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From |
"Stephen P. Jenkins" <[email protected]> |

To |
<[email protected]> |

Subject |
st: interpretation of exponentiated coefficients (cloglog) |

Date |
Tue, 5 Jul 2005 09:33:25 +0100 |

> Date: Mon, 4 Jul 2005 10:49:52 +0100 > From: "David Harrison" <[email protected]> > Subject: RE: st: interpretation of exponentiated coefficients > > I don't think the -eform- could ever be "not appropriate" for > a GLM... it is just easier to interpret with some link > functions than others. In the case of -cloglog-, if we take > the easiest case of a binary variable, the exponentiated > coefficient would be: > > - -log(1-p)/-log(1-q) > > where p is the probability of the outcome given our binary > variable is true and q is the probabilty of the outcome given > our binary variable is false. As far as I know, this has no > name. By comparison, the relative risk would be p/q, and the > odds ratio (p/(1-p))/(q/(1-q)). > > There does seem to be some relationship with hazards, as the > cumulative hazard function is -log(1-F(t)), where F(t) is the > distribution function of the time to an event. If the outcome > Y is the probability that this event happens before a fixed > time t then you have P(Y=1) = P(T<t) = F(t) and the -eform- > of the -cloglog- model is the ratio of the cumulative hazard > functions for this event, evaluated at t. I still wouldn't > really call this a hazard ratio. The -cloglog- model is the discrete time (a.k.a. grouped data or interval-censored) model representation of the continuous time proportional hazard model (see entry -discrete- in the [ST] manual). The beta (regression slope) coefficients estimated in the -cloglog- model are the beta (regression slope) coefficients from the underlying PH model. exp(beta_k) for the k_th regressor is indeed a "hazard ratio". Given this important interpretation, and since most people probably use -cloglog- for hazard regression applications, I've been asking StataCorp to add the eform option to -cloglog- for years (at User Group meetings). It hasn't been implemented perhaps because one can also now estimate a -cloglog- model by ML using -glm- and get eform coefficients that way. But that is not a very good reason because we can also estimate a -logit- model using -glm- and get eform coefficients ... and yet, of course, we can get odds ratios directly via -logistic-. I would support addition of an eform option to -cloglog-. Stephen ------------------------------------------------------------- Professor Stephen P. Jenkins <[email protected]> Institute for Social and Economic Research University of Essex, Colchester CO4 3SQ, U.K. Tel: +44 1206 873374. Fax: +44 1206 873151. http://www.iser.essex.ac.uk * * 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: Re: interpretation of exponentiated coefficients (cloglog)***From:*"josemaria" <[email protected]>

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