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st: RE: truncreg and discontinous likelihood


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: truncreg and discontinous likelihood
Date   Thu, 24 Sep 2009 11:54:21 -0400

Rich Steinberg wrote:

>>a) I understand what lack of concavity and backing up is about.  But I 
am baffled by "discontinuity" of the likelihood function -- is there a 
simple explanation of what could cause it? <<

Well -truncreg- is fitting a pretty complex likelihood function. If you look at it in the documentation, it's basically OLS plus terms involving the normal CDF to fix things up for the effect of the truncation. These kinds of likelihoods can be quite nasty. 

I suspect that it's something akin to perfect prediction in logistic regression. That is some configuration of the predictors predicts that cases are below the truncation point, you really don't know anything about them beyond that they're smaller than the truncation. That's just a guess, though---you could have something else going on. 



>>b) Checking that "disable" box led to convergence, but since I don't 
understand the algorithmic issue here, can you reassure me that this 
solution is plausibly the correct one to the problem I was having.<<

It probably isn't a valid solution. I suspect you're at a point in the likelihood that's essentially a "crease" or a boundary solution. This might be caused by perfect prediction, as I mentioned previously. If you are at a crease the solution won't be unique. This sort of thing is common in relatively complex models when your dataset is small relative to the number of predictors and/or you have collinearity. 


>>c) Are my flakey results inherent in doing truncated regression, or do 
they suggest that I am doing something else wrong (or, heaven forbid, 
that stata is doing something wrong). <<

I doubt that Stata is doing anything wrong but their tech support might be interested in your dataset. 

Jay

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