profile likelihood [ was Re: R-beta: R0.62.3 problems]
Douglas Bates
bates at stat.wisc.edu
Tue Sep 1 16:54:38 CEST 1998
>>>>> "Bill" == Bill Simpson <wsimpson at uwinnipeg.ca> writes:
>> 4. Is there no way to convince core that the default option for
>> signif stars should be FALSE??? At a minimum, modern software
>> should be printing out profile likelihood intervals (even SAS
>> does for logistic regression now) and not standard errors for
>> non-normal models. The intervals, let alone tests, based on s.e.s
>> can be meaningless for glms. Are there no likelihoodlums (except
>> me) or Bayesians out there?
Bill> Hi Jim,
Bill> I agree with you 100%. I am likelihood freak too and would
Bill> like to have profile likelihood conf intervals.
Bill> Also I would love to know how to compute profile likelihood
Bill> confidence intervals when doing MLE with nlm. I have never
Bill> seen this described anywhere in enough detail to do it
Bill> myself. (I would incorporate that into the little nonlinear
Bill> model fitting section I wrote for Notes on R.)
The splines library contains constructors and methods for
"backSplines". These are piecewise polynomials that provide inverse
interpolation of a monotone function. They would be used to construct
profile likelihood intervals by
- determine the MLE and approximate standard errors
- for each parameter {
while (statistic < critical value) {
create a step size as some fraction of the standard error
step from the MLE of that parameter
re-optimize on the other parameters
convert the change in likelihood (or residual sum-of-squares) to
a z-like or t-like statistic
adjust step size if needed
} # I skipped the part about do this in both directions
fit an interpolation spline to the values of the statistic versus
the parameter being profiled
form a backSpline and evaluate it at +/- critical value
Of course, the tricky part is setting up the optimization for all but
the parameter being profiled. The backSplines just give you a
convenient way of evaluating the interval once you have done all the
real work.
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