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

[Nick Cox <njcoxstata@gmail.com>]

Good that you seem to be making progress.

Just to comment on a side detail: I see no grounds for thinking that
cloglog link implies a discrete response. In principle, it could make
sense for continuous proportions too. As I recall, the original
application (R.A. Fisher, no less) was for precisely this purpose.

Nick

On Tue, Mar 26, 2013 at 8:01 PM, Karen Ruckman <ruckman@sfu.ca> wrote:
> thanks guys for the information.  i see that the loglog link is not the same thing as the loglog distribution in survival analysis.  (even though the loglog link is not actually listed anywhere...i digress.)  i most definitely was not looking to run a cloglog.  that was suggested by someone else.  i do not have a discrete dependent variable, so cloglog is not appropriate.
>
> tricking -gllamm- to use poisson was exactly what i was after.  in the gllamm manual on p.80, the authors give two commands, both the equivalent of each other:
> streg secondp after decl, dist(exp)
> poisson unceni secondp after decl, offset(lny) irr
>
> they do not show it but claim they would produce identical results.  i would use the same (although in the -gllamm- command) except the problem is my underlying survival analysis hazard rate doesn't have an exponential structure. i use a log-logistic structure but log-normal would be fine too.  i am unsure how to get this to work in -poisson- or in -gllamm-.
>
>
>
> ----- Original Message -----
> From: "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
> To: statalist@hsphsun2.harvard.edu
> Sent: Tuesday, March 26, 2013 12:42:30 PM
> Subject: Re: st: equivalence of log-logistic survival estimation with gllamm
>
> On Tue, Mar 26, 2013 at 2:43 PM, Nick Cox <njcoxstata@gmail.com> wrote:
>
>>
>> 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.
>
> I'm with Nick. It's pretty clear there's some confusion going on.
>
> However, there are discrete time proportional hazards survival models
> that involve the cloglog link, and maybe that's what the original
> poster wanted? I just checked Multilevel and Logitudinal Modeling
> Using Stata, Volume II: Categorical Responses, Counts, and Survival,
> Third Edition, S. Rabe-Hesketh and A. Skrondal, 2012, Stata Press.
> They give an example using -xtcloglog- on p. 783, and discuss how this
> could be fit using -gllamm-.
>
> For a continuous time parametric survival model, I'm guessing that
> some kind of censored normal model on the log-transformed time would
> be necessary. That would be the lognormal model, not the log-logistic.
> Out of my area, but I wonder if it would be possible to trick -gllamm-
> to use the same basic "Poisson" likelihood discussed here, but with
> censoring?
>
> http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/
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