# Re: st: st: question about multinomial transition model

 From "Stephen P. Jenkins" <[email protected]> To [email protected] Subject Re: st: st: question about multinomial transition model Date Tue, 13 May 2003 14:22:43 +0100 (GMT Daylight Time)

```On Tue, 13 May 2003 13:03:20 +0100 [email protected] wrote:

> Hi,
>   The full reference is Diggle & Zeger (1994) Analysis of
Longitudinal data. Oxford : Oxford university press. >   My model is
about competing risk factor model. I have four competing risk factors,
let say A, B , C and D and 6 explanatory variables. I want to estimate
the transitions from state A at one time to the next time or visit with
include the explanatory variables. It mean tried to estimate the rates
transition probabilities pr(Yij |Yij-1)plus the effect of explanatory
variables (sort of Markov chain regression model for multinomial
responses). >
>  Thank you in advance for the sugessions of software that can fit the
above model. >

I do not have access to the 1994 book or the second edition. (By Diggle
and others, 2002.)  However, let me argue that you can probably
estimate the model in Stata.

Assume you have an /independent/ competing risks (ICR) model.  Next
decide whether the process generating your survival times
(i) occurs in continuous time and exact survival times are
available (dates), or
(ii) occurs in continuous time but observed survival times are grouped
into intervals ('interval censoring'), or
(iii) you have an intrinsically discrete time process.

(ii) is perhaps the most common situation in the social sciences.
In cases (i), (ii), it turns out that the likelihood for the k-state
ICR model can be factored into k separate models that can be estimated
independently (using destination-specific censoring indicators) using
standard single-risk models. For case (i), use -streg-, -stcox-, and so
on, in Stata. For case (ii), supposing intervals of equal length
(e.g. a 'month' or 'year'), use -cloglog- or -logit- applied to data
reorganised so that there is one obs for each interval that each
subject is at risk of event occuring.
For case (iii), the ICR likelihood does not factor conveniently but can
be estimated straightforwardly using a multinomial logit model program
(-mlogit- in Stata).

The result for case (i) appears in any standard survival analysis text.
Result (ii) is not so well-known, but is stated by Narandrenathan &
Stewart (Applied Statistics 1993).  Both results are informally
explained in chapter 8 of the notes available at:
http://www.iser.essex.ac.uk/teaching/stephenj/ec968/pdfs/ec968lnotesv2r.pdf
The result re (iii) is stated informally by P. Allison (1984), Survival
Analysis, Sage.

I conjecture that the Diggle/Zeger multinomial model that you referred
to longitudinal data as if they were of case (iii). However check also
whether case (ii) applies to you.

Stephen
----------------------
Professor Stephen P. Jenkins <[email protected]>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester, CO4 3SQ, UK
Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151.
http://www.iser.essex.ac.uk

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