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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Maximum likelihood estimation of a probit with free variance and constrained coefficient |

Date |
Wed, 7 Mar 2012 10:59:40 -0500 |

Martin, you need to give better starting values. -ml- by default tries to start from a zero vector, so any division by `sigma' results in a division by zero which gives missing values. Set your sigma parameter to 1, or give -ml- the whole vector of coefficients to start from. On Wed, Mar 7, 2012 at 5:49 AM, Martin Nybom <martin.nybom@sofi.su.se> wrote: > Hello, > > I want to use maximum likelihood to estimate a probit with "free" variance > coefficient (or sigma). I want to have a coefficient parameter for one of > the independent variables (denoted beta_hat) as constraint, so that > identification is possible. This beta_hat I have from an earlier step of a > "structural" model. I have used the following synthetic data set to try to > make the ml routine for this to work: > > ************************ > > clear all > program define syndata > version 12.0 > args obs > qui { > set obs `obs' > gen x1 = uniform()*4 > gen x2 = uniform()*2 - 1 > gen e = logit(uniform()) > scalar b0 = -2 > scalar b1 = 1 > scalar b2 = 2 > gen y_1 = scalar(b0) + scalar(b1)*x1 + scalar(b2)*x2 + e > gen pr_y = invlogit(scalar(b0) + scalar(b1)*x1 + scalar(b2)*x2 + e) > gen y = (pr_y>=0.5) > } > end > > ************************* > > And then the ml code proceeds as follows: > > ************************* > > syndata 1000 > > set more off > constraint define 1 x2 = 2 > global ML_y1 `y' > cap program drop probit2_lf > program define probit2_lf > version 12.0 > args lnf xb sigma > tempvar lnlj > qui { > gen double `lnlj' = ln(normal( `xb'/`sigma')) if $ML_y1 == 1 > replace `lnlj' = ln(normal(-`xb'/`sigma')) if $ML_y1 == 0 > replace `lnf' = `lnlj' > } > end > > ml model lf probit2_lf (y = x1 x2) /sigma, constraints(1) > ml maximize > > *************************** > > This however doesn't work. The iterations give the "not concave" message > directly from iteration 1. Since the model is simple and there shouldn't be > any problem with the data, I suspect that I have a problem either somewhere > in the coding or with how I write down the likelihood functions. I have > tried the option "offset()" and also putting the ", constraint(1)" directly > after the equation. Then I get the message the "could not calculate > numerical derivatives - discontinuous region with missing values > encountered". Any help on this is highly appreciated! > > Thanks for your consideration! > > Martin Nybom > > -- > Martin Nybom > Institute for Social Research > Stockholm University > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Maximum likelihood estimation of a probit with free variance and constrained coefficient***From:*Martin Nybom <martin.nybom@sofi.su.se>

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