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Re: st: Question about how streg using the constant-only model for starting values


From   Steve Samuels <sjsamuels@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Question about how streg using the constant-only model for starting values
Date   Thu, 12 Dec 2013 17:45:56 -0500

See Formulas and Methods in the Manual entry for -streg- (p. 387, Stata
13 Survival Manual). the frailty parameter multiplies S(t) and h(t) in
the log-likelihood, and these terms are functions of the regression
coefficients and the two other constants, and so are computed first. The
frailty parameter is fitted last: the value (0.92) from the constants only
model  is not useful, might not even  be feasible, as a starting
value for the full model, where the eventual estimate is 0.33.

Steve


On Dec 12, 2013, at 3:55 PM, Jonathan Eggleston wrote:

I have a question about how Stata uses the constant-only model in streg.  My understanding is that Stata uses the constant-only model to generate starting values for the main model.  I've used the "trace" option to see how this works, but I'm confused about how this works when I use frailty.  If I do

webuse bc, clear
stset t, fail(dead)

and then I run

streg age smoking, d(weibull)  trace

I get this as part of my output

-------------+----------------------------------------------------------------
Iteration 4:
Coefficient vector:
          _t:      ln_p:
       _cons      _cons
r1  -.6860931  -.3380965
                                                  log likelihood = -138.83047

-------------+{hline 64


Fitting full model:

--------------------------------------------------------------------------------------------------------------------------
Iteration 0:
Parameter vector:
          _t:        _t:        _t:      ln_p:
         age    smoking      _cons      _cons
r1          0          0  -.6860931  -.3380965

                                                  log likelihood = -138.83047


So without frailty, it makes sense how Stata uses the constant-only model.  However, when I add frailty with the command

streg age smoking, d(weibull) frailty(gamma) trace

I get this for the output

Iteration 4:
Parameter vector:
          _t:      ln_p:    ln_the:
       _cons      _cons      _cons
r1  -2.368818   .2681029   .9247814

                                                  log likelihood = -136.01201
--------------------------------------------------------------------------------------------------------------------------

Fitting full model:

--------------------------------------------------------------------------------------------------------------------------
Iteration 0:
Parameter vector:
          _t:        _t:        _t:      ln_p:    ln_the:
         age    smoking      _cons      _cons      _cons
r1   .1644213   .9056537  -11.20242   .3633523          0

                                                  log likelihood = -85.933969


Without a clear connection between these two iterations.  Does anyone know how Stata uses the constant-only model with frailty? Thank you.



-- 
Jonathan Eggleston
PhD Candidate
Department of Economics
University of Virginia

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