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

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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.)


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