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RE: st: r-square in -betafit-


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: r-square in -betafit-
Date   Fri, 18 Jun 2010 09:35:50 +0100

I am another co-author of -betafit- (SSC) and author of the FAQ referred to. 

I see no great harm in computing a R-square measure as an extra descriptive measure. How useful and reliable it is will depend on the science of what you are doing and how far it makes sense as a summary, which is best judged graphically by considering a plot of observed vs fitted. 

Wanting to go further, if you do, in terms of formal inference with R-square would in my judgement be a bad idea. As Maarten indicates, the machinery supplied by -betafit- is superior for that purpose. 

Nick 
n.j.cox@durham.ac.uk 

Maarten buis

--- On Fri, 18/6/10, SURYADIPTA ROY wrote:
> The -betafit- option does not supply a value of r-square or
> similar measure of goodnees of fit.

It gives you the log likelihood, which means that for model
comparison you can use likelihood ratio statistics or AICs
or BICs.

> I actually followed this FAQ:
> http://www.stata.com/support/faqs/stat/rsquared.html
> and implemented the procedure as suggested by Nick. Here
> are the results:
> It would have been very helpful to get some suggestions if
> this procedure can be relied upon in this case, and if the
> value of calculated r-square here can be compared with the
> OLS r-squared (say).

I would in that case rely more on comparing AICs and BICs 
(which are also available after -regress-)

> Also, it would have been very helpful to get some help in
> understanding the difference between the results for
> -proportion- and -xb- following -predict- after -betafit-
> since the mean of the linear prediction (xb = -5.38) is
> found to be wildy beyond (0,1), while the mean of the
> default (i.e. the proportion) is found to be very close to
> the average value of the dependent variable (0.01 vs 0.007).

What -betafit- does is model the mean dependent variable as
invlogit(xb), xb is the linear predictor and invlogit(xb) is
the predicted probability. invlogit(xb) is the function
exp(xb)/(1+exp(xb)). So typically what you are interested
in is the predicted proportion rather than the linear 
predictor. 


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