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RE: st: left censoring in discrete-time duration model
> Date: Thu, 16 Nov 2006 13:57:13 -0500
> From: Daniel Simon <firstname.lastname@example.org>
> Subject: RE: st: left censoring in discrete-time duration model
> Stephen - first let me say that I have consulted your
> website materials
> for a variety of issues and found them extremely useful.
> Regarding your
> comment, this is part of what has had me confused: whether
> it's truncation
> or censoring. As you suggest, magazines become at risk of
> establishing a
> website "the later of either the year web
> technology became available or the year when the firm itself was
> established." But, in some cases, they establish a website
> before I can
> observe it. So, this sounds like truncation. If so, my
> question is: using
> your easy-estimation methods, which observations do I throw away. In
> particular, in my case, do I throw away all observations for
> 1996? 1996 is
> the first year of the analysis period because it is the first
> year in which
> I observe which magazines have websites. But, I have no way
> to distinguish
> those magazines that had websites before 19996 and those that
> did not.
> After 1996, I can tell which magazines adopted new websites
> (by comparing
> whether they already had one the year prior). I hope this
> makes sense.
> thanks again for the help. Daniel
"establish a website before I can observe it" is a classic case of
left-censoring -- see e.g. Klein & Moeschberger, _Survival Analysis_,
who also provide an expression for the likelihood contribution in this
This definition of left-censoring differs a bit from the one in common
use in the social sciences -- left-censoring referring to all cases in
which the date of the start of the spell is unobserved. In this
situation, it is often recommended to drop these cases -- implicitly
appealing to some sort of independence assumption. After all, what
else can one do without the information? But there are potential
problems -- of the sort raised by Jason Yackee <email@example.com>
-- if spell length (time to event) and start date are systematically
You may have left-censoring (classical sense) and left truncation.
Whatever the case, estimating a model incorporating unobserved
heterogrenity (frailty) is probably harder than you'd hoped. As I
said, I doubt whether an 'easy estimation' method is available.
Professor Stephen P. Jenkins <firstname.lastname@example.org>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374. Fax: +44 1206 873151.
Survival Analysis using Stata:
Downloadable papers and software: http://ideas.repec.org/e/pje7.html
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