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Re: st: equivalence of log-logistic survival estimation with gllamm


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: equivalence of log-logistic survival estimation with gllamm
Date   Tue, 26 Mar 2013 18:43:04 +0000

Some confusion here, I think. You appear to be assuming that the

log-logistic distribution in survival analysis

matches either or both of the

log-log and complementary log-log link functions in generalised linear models

-- is that guess right about what you are asking?

The loglog and cloglog link functions have no application to survival
times whatsoever. They are relevant _only_ to mean responses bounded
by 0 and 1.

The common characters "log-log" aren't diagnostic here.

It is not a limitation of -gllamm- to disallow what makes no sense.
-gllamm- is not being difficult or incomplete here.

BTW, please explain where user-written programs come from. -gllamm-
may be downloaded from SSC.

I'd look at an introduction to generalised linear models before even
venturing into the more advanced kind, as link functions and
distribution families are different beasts and you are conflating
them.

Nick

On Tue, Mar 26, 2013 at 6:19 PM, Karen Ruckman <ruckman@sfu.ca> wrote:

> yes, i have looked at p.12 of the manual.  but not every link is available for each family.  complementary log-log is not the same thing as log-log.  complementary log-log is for binomial dependent variables.  my survival analysis has a dependent variable which is the length of time to an event where every observation achieves the event (non-discrete survival analysis).  i have been using the log-log distribution in survival analysis with good results and it has the appropriate assumptions about the hazard rate.  i would like to recreate the same results using -gllamm- but am having trouble doing so.
>
> what i have:
> streg x, d(ll)
>
> what i would like to do:
> gllamm y x, family(poisson???) link(???)

William Buchanan" <william@williambuchanan.net>

> Maybe you weren't looking at the documentation?  On page 12 of the GLLAMM manual (http://biostats.bepress.com/cgi/viewcontent.cgi?article=1160&context=ucbbiostat), the authors explicitly list each of the links and families (as well information for ordered categorical data).  On that page, the authors list "complimentary log-log" as one of the link functions.  Maybe you should first try explaining your data and what inference you hope to make/models you would like to fit and see if anyone has other suggestions for fitting a model that would be easier to defend and/or interpret.

On Mar 26, 2013, at 10:53 AM, Karen Ruckman <ruckman@sfu.ca> wrote:

>> in my quest to run an IV estimation with the first stage being a survival analysis, i am trying to figure out how to use -gllamm-.  the appropriate first stage survival distribution is log-logistic (or log-normal) but there does not seem to be this option for -gllamm-. (it is hard to tell as there is no list of the available links for each family anywhere and the writer of the command does not respond to emails.)  -gllamm- offers the family(poisson) distribution but no loglog link.  does anyone know if there is there is a way to recreate survival analysis log-log results using a -gllamm- regression?

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