# RE: st: interpretation of exponentiated coefficients

 From "David Harrison" <[email protected]> To <[email protected]> Subject RE: st: interpretation of exponentiated coefficients Date Mon, 4 Jul 2005 10:49:52 +0100

```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.

Hope this helps

David

*
*   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/
```