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Re: st: KcKelvey & Zavoina's R2 in -fitstat- after -gologit2-


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: KcKelvey & Zavoina's R2 in -fitstat- after -gologit2-
Date   Wed, 05 Mar 2008 09:05:25 -0500

At 05:42 AM 3/5/2008, Sara Mottram wrote:
Dear Statalist,

I have fitted a partial proportional odds model in Stata 9.2 using -gologit2-. In their book, Regression Models for Categorical Dependent Data using Stata, Long and Freese suggest that McKelvey & Zavoina's R2 most closely approximates the R2 from linear regression models (which I assume makes this the most suitable R2 to use). Following the advice on Richard William's website to use the v1 option, I have been able to use -fitstat- with -gologit2-, however, it does not produce the M&Z R2.
Please could someone tell me if this is because it does not make sense with a partial proportional odds model, in which case, is there a more appropriate measure of fit that I can use? Or do I need to specifically ask for M&Z R2 via an option?
First off, I don't think any of the pseudo R^2 measures is clearly superior to the others. Borrowing heavily from Long & Freese, I discuss them at

http://www.nd.edu/~rwilliam/xsoc73994/L04.pdf

Second, you also don't get M&Z R2 after using mlogit. The formula for the statistic involves V(Y*), where Y* is the underlying latent variable that gives rise to the observed variable. But, with mlogit, there is no such underlying latent variable; and with gologit, it is not clear that there is such an underlying latent variable either (or if there is, I don't know how you would compute its variance). So, if you must use a Pseudo R^2, use one of the others. McFadden's R^2, which is the one generally reported by Stata, seems as good to me as any. (Although, from an aesthetic standpoint, I kind of like Cox Snell R^2. As pointed out in my notes, it isn't just a logical analog to OLS R^2; it is actually the same formula, albeit expressed in a way that nobody ever uses! But whether that makes it the best formula is another matter.)


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Richard Williams, Notre Dame Dept of Sociology
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EMAIL: Richard.A.Williams.5@ND.Edu
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