Presumably, you've been dying to know why it is that when you estimate a maximum-likelihood model without any weights or clustering in Stata, the likelihood that is maximized is called a "pseudolikelihood" if the variance-covariance matrix of the estimates are based on the formula for so-called "robust" standard errors, but is called a "likelihood" if the variance-covariance matrix of estimates is computed by the bootstrap method.
Yeah, me neither. Moreover, I resent the two hours of my life* this has taken up today. Especially since (a) it is so nice outside, (b) the answer isn't particularly important for my purposes anyway--it's just the inexplicable inconsistency that I can't deal with--and (c) I still don't know the answer.
* Proclamation: I recently decided that I would forever cease calling things as being a "waste of two hours of my time" and instead refer to them as a "waste of two hours of my life", since the latter seems more accurate. Time just happens to be what my life is made out of.
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4 comments:
I think it's that unless your data are normally distributed by construction, the formula diverges from whatever the true likelihood is. One of my econometrics profs called this a "quasi-ML" estimator; some texts use "quasi" and "pseudo" interchangeably, for instance Davidson & MacKinnon's Estimation and Inference in Econometrics (Oxford). In the other case, the boostrap procedure is presumably set up so that it converges on the VC matrix of the "true" MLE.
what are jeremys made of? snips and snails and time and extra, extra malt.
also, you know i hate it when you post about stats and methods. stop.
Tom:
Thanks. I have a query out to an statistician at [software company] about this. The key thing for my purposes are the conditions under which one shouldn't be using a likelihood-ratio test. Not having your econometric erudition, I've just followed the reasoning that under conditions in which robust standard errors are correct, the likelihood ratio test can't be correct, since the likelihood ratio test gives non-equivalent results for equivalent tests. But, the same would seem to apply to any case where the bootstrap vce differs from the naive vce. In other words, either there isn't any especial reason to use the bootstrap vce, or, if there is, then you shouldn't be treating the likelihood as a true likelihood. This is where I get hung up.
Dorotha:
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