Re: st: Factor analysis(?) question - missing data

[Phil Schumm <pschumm@uchicago.edu>]

On Apr 22, 2008, at 1:06 PM, Glenn Hoetker wrote:
> This is perhaps more of a statistical questions than a Stata  
> question.  My situation is this.  I have a large dataset in which  
> there are 5-6 indicators each for a bunch of latent variables. Let  
> me take as an example having 5 measures for innovative output, x1- 
> x5.  The problem is that very few observations have all 5 measures;  
> some are missing x1, some x2, etc. Almost every observation has at  
> least 3 measures and most 4.
>
> Is there anyway to optimally combine these indicators to measure  
> the underlying construct of innovative output that would use all  
> available measures for a given observation, i.e., x1-x4 for one  
> observation, [x1-x3,x5] for another, etc.  If I thought these were  
> equally weighted, I could just average over the available variables  
> in each, setting aside issues of measurement error.  However, I'm  
> not convinced they are equally weighted and would like to do this  
> in a more rigorous fashion.

How you approach this will depend critically on whether the missing  
data are missing at random (MAR), or, more precisely, on whether you  
are willing to assume that this is so.  It is often difficult, if not  
impossible, to investigate this rigorously.

If you are willing to assume MAR, then you have at least 3 options.   
You can fit a factor analytic (or other similar) model directly using  
an algorithm that can accommodate missing data (e.g., the EM  
algorithm, or, better yet, the ECME algorithm; see, for example, Liu  
and Rubin, Statistica Sinica 8 (1998), 729-747).  I once programmed  
this (EM) in Stata to handle multiple regression with missing data --  
perhaps others have done more.  Second, you can fit the model using - 
gllamm-, which will accommodate missing data under the MAR  
assumption.  And finally, you could use multiple imputation, as  
implemented for example in Royston's excellent -ice- package (try - 
ssc describe ice-).  In all cases, you could then use empirical Bayes  
estimates of the latent factors in subsequent analyses, or go on to  
fit a full structural model.

I'm sure others will have more to say...


-- Phil

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