[19244] in s-news-athena
RE: [S] Fisher Information?
daemon@ATHENA.MIT.EDU (Annis, Charles G. Jr.)
Fri Sep 17 09:45:04 1999
Message-Id: <AF7D41B26A42D211AD9B00805FC1CF81ACA856@pwflml11.pwfl.com>
From: "Annis, Charles G. Jr." <annis@pwfl.com>
To: "'s-news@wubios.wustl.edu'" <s-news@wubios.wustl.edu>
Date: Fri, 17 Sep 1999 09:38:02 -0400
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Hi, Everybody:
Yesterday I asked:
> How can I get at the Fisher Information matrix that I assume is an adjunct
> to the parameter estimation machinations carried out by the censored
> regression algorithms of Parametric Survival?
Terry M. Therneau answered for surveg:
>>> snip >>>>>>>>>>>>>>>>>>>>>>>>>>
For the survreg routine:
fit <- survreg(Surv(time, status) ~ age + sex, data=lung)
the component fit$var contains the inverse Hessian. So
> solve(fit$var)
(Intercept) age sex Log(scale)
(Intercept) 290.19140 18364.717 383.404514 14.049320
age 18364.71683 1183113.855 24198.547666 1128.508704
sex 383.40451 24198.548 569.830738 -2.428344
Log(scale) 14.04932 1128.509 -2.428344 271.049477
is the matrix you are interested in. Internally, the routine uses
log(scale) rather than scale as the parameter, because the iteration has
proven to be much more stable.
>>> snip >>>>>>>>>>>>>>>>>>>>>>>>>>>
The same method works for censorReg:
> fit<-censorReg(formula = censor(log10(FSH), censored, type = "right") ~
log10(diameter.size.) + ... etc.
> fit$var
(Intercept) log10(diameter.size.) depth
System Hole.Type1
(Intercept) 0.0315660536 0.01723570563 -0.00275711645
4.525893e-004 -0.00135281053
log10(diameter.size.) 0.0172357056 0.00990256667 -0.00029283235
2.346990e-004 -0.00046046000
depth -0.0027571165 -0.00029283235 0.00400469871
-2.177125e-005 0.00088403607
System 0.0004525893 0.00023469904 -0.00002177125
2.434062e-004 -0.00001836242
Hole.Type1 -0.0013528105 -0.00046046000 0.00088403607
-1.836242e-005 0.00068110472 etc.
produces the variance-covariance matrix, whose inverse is the Fisher
Information (Cramér-Rao inequality notwithstanding).
My thanks to Dr. Therneau for his help, and for the suggestions of Professor
Bill Meeker and Paul Monaghan.
Charles Annis, P.E.
AnnisC@ASME.org
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