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RE: st: left censoring in discrete-time duration model

From   "Stephen P. Jenkins" <>
To   <>
Subject   RE: st: left censoring in discrete-time duration model
Date   Fri, 17 Nov 2006 08:56:53 -0000

> Date: Thu, 16 Nov 2006 13:57:13 -0500
> From: Daniel Simon <>
> 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 <>
-- 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 <>
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:

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