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From |
<alfonsomirand4@yahoo.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: second version |

Date |
Thu, 22 Aug 2002 08:20:07 -0700 (PDT) |

Dear Statalist, While doing an extension of the code weibhet_glfa I found what I believe is a mistake in the log-likelihood expression of this code. Consider that the mixed survivor function is given by Sm(t)= [ 1 – theta*ln{S(t)}]^(-1/tetha) (1) Where S(t) is the survivor function corresponding to the case in which there is no unobserved heterogeneity; and theta is the variance of the gamma distribution that it has been assumed for the unobserved characteristic. Now, using the fact that -dln(Sm)/dt = hm(t) I obtain the mixed hazard function: hm (t)= - {S’(t)/S(t)}*{1-theta*ln{S(t)}}^(-1) (2) Using (1) and (2) I have written down the log-likelihood obtaining (in an intermediate expression that helps comparison) the expression: Logl = ln{1+theta*exp[-x’b*p]*t^(p)}^(-(1/theta + d)) + + ln{exp[-x’b*p]*p*t^(p-1)} (3) Where x is the vector of observed characteristics and b is its corresponding vector of coefficients. In the weibhet_glfa code the log-likelihood is written as Logl = ln{1+theta*exp[-x’b*p]*t^(p)}^(-(1/theta + d))+ + ln {exp[-x’b*p]*p*t^(p)} (4) Notice that while in (3) we have a term t^(p-1), in (4) the corresponding term is t^(p) (look in the second ln(.)). After checking the consistency of (3) with the log-likelihood that Lancaster (1979) would write using his own expressions for Sm(t) and hm(t), I have become to believe that (4) is incorrect and that the code of weibhet_glfa requires a slight correction. Could you double-check my calculations so that I have a second opinion on the issue?. Thank you, Alfonso Miranda Research Student Economics Department, University of Warwick. References 1. Stata maunal pp. 343-375 (on the st streg code) 2. Lancaster (1979) Econometric Methods for the Duration of Unemployment. Econometrica 47 (4), pp. 939-956. __________________________________________________ Do You Yahoo!? HotJobs - Search Thousands of New Jobs http://www.hotjobs.com * * 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/

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