Re: st: Including components of a summative score in regression

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 02:46 PM 7/30/2012, Donald Spady wrote:
> Dear Statalisters
>
> I am doing some logistic regression analysis, some of the variables 
> of which are made up of the values of other variables; e.g. N = A + B + C/D.
> Is it reasonable, or appropriate, to include A,  B, C, or D in the 
> equation if N is already in it.
> i.e.
> logistic X F G H N A B C D, where F G H are some variables, and N is 
> made up of A B C D, but for some reason or other A B C D are desired 
> to be in the equation.
>
> My impression is that statistical theory would say this is a no-no, 
> largely because of collinearity; however, if I do it, sometimes I 
> get a better 'fit' to the equation (using estat gof, group(10)).
>
> Thanks
>
> Donald Spady

I believe the improvements in fit stem from

* N constrains the coefficients of A and B and C/D to be equal; 
adding A and B relaxes two of those constraints.

* The linear effects of C and D are not captured by N

So sure, adding those vars can improve fit.

I could be wrong, but I believe if you ran

logistic X F G H A B C D C/D

you would get the same fit as you are getting now. That might seem a 
little less convoluted to me. But I don't think what you are doing is 
inherently evil; you just have to understand what the parameters mean 
and why you get a better fit.


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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