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Re: st: log likelihood using Stata vs. TDA


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: log likelihood using Stata vs. TDA
Date   Tue, 16 Jul 2002 09:05:08 +0100 (GMT Daylight Time)

On Mon, 15 Jul 2002 18:51:49 -0700 Shige Song <sgsong@ucla.edu> wrote:

> Dear All,
> 
> I want to thank both Roberto and Jesper for their great comments (and
> sorry for not being to do this sooner because I was bounced out the 
list > for no obvious reasons).  
> > I have something else to say about the  the AFT vs. PH. Based on 
what I > know, there is no way to parameterize ordinary log-logistic 
hazard model > (as implmented in Stata and many other packages) as PH. 
But TDA > implements an extension of the ordinary log-logistic hazard 
model > proposed by Bruederl&Diekmann (1995). They replace the scale 
parameter > with two that represent the "timing effect" and the 
"intensity effect". > The timing effect can only be parameterized as 
AFT, but the intensity > effect can be parameterized either as AFT and 
PH. > 
> Again, thank you very much for the comments. > 
> Shige Song > Department of Sociology, UCLA
> > Reference:
> Bruederl, J., and A. Diekmann. 1995. "The Log-Logistic Rate Model - 2 
Generalizations with an Application to Demographic-Data." Sociological 
Methods & Research 24:158-186.

A footnote following the clear and helpful explanations of Bobby 
Gutierrez ...

Not having access to the original Bruederl and Diekmann paper, I'm not 
clear how the PH/AFT distinction and scale/intensity distinctions 
were made in the context of their model. But, according to Blossfeld & 
Hamerle (2002, pp. 198-9), the B/D model can be written:

hazard rate r(t) =    b(at)^(b-1)    a, b, c > 0
                    c -----------
                      1 + (at)^b

survivor fn G(t) = 1/ [1 + (at)^b]^(c/a)

which may be contrasted with their parameterisation of the 'standard' 
log-logistic model:

hazard rate r(t) =    b(a^b)(t)^(b-1)    a, b > 0
                      -----------
                      1 + (at)^b

survivor fn G(t) = 1/ [1 + (at)^b]^(c/a)

Thus in the 'extended' B/D model there is an additional parameter c, 
which might depend on covariates. So, taking 2 cases i and j with the 
same a, b, and t, but different c, then  the ratio of their hazard 
rates would be c_i/c_j ... which is sort-of PH-like.

Blossfeld, H.-P., and Rohwer, G. (2002) Techniques of event history 
modeling : new approaches to causal analysis, Lawrence Urbaum 
Associates. 

NB Rohwer is the author of TDA, information about which can found at
http://www.stat.ruhr-uni-bochum.de/tda

I prefer Stata

Stephen
----------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
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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