Re: st: Can Y be a predicted variable?

[Constantine Daskalakis <C_Daskalakis@mail.jci.tju.edu>]

At 03:45 PM 9/9/2005, Tinna wrote:
> So will I get fried if I do it my proposed way, or will the results
> just be difficult to read for non-statisticians.
> Tina
> > At 18:31 09/09/2005, Tina wrote:
> > >Dear statalisters,
> > >
> > >I have a dependent variable in 5 levels (Self-Assessed Health Status
> > >from very good to very poor). I am currently assuming a latent
> > >continuous variable, but that is problematic for some of my analysis.
> > >I have some other measures of health in my data and was wondering if
> > >it was appropriate to create a new one that would be continuous. My
> > >suggestion would be:
> > >
> > >1. regress SAHS on other health variables.
> > >2. Predict SAHS (lets call it SAHShat) based on the previous regression.
> > >3. The new measure would be calculated as an average of SAHS and SAHShat
> > >
> > >This looks like a good idea to me, but I wonder why I don't see anyone
> > >else doing this if it is OK. Those of you that fell of your office
> > >chairs in laughter could maybe get back on and explain why not,
> > >because it seems fine idea to me right now.
> >

I am not laughing, but I think there are plenty of reasons why this is NOT 
done.

For one, the "predicted" variable (SAHShat) is not an observed outcome but 
one that you have "imputed" (via your regression of SAHS on other health 
variables). How good the prediction is can be debatable. And what beast 
this "predicted" variable really is can be equally debatable.

Second, it is not clear how you would even regress the ordinal SAHS 
variable on other variables. Through some ordinal regression model? Then, 
your predicted values would still be discrete. Through some linear 
regression model? But if your original SAHS variable were continuous enough 
for that, you wouldn't worry in the first place.

Third, the fact that those values are imputed rather than observed adds 
variability that will not be accounted for in your main analyses. Usual 
methods take Y to be an actually observed outcome.

Fourth, why "average" the observed and predicted? What is the rationale for 
that and what do you get out of it?


In addition to Roger's suggestions, another avenue might be to actually do 
a formal latent variable analysis, where you would use SAHS (and possibly 
other covariates) as proxies of your unobserved latent outcome. I think 
structural equations come into this but it is not my field.


Constantine





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________________________________________________________________
Constantine Daskalakis, ScD
Assistant Professor,
Thomas Jefferson University, Division of Biostatistics,
211 S. 9th St., Suite 602, Philadelphia, PA 19107
   Tel: 215-955-5695
   Fax: 215-503-3804
   Email: c_daskalakis@mail.jci.tju.edu
   Webpage: http://www.jefferson.edu/clinpharm/bio/  
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