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st: RE: Discrete-time models with repeated events

From   "Luis Ortiz" <[email protected]>
To   <[email protected]>
Subject   st: RE: Discrete-time models with repeated events
Date   Fri, 25 Jan 2008 10:57:13 +0100

Many thanks for the references and the suggestions, Stephen

Luis Ortiz

-----Mensaje original-----
De: [email protected]
[mailto:[email protected]] En nombre de Stephen P.
Enviado el: viernes, 25 de enero de 2008 10:23
Para: [email protected]
Asunto: st: Discrete-time models with repeated events

> ------------------------------
> Date: Thu, 24 Jan 2008 11:30:25 +0100
> From: "Luis Ortiz" <[email protected]>
> Subject: st: Discrete-time models with repeated events
> Dear Statalisters,
> I'm carrying out survival analysis of a process that 
> conceivably occurs in
> continuous time, but for which observed survival times are 
> grouped into
> intervals. Quite unfortunately, my data do not allow for 
> more. According to
> various sources, amongst them the valuable Stephen Jenkins' lessons,
> discrete time models (i.e. logistic or cloglog) are called 
> for. My first
> question would be which one of these discrete models to 
> choose. I'm afraid I
> have not drawn a clear idea of the added value of the cloglog
> relative to logistic.

A complementary log log specification for the grouped data hazard has
the advantage that the regression coefficients are the regression
coefficients for a proportional hazards model specified in continuous
time.  When the interval width used to group data is `'small', then a
logit model for the grouped data hazard provides very similar
estimates to the complementary log log model.

This stuff is in the references that you cite, and the papers cited

> My second question relates to the event I'm analyzing. The 
> event may occur
> several times for the same individual in the panel; in other words,
> repeated-events model seems to be called for. Is there any 
> way of using either the logistic or cloglog for a model with
repeated events?

You're confusing a cloglog (or logit) specification for the hazard,
and the -cloglog- or -logit- commands.  You want the latter to
estimate a model where you have the former plus repeated spells for
the same individual. You can't; you will need to write your own
program -- at least for the case which is of most relevance.

If there is no unobserved heterogeneity, then all differences in
hazards are summarized by the observed explanatory variables (X).
Aside from issues of initial conditions and all that then, conditional
on the X, the spells are independent. So you can simply pool the
spells, and carry on as before.  If you have unobserved heterogeneity,
then the unobserved individual effect for each individual is
correlated across spells, and you have to control for that.  One
method, viewed as crude by economists, is simply to adjust the
standard errors from the pooled spell model using a form of sandwich
estimator. (Allison's little Sage book refers to this.)  Economists
prefer to /model/ the unobserved heterogeneity using either a discrete
distribution (latent class idea due to Heckman and Singer) or a
continuous distribution for the frailties such as normal or gamma.
[Again you cannot simply apply programs allowing for frailty such as
-hshaz- or -pgmhaz8- to repeated event data as they assume no repeated
events per person.]  Please read the literature on "mixed proportional
hazards models" -- a good start is the chapter by Gerard van den Berg
in the Handbook of Econometrics Vol 5, Elsevier, 2001.

Professor Stephen P. Jenkins <[email protected]>
Director, Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.  
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