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Re: st: pgmhaz-testing the slope

From   Jenkins S P <>
Subject   Re: st: pgmhaz-testing the slope
Date   Sun, 31 Aug 2003 09:24:13 +0100 (BST)

On Sat, 30 Aug 2003 wrote:

> I'm using pgmhaz command for estimating a discrete time (grouped duration data)
> proportional hazard model - how can I test the slop of the non-parametric
> baseline hazard rate for models [1 and 2?]

I am not sure your question can be answered as it stands. Against what
reference point do you wish to "test the slope"? A constant baseline
hazard? Piecewise constant? Or one that is some polynomial in time? One
corresponding to a continuous time Weibull? And so on.

Some alternative hypotheses about the baseline hazard function shape can
be tested straightforwardly if they are easily nested within yours. For
example, to test whether the baseline hazard is constant, you can use a
Wald test (-test-)  about the coefficients in the model corresponding to
those for the baseline. (Or you could estimate the nested model and use an
LR test.)

To test whether the estimates of the discrete time (grouped data) baseline
hazard are consistent with various other hypotheses about the baseline
hazard for the underlying continuous time proportional hazard model is
trickier. There is an article by Sueyoshi, G.T. (1995), `A class of binary
response models for grouped duration data', Journal of Applied
Econometrics 10, 411-431 -- this explains the restrictions. See also
Narandranathan, W. and Stewart, M. (1993), `Modelling the probability of
leaving unemployment: competing risk models with flexible base-line
hazards', Applied Statistics 42, 63-83. This provides an application --
they test whether their equivalent of a "-pgmhaz- Model 1"-type model is
consistent with a continuous time Weibull model.  There is also some
textbook-like discussion of the relationship between discrete time
(interval censored a.k.a. grouped data) models and continuous time models
in the Lecture Notes downloadable from

(author of -pgmhaz-)
Professor Stephen P. Jenkins <>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester CO4 3SQ, UK
Phone: +44 1206 873374.  Fax: +44 1206 873151.

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