Multiple Imputation for Index Variable

[Shania Patel]

Hello,

I have large survey data in which I am constructing indices using some of the variables.

When conducting multiple imputations, would I:
1. Generate the indices prior to mi. Then register both the components with -mi register imputed- and the indices under -mi passive-. Then only include the index variables during regression?
2. First register the components with -mi register imputed- and then construct the index after?

I have tried the Stata documentation/online resources but I find myself still lost on the topic.

Any help is greatly appreciated! Let me know if any other information is required or if clarification is needed on how I worded my question.

[Rich Goldstein]

this is one of the major controversies remaining in MI - the first is often referred to as just-another-variable (JAV) and the second as "passive" - there are good points and bad points about each (e.g., is you use #1, it is almost certainly the case that the imputed index will not be what would get if you followed #2 - in fact, they can be quite inconsistent (and some people very much dislike that) - but #2 can lead to "uncongeniality" which, in some cases can be disastrouss - there are studies, using simulation, that come down for #1 and other studies, using other simulations, that come drown for #2; further, there is a more recent line of lit that dismisses both and says to use "factored regressions" (not available in Stata); since your question was very general, my answer is also

[Shania Patel]

this is one of the major controversies remaining in MI - the first is often referred to as just-another-variable (JAV) and the second as "passive" - there are good points and bad points about each (e.g., is you use #1, it is almost certainly the case that the imputed index will not be what would get if you followed #2 - in fact, they can be quite inconsistent (and some people very much dislike that) - but #2 can lead to "uncongeniality" which, in some cases can be disastrouss - there are studies, using simulation, that come down for #1 and other studies, using other simulations, that come drown for #2; further, there is a more recent line of lit that dismisses both and says to use "factored regressions" (not available in Stata); since your question was very general, my answer is also

To clarify if I choose the JAV approach, during -mi impute chained- I would impute both the components and the index itself? Even though the components will not be used again?

Ex.

 
mi register imputed component1 component2 component3 index depvar
mi impute chained (logit) component1 component2 component3 depvar (ologit) index
mi estimate logit depvar i.index

Or would it be like:

 
mi register imputed component1 component2 component3 depvar
mi register passive index
mi impute chained (logit) component1 component2 component3 depvar = index
mi estimate logit depvar i.index

[Rich Goldstein]

yes, if using the JAV approach, you "would impute both the components and the index itself"