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Re: st: Factor Analysis and Multiple Imputation

From   Maarten buis <>
Subject   Re: st: Factor Analysis and Multiple Imputation
Date   Thu, 22 Jul 2010 23:38:21 -0700 (PDT)

--- On Thu, 22/7/10, wrote:
> I would like to run a couple of regressions using the
> factor score from an explorative factor analysis  as
> the dependent variable but I am not sure how I should handle
> missing data. In particular, I want to 
> a) construct the dependent variable from 8 items using
> explorative factor analysis
> b) run some regressions using the factor score as the dep.
> variable
> There are missing values for pretty much all the variables
> including the 8 items as well as the independent variables
> in the regression. What is the best approach to handle the
> missing data problem? What is the right imputation procedure
> in this case? 
> Should I first use all available information in the data to
> recover the missing data across all the variables, and then
> run the factor analysis? But how do I do this in Stata given
> that mi does not support factor analysis?

The aim of an imputation model is to reproduce the observed patterns in
the data on to the missing values. You need to make sure that you 
reproduce the relevant patterns for your model of interest, but that 
does not mean that you need to use the same model as you intend to use
in your final analysis. The factor score is just a linear combination 
of your observed items, so it is enough for the regression part of your
model, to reproduce the association between the observed items and your 
explanatory variables. Factor analysis just uses the correlation between 
the observed items, so as long as your imputation model reproduces the 
correlations between the items you are ok for the factor analysis part. 

So taking the two together: As long as your imputation model reproduces 
the patterns between all the directly observed variables (items and 
explanatory variables) you are ok, and your imputation model does not
need to include the factor scores. You can use either the official Stata 
-mi- commands for that or -ice- (see:  -findit ice- for several articles 
on that, and download the software from SSC, type in Stata 
-ssc install ice-)

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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