Clint Thompson <[email protected]> asks:
> I need to estimate both parameters from the Weibull distribution (beta &
> theta) using the maximum likelihood estimation method. I have referenced
> the reference manual and it assumes that I am using a specific data set with
> a Weibull distribution but I need the estimates using the general Weibull
> pdf. I also want to estimate the variance-covariance matrix of the MLEs.
> Any suggestions (aside from computing it by hand)?
Very easy in Stata 8.
Clint can fit a Weibull model without covariates on his univariate data and
then use -nlcom- to remap the estimates to those from a more "typical" Weibull
pdf. For example, if the pdf in question is
f(t) = theta/beta * t^(theta-1) * exp(-t^theta/beta)
and if one fits the Weibull model using the default proportional hazards (PH)
parameterization, then the remapping would take place as follows:
. webuse cancer
. stset studytime /* studytime is the univariate response, no censoring */
. streg, dist(weibull) nolog nohr
(output omitted)
. nlcom (theta:exp([ln_p]_b[_cons])) (beta:exp(-_b[_cons]))
theta: exp([ln_p]_b[_cons])
beta: exp(-_b[_cons])
------------------------------------------------------------------------------
_t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
theta | 1.518202 .1766894 8.59 0.000 1.171897 1.864506
beta | 74.91051 42.54283 1.76 0.078 -8.471904 158.2929
------------------------------------------------------------------------------
The estimated variance covariance matrix (VCE) of the remapping is returned
in r(V).
. mat list r(V)
symmetric r(V)[2,2]
theta beta
theta .03121916
beta 7.2700449 1809.8925
As for a pre-Stata 8 solution, Clint would have to use -testnl- to obtain
the derivative matrix and perform the delta method matrix calculations himself.
A bit more prone to error, hence the motivation for -nlcom-.
--Bobby
[email protected]
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