Re: st: Fixed effects duration model with only one spell per individual

[Steven Samuels <sjsamuels@gmail.com>]

Maria & Juan:


Presumably you are referring to an early version of  Allison, Paul D. and Nicholas Christakis (2006) “Fixed effects methods for the analysis of nonrepeated events.” pp. 155-172 in Ross M. Stolzenberg (ed.), Sociological Methodology 2006.  A pre-print is at http://www.pauldallison.com/Download2.html.

You had two questions:

> 1. "Is it in fact true that because we cannot include in estimation the
> baseline duration dependence parameters the other coefficients in the
> model are biased because in fact we do not control for duration
> dependence and the model is not really a duration model?"
> 
Yes.

> 2." If we do not include baseline duration parameters in the model but
> only the interactions of them with other covariates in the model
> (something that has no problems with the conditional logit), are we
> still estimating a proper duration model or something with a different
> interpretation?"
> 
This would not be a "proper duration model". Omission of the "main effect" duration terms from the model (e.g. t or log(t))  will cause omitted-variable bias analogous to that in OLS.

Conditional logistic regression starts out with an implied full logistic model, which includes a panel-specific intercept,  panel-constant covariates, time-varying covariates, and interactions. The intercept and  main effects of the panel-constant covariates cancel out of the conditional likelihood equations precisely because they are constant.  Duration main effects are, by definition, not constant within a panel and will not cancel out.

Perhaps the "case-time-control" model in Allison's paper will serve your purposes. With it one can consistently estimate the odds ratio for a one binary time-varying covariate at a time by switching the roles of outcome and predictor in a conditional logistic regression that includes duration terms and other covariates. 

Steve

Steven J. Samuels
Consulting Statistician
18 Cantine's Island
Saugerties, NY 12477 USA
Voice: 845-246-0774
Fax:   206-202-4783 
sjsamuels@gmail.com




>> Dear Sir/madam,
>> 
>> We are estimating with STATA a duration model transformed in a binary
>> choice model (as suggested by Allison, 1982, and Jenkins, 1995) that we
>> wanted to estimate using the stata command clogit, because we are
>> interested in allowing for fixed effects in the duration model. But
>> doing so we had the problem of not being able to estimate the duration
>> dependence parameters because the model does not converge when we
>> include them. In relation to this problem we have found a working paper
>> by Paul D. Allison and Nicholas Christakis (2000) that seems to imply
>> that duration dependence parameters or covariates that change
>> monotonically with time cannot be estimated with conditional logit
>> applied to duration data, not because they disappear with the
>> conditional probability (something that happens with time constant
>> covariates) but because there is a lack of convergence driven by a
>> perfect prediction of the outcomes in these type of models (where there
>> is a dependent variable with value 1 only when the spell finishes for a
>> given individual). Therefore, if we estimate the duration model with the
>> conditional logit approach (not including the duration dependence
>> dummies) it seems we are not in fact controlling for duration dependence
>> and, this can bias our estimates of all the other covariates in our
>> model.
>> 
>> From all this thinking we summarize our questions:
>> 
>> 1. Is it in fact true that because we cannot include in estimation the
>> baseline duration dependence parameters the other coefficients in the
>> model are biased because in fact we do not control for duration
>> dependence and the model is not really a duration model?
>> 
>> 2. If we do not include baseline duration parameters in the model but
>> only the interactions of them with other covariates in the model
>> (something that has no problems with the conditional logit), are we
>> still estimating a proper duration model or something with a different
>> interpretation?
>> 
>> 3. If the answer to question 2 was yes, do we still have to bother about
>> the other covariate parameters in the model to be estimated with bias
>> (given that we could not include in estimation also the baseline
>> duration parameters by themselves but only interacted with other
>> covariates)?
>> 
>> Many thanks in advance, 
>> Yours faithfully,
>> Maria Rochina and Juan Sanchis
>> ================
>> 
> Maria also wrote to me privately asking the same question. My response
> to her (written before seeing the Statalist post) was the following:
> 
> Fixed effects duration models?  I don't think they are possible to
> estimate.   All existing frailty specifications are random effects
> models. ... If fixed effects models were possible, one might ask why
> others haven't published papers using them ...  However I must say that
> I am not aware of the Allison and Christakis (2000) paper -- what is the
> citation please?
> 
> My intuition about this is the following:
> 
> We typically identify fixed effects logit models from the observations
> with changes in status. In a discrete time duration data model, with the
> data "expanded" to person-period form, that would mean that all of the
> data for persons with censored spells would not be used; only the data
> for people with an "event".  Surely such sample selection must provide
> us with biased estimates of the patterns of events with elapsed
> duration. And it is also likely to lead to problems with fitting in any
> case e.g. because the effective sample size may be relatively small, or
> at least fraction of 'events' in the data. (There'll be the usual
> problem of identifying coeffs on covariates that are fixed over time
> too, I think.)
> 
> 
Stephen
-------------------------------------
Professor Stephen P. Jenkins  <s.jenkins@lse.ac.uk>
Department of Social Policy and STICERD
London School of Economics and Political Science
Houghton Street, London WC2A 2AE, U.K.
Tel. +44 (0)20 7955 6527
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/survival-analysis
Downloadable papers and software: http://ideas.repec.org/e/pje7.html



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