methodology to do what I'm trying to do with Amelia. Thank you very much in advance. [1] http://lists.gking.harvard.edu/lists/amelia/2010_09/msg00012.html --- Fernando Mayer URL: http://sites.google.com/site/fernandomayer e-mail: fernandomayer [@] gmail.com - Amelia mailing list served by Harvard-MIT Data Center [Un]Subscribe/View Archive: http://lists.gking.harvard.edu/?info=amelia More info about Amelia: http://gking.harvard.edu/amelia