Imputation of missing data

My goal is to estimate nutrition indicators of children less than 5 years old at the subnational level (say provinces) in a given country. I have two datasets:

i) survey data that includes this nutritional information and some variables regarding the socioeconomic status of the household in which the children lives.
ii) census data, which includes only the socioeconomic characteristics information, as in the survey data (no nutrition).

The methodology (called nutrition mapping) relies on two stages: first, using survey data, model the nutrition status (left-hand variable) using the household characteristics (right-hand variables) and get a vector of '$\hat{b}$'. Second, using $\hat{b}$, impute the nutrition values using the more comprehensive information from census data. What I would like to have is some measure of the quality of the prediction/forecast in this second stage. How can I get some kind of robust confidence level or standard error that includes the first stage modelling? Any orientation will be greatly appreciated.

• You could always just make cross-validated or bootstrapped predictions, treating your imputation strategy as a predictive model like any other. – shadowtalker Nov 3 '16 at 11:08
• Also what kind of model are you using? With a Bayesian method you could use WAIC or something like that – shadowtalker Nov 3 '16 at 11:10
• @ssdecontrol: In the first stage I use OLS. Sadly, I barely know the Bayesian method of estimation. – olbap79 Nov 3 '16 at 11:17
• Isn't this just a prediction exercise? Or are you then using $\hat b$ as an input to some other model? If so, what is that other model? Also, how many $b$ variables are there? – shadowtalker Nov 3 '16 at 12:04
• Number of b variables is 25. This would be just an exercise of prediction, the b's are used with another set of information (census) – olbap79 Nov 3 '16 at 14:22