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st: RE: Pseudo Rsquared with IVPROBIT


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Pseudo Rsquared with IVPROBIT
Date   Thu, 19 Mar 2009 11:30:20 -0400

Sophia Rüster wrote:


>>With my dataset I wish to use the regression method IVPROBIT (probit model
with continuous endogenous regressor). The regression seems to work fine.
However, no goodness-of-fit indicator is reported. I wondered whether it
would be possible to calculate a pseudo-R² for example, whether this
technically is not feasible or whether this would make no sense from an
interpretational point of view.<<

Generally if Stata doesn't report something, there are reasons why. Usually this means that there is substantial controversy over interpretation. 

I don't know about -ivprobit- specifically but the general problem with defining pseudo-R^2 measures is the choice of reference model. In ordinary regression this is the no-regressors model, but as we all know, this can be a very poor reference, making a poorly functioning model look great (i.e., have high R^2) even though it provides little utility. Regressions with lagged dependent variables are canonical examples of this. What may help you is if you can figure out a way to situate the models you fit between something that's too simple and too complex. For instance, maybe you're primarily interested in a subset of variables and have some other controls (and the instrument) that are in all models. Then the it makes sense to judge the performance of the variables of interest against the model with controls and the instrument. 

An alternative strategy is to use the information-theoretic model selection strategy discussed in books like Burnham and Anderson (2003): http://www.amazon.com/Selection-Multi-Model-Inference-Kenneth-Burnham/dp/0387953647/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1237476507&sr=8-1



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