[R] log(0) problem in max likelihood estimation
ben@zoo.ufl.edu
ben at zoo.ufl.edu
Thu Jan 11 02:30:12 CET 2001
You can use the "log" and "lower.tail" options to get around these
numeric difficulties; essentially, "log" returns the log-probability
calculation directly from pnorm().
You're right that this is a fairly standard problem in maximizing
likelihoods.
py<-function(b,x,...) pnorm((x-b[1])/b[2],log=TRUE,...)
loglike<-function(b) -sum( yes*py(b,x) + no*py(b,x,lower.tail=FALSE))
out<-nlm(loglike,p=c(3,1),hessian=TRUE)
On Tue, 9 Jan 2001, Bill Simpson wrote:
> This practical problem in maximum likelihood estimation must be
> encountered quite a bit. What do you do when a data point has a
> probability that comes out in numerical evaluation to zero? In calculating
> the log likelihood you then have a log(0) problem.
>
> Here is a simple example (probit) which illustrates the problem:
>
> x<-c(1,2,3,4,100)
> ntrials<-100
> yes<-round(ntrials*pnorm((x-3)/1)) #points fall on normal CDF mean=3, sd=1
> no<-ntrials-yes
> pyes<-yes/ntrials
> py<-function(b,x) pnorm((x-b[1])/b[2])
> loglike<-function(b) -sum( yes*log(py(b,x)) + no*log(1-py(b,x)) )
> out<-nlm(loglike,p=c(3,1),hessian=TRUE)
>
> In this example the right-most point gives a p(yes) of 1; 1-1=0; log(0)
> gives "NA/Inf replaced by maximum positive value"
>
> Please tell me how to deal with this problem. Thanks very much for any
> help.
>
> Bill Simpson
>
> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
> r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
> Send "info", "help", or "[un]subscribe"
> (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch
> _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
>
--
318 Carr Hall bolker at zoo.ufl.edu
Zoology Department, University of Florida http://www.zoo.ufl.edu/bolker
Box 118525 (ph) 352-392-5697
Gainesville, FL 32611-8525 (fax) 352-392-3704
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
More information about the R-help
mailing list