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


From   Roberto Liebscher <[email protected]>
To   [email protected]
Subject   st: Goodness of Fit Measure for Generalized Linear Models with Adjustment for the Number of Parameters
Date   Tue, 04 Mar 2014 18:04:06 +0100

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:   [email protected]
Internet: http://www.ku.de/wwf/lfb/

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