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From |
"James Hardin" <jhardin@stat.tamu.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Re: Random Effects Probit |

Date |
Tue, 17 Sep 2002 10:33:40 -0500 |

** My apologies if this comes through twice. ** Several people have written about the random effects probit estimator in Stata. There are several issues here. (*) Limdep uses BHHH in fitting this model (and uses it in many of the models it fits; check the documentation). That is why the standard errors do not match between the packages. Stata uses the usual or observed Hessian (inverse matrix of second derivatives). (*) Stata fits a constant only random effects probit estimator at the first stage. It keeps this log-likelihood for a future test of the fully specified model. (*) When Stata starts to fit the full model, it takes the values for a regular probit model and then calculates the log-likelihood of the random effects probit model using those coefficients with rho=0.0, 0.1, 0.2, ... It continues to fit these models until the log-likelihood fails to improve. It then starts the optimization using the (regular) probit estimates along with the "best" value of rho it found in this simpleminded search. So , several have asked why Stata doesn't use the regular probit answers as the starting value. The answer is that Stata does use those values, but immediately tries to find a better starting value for rho before starting the optimization process. I believe that all of the random-effects models in Stata that use Gauss-Hermite quadrature take this same sequence of steps. It is easy to verify these starting values by specifying the -trace- option on the command (and running the regular probit command separately honoring any sample selection that occurs in the xtprobit command). (*) Typically, Stata has no problems fitting this model except when rho is very small (it could have problems when rho is close to one, but this is not very common). When rho is very small, the parameterization of the correlation using the arctan wants to march off to negative infinity. The calculation of the second derivatives becomes numerically difficult and results with missing standard errors are not uncommon. (*) Users can specify their own starting values, but must remember to specify a value for the correlation parameter in the arctangent metric. (*) As has been shown in a very nice article in The Stata Journal, the model may be fit much more efficiently (and numerically stable) using adaptive quadrature. So, use the -gllamm- command instead. (*) Whether one would want to use BHHH calculated standard errors or use this for the optimization step-size calculations is open for debate. Personally, I want the standard errors that Stata reports. The xtprobit command is mostly internal calculations. It was written at a time that internal commands used a different (but very similar) collection of optimization routines from the -ml- collection. Nowadays, I think that they may use the same routines. Coding your own estimator using the -d2- form of the -ml- command allows you to use whatever method you want to form the stepsize matrix for the optimization. (*) You can affect the answers that you get using several of the options on the -xtprobit- command. You can specify a less conservative tolerance for the log-likelihood. You can specify a small number of maximum iterations. You can specify a different number of quadrature points, though as mentioned earlier you are likely better off using a command that offers adaptive quadrature in the calculation. To be clear, the quadrature is used to calculate the log-likelihood, the gradient, and the hessian matrix. You can specify different starting values -- at the very least this will assist you in determining if values from another package result in a better log-likelihood than that found at the last step in Stata. (*) Running -quadchk- is a must. You should always do this and the manuals give this advice. With the availability of gllamm, I would run that command instead specifying the adapt option. At the very least I would use the gllamm with adapt to verify the answers in xtprobit. Best, James ---------------------------------------------------------------------- James W. Hardin, Ph.D., Lecturer jhardin@stat.tamu.edu Department of Statistics, Blocker 416G 979-845-3141 (phone) Texas A&M University Mail Stop-3143 979-845-3144 (fax) College Station, TX 77843-3143 http://stat.tamu.edu/~jhardin ---------------------------------------------------------------------- * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: Censored Medical cost***From:*anirban basu <abasu@midway.uchicago.edu>

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