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Re: st: r-square in -betafit-


From   SURYADIPTA ROY <sroy9163@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: r-square in -betafit-
Date   Fri, 18 Jun 2010 08:10:27 -0400

Dear Maarten and Nick,

Thank you so much for these invaluable comments and suggestions!
Regards,
Suryadipta.

On Fri, Jun 18, 2010 at 4:35 AM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> 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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