发帖
雷达卡
Question:
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I recently ran a do-file that contained several tobit and xttobit models and later decided to rerun one of the xttobit models. I was surprised to find that I got different results. The puzzle to me is that the iterations that fit the full model are identical to what I estimated the other day (through iteration 6), and then they diverge.
The data have not changed, and the correct sample and variables are being used. The only difference is that I am running one regression instead of many. Is there some random component due to the use of quadrature?
Answer:
For those not familiar with xttobit, it and several other commands that estimate random-effects models use Gauss–Hermite quadrature and adaptive quadrature to approximate the high-dimension integrals that are part of the likelihood for these models. The quadrature approximation can be poor for some datasets, and I suspect this is what this user is encountering.
As the user suggests, there is a random component to quadrature in that the within-panel sort will almost certainly be different unless you start Stata fresh and run exactly the same commands before running xttobit. Sort order is not important to the likelihood, but if the likelihood for the dataset cannot be approximated well by quadrature, the order can affect the quadrature computation (more on this later).
Quadrature is one of the most accepted approaches to estimating these models, but there are three cases where it often breaks down: (1) large panel sizes, (2) high within-panel correlation, or (3) variables that are constant or near constant within panel. I don’t know if any of these are true for these data, but any observation that contributes in an extreme way to the likelihood can cause problems. See [XT] quadchk for a good discussion of these issues.
Stata’s quadchk command can help tremendously in assessing whether your data are appropriate for estimation using the quadrature approximation. quadchk works with all of the estimation commands that use quadrature and I definitely recommend that the user try quadchk on the model. I also heartily recommend that people estimating a random-effects model by quadrature check whether the quadrature is stable for their model. If you’re using Stata, use quadchk to do this.
We have tried to point everyone using commands that employ quadrature to quadchk by providing a Technical Note or example in the manual entry. In hindsight, these suggestions could have been stronger.
We at StataCorp could have artificially forced Stata to produce the same answer always from xttobit by performing a sort during quadrature, but we purposely did not do that. That strikes us as ducking the issue. If quadrature is not stable, better not to hide it.
Commands using quadrature have been the source of some debate around StataCorp. None of us are wholly comfortable with estimators that are prone to instability, even if that instability arises only in extreme cases. That is why we feel so strongly about providing quadchk to assess the appropriateness of the estimator for a given dataset. The near consensus here is that these estimators are valuable to those who need them even though they require care from all who use them. They are stable for most datasets. Admittedly, these are leading-edge models, and estimating them requires more understanding of numerical and approximation issues on the part the user than do most other estimation commands.
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