st: Goodness of Fit Measure for Generalized Linear Models with Adjustment for the Number of Parameters

[Roberto Liebscher <roberto.liebscher@ku.de>]

Hello Statalisters,

I model a fractional response variable with a GLM similar to Papke, 
L.E., Wooldridge, J.M., 1996. Econometric Methods for Fractional 
Response Variables with an Application to 401(K) Plan Participation 
Rates. Journal of Applied Econometrics 11 (1). 619–632.

I would like to obtain a goodness-of-fit measure that incorporates the 
number of parameters in a fashion similar to the adjusted R-squared. It 
is tempting to compute the correlation between the predicted and the 
observed values (like in Christopher F Baum's example here: 
http://fmwww.bc.edu/EC-C/S2013/823/EC823.S2013.nn06.slides.pdf ) and 
compute the adjusted R-squared according to the formula 
$R^2-(1-R^2)\frac{p}{n-p-1}$. Since I have never seen something similar 
in papers so far my question is if there is something wrong about it?

Moreover, from a computational point of view one could also estimate the 
quasi log likelihood function of the unrestricted and the restricted 
model and follow McFadden's procedure (McFadden's adjusted R^2: 
http://www.ats.ucla.edu/stat/mult_pkg/faq/general/Psuedo_RSquareds.htm 
). If the only goal is to compare non-nested models is there any reason 
not to use such a measure?

Any help is highly appreciated.

Roberto

--
Roberto Liebscher
Catholic University of Eichstaett-Ingolstadt
Department of Business Administration
Chair of Banking and Finance
Auf der Schanz 49
D-85049 Ingolstadt
Germany
Phone:  (+49)-841-937-1929
FAX:    (+49)-841-937-2883
E-mail:   roberto.liebscher@ku-eichstaett.de
Internet: http://www.ku.de/wwf/lfb/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/