Hi,
I'm having difficulties using censorReg to estimate the parameters
(shape and scale) of a Weibull distribution. My simulated dataset consists
of left-truncated and right-censored observations from a Weibull
distribution with shape parameter beta=1.5, and scale parameter lambda=1.
To carry out non-parametric inference with left-truncated and
right-censored observations one can use the coxph in combination with the
survfit; that is,
survfit(coxph(Surv(start, end, status) ~ 1, data=my.data))
Based on the previous syntax, I used the following line to fit my
parametric Weibull with left-truncated and right-censored observations:
> censorReg(censor(start, end, status)~1, data=my.data)
Call:
censorReg(formula = censor(start, end, status) ~ 1, data = my.data)
Distribution: Weibull
Coefficients:
(Intercept)
-0.9243332
Dispersion (scale) = 0.7966223
Log-likelihood: -1.534647
Observations: 100 Total; 15 Censored
Parameters Estimated: 2
Transforming back to the original parameterization, I get:
lambda = exp(0.9243332) = 2.520187
beta = 1/0.7966223 = 1.2553
That is, an estimate of beta relatively close to the theoretical
value of 1.5, but a an estimate of lambda far away from the theoretical
value of 1. However, using Newton-Raphson I get the following estimates:
lambda = 0.877687 and beta = 1.364497. Both are closer to the theoretical
values. Moreover, the log-likelihood corresponding to lambda = 2.520187
and beta = 1.2553 is -137.9927; compared to -1.534647 with censorReg.
Also, the log-likelihood corresponding to lambda = 0.877687 and beta =
1.364497 (the estimates from the Newton-Raphson method) is -75.61563.
Thus, I don't really know what I'm doing wrong. I'm mainly
wondering about my syntax for censorReg and about my transformation to the
original parameterization, but I couldn't find anything in the S-Plus help
to tell me what is going wrong.
Thanks
Christian
___------__
|\__-- /\ _-
|/ __ - Christian Boudreau
//\ / \ /__ cboudreau@math.uwaterloo.ca
| o| 0|__ --_
\\____-- __ \ ___- Department of Statistics
(@@ __/ / /_ and Actuarial Science
-_____--- --_ University of Waterloo
// \ \\ ___- office: MC 6232
//|\__/ \\ \ (519) 888-4567 ext 6297
\_-\_____/ \-\ fax: (519) 746-1875
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