[R] Warning message with maxLik()

[Maram SAlem]

Dear Arne,

The elements of the theta vector are indeed strictly positive. I've just tried to use instead : lamda = log (theta), which means that theta = exp (lamda),  so as to get rid of the log() function that appears in the log-likelihood and is causing the 50 warnings, but still the estimates I got for lamda and then those I got for theta (using theta=exp(lamda)) are irrelvant and their standard errors are infinite, which means that therer is still a problem that I can't yet figure out.

Thanks,
Maram

> On 18 July 2015 at 08:01, Arne Henningsen <arne.henningsen at gmail.com> wrote:
> Dear Maram
> 
> - Please do not start a new thread for the same issue but reply to
> previous messages in this thread [1].
> 
> - Please read my previous responses [1] more carefully, e.g. to use
> "theta <- exp( param )" which guarantees that all elements of "theta"
> are always positive.
> 
> [1] http://r.789695.n4.nabble.com/NaN-produced-from-log-with-positive-input-td4709463.html
> 
> Best regards,
> Arne
> 
> 
> 
> 2015-07-18 2:46 GMT+02:00 Maram SAlem <marammagdysalem at gmail.com>:
> > Dear All,
> > I'm trying to get the MLe for a certain distribution using maxLik ()
> > function. I wrote the log-likelihood function as follows:
> > theta <-vector(mode = "numeric", length = 3)
> > r<- 17
> > n <-30
> >  T<-c(7.048,0.743,2.404,1.374,2.233,1.52,23.531,5.182,4.502,1.362,1.15,1.86,1.692,11.659,1.631,2.212,5.451)
> > C<-
> > c(0.562,5.69,12.603,3.999,6.156,4.004,5.248,4.878,7.122,17.069,23.996,1.538,7.792)
> > # The  loglik. func.
> > loglik <- function(param) {
> >  theta[1]<- param[1]
> >  theta[2]<- param[2]
> >  theta[3]<- param[3]
> >  l<-(r*log(theta[3]))+(r*log(theta[1]+theta[2]))+(n*theta[3]*log(theta[1]))+(n*theta[3]*log(theta[2]))+
> > (-1*(theta[3]+1))*sum(log((T*(theta[1]+theta[2]))+(theta[1]*theta[2])))+
> > (-1*theta[3]*sum(log((C*(theta[1]+theta[2]))+(theta[1]*theta[2]))))
> > return(l)
> >  }
> >
> > then, I evaluated it at theta<- c(40,50,2)
> >
> > v<-loglik(param=theta)
> > v
> > [1] -56.66653
> >
> > I used this same log-likelihood function, once with analytic gradient and
> > another time with numerical one, with the maxLik function, and in both
> > cases I got the same 50 warning messages and an MLE which is completely
> > unrealistic as per my applied example.
> >
> > a <- maxLik(loglik, gradlik, hesslik, start=c(40,50,2))
> >
> > where gradlik and hesslik are the analytic gradient and Hessian matrix,
> > respectively, given by:
> >
> > U <- vector(mode="numeric",length=3)
> > gradlik<-function(param = theta,n, T,C)
> >  {
> > U <- vector(mode="numeric",length=3)
> > theta[1] <- param[1]
> > theta[2] <- param[2]
> > theta[3] <- param[3]
> > r<- 17
> > n <-30
> > T<-c(7.048,0.743,2.404,1.374,2.233,1.52,23.531,5.182,4.502,1.362,1.15,1.86,1.692,11.659,1.631,2.212,5.451)
> > C<-
> > c(0.562,5.69,12.603,3.999,6.156,4.004,5.248,4.878,7.122,17.069,23.996,1.538,7.792)
> >  U[1]<- (r/(theta[1]+theta[2]))+((n*theta[3])/theta[1])+(
> > -1*(theta[3]+1))*sum((T+theta[2])/((theta[1]+theta[2])*T+(theta[1]*theta[2])))+
> > (-1*(theta[3]))*sum((C+theta[2])/((theta[1]+theta[2])*C+(theta[1]*theta[2])))
> > U[2]<-(r/(theta[1]+theta[2]))+((n*theta[3])/theta[2])+
> > (-1*(theta[3]+1))*sum((T+theta[1])/((theta[1]+theta[2])*T+(theta[1]*theta[2])))+
> > (-1*(theta[3]))*sum((C+theta[1])/((theta[1]+theta[2])*C+(theta[1]*theta[2])))
> > U[3]<-(r/theta[3])+(n*log(theta[1]*theta[2]))+
> > (-1)*sum(log((T*(theta[1]+theta[2]))+(theta[1]*theta[2])))+(-1)*sum(log((C*(theta[1]+theta[2]))+(theta[1]*theta[2])))
> > return(U)
> > }
> > hesslik<-function(param=theta,n,T,C)
> > {
> > theta[1] <- param[1]
> > theta[2] <- param[2]
> > theta[3] <- param[3]
> > r<- 17
> > n <-30
> > T<-c(7.048,0.743,2.404,1.374,2.233,1.52,23.531,5.182,4.502,1.362,1.15,1.86,1.692,11.659,1.631,2.212,5.451)
> > C<-
> > c(0.562,5.69,12.603,3.999,6.156,4.004,5.248,4.878,7.122,17.069,23.996,1.538,7.792)
> > G<- matrix(nrow=3,ncol=3)
> > G[1,1]<-((-1*r)/((theta[1]+theta[2])^2))+((-1*n*theta[3])/(theta[1])^2)+
> > (theta[3]+1)*sum(((T+theta[2])/((theta[1]+theta[2])*T+(theta[1]*theta[2])))^2)+(
> > theta[3])*sum(((C+theta[2])/((theta[1]+theta[2])*C+(theta[1]*theta[2])))^2)
> > G[1,2]<-((-1*r)/((theta[1]+theta[2])^2))+
> > (theta[3]+1)*sum(((T)/((theta[1]+theta[2])*T+(theta[1]*theta[2])))^2)+
> > (theta[3])*sum(((C)/((theta[1]+theta[2])*C+(theta[1]*theta[2])))^2)
> > G[2,1]<-G[1,2]
> > G[1,3]<-(n/theta[1])+(-1)*sum(
> > (T+theta[2])/((theta[1]+theta[2])*T+(theta[1]*theta[2])))+(-1)*sum((C+theta[2])/((theta[1]+theta[2])*C+(theta[1]*theta[2])))
> > G[3,1]<-G[1,3]
> > G[2,2]<-((-1*r)/((theta[1]+theta[2])^2))+((-1*n*theta[3])/(theta[2])^2)+
> > (theta[3]+1)*sum(((T+theta[1])/((theta[1]+theta[2])*T+(theta[1]*theta[2])))^2)+(
> > theta[3])*sum(((C+theta[1])/((theta[1]+theta[2])*C+(theta[1]*theta[2])))^2)
> > G[2,3]<-(n/theta[2])+(-1)*sum((T+theta[1])/((theta[1]+theta[2])*T+(theta[1]*theta[2])))+(-1)*sum((C+theta[1])/((theta[1]+theta[2])*C+(theta[1]*theta[2])))
> > G[3,2]<-G[2,3]
> > G[3,3]<-((-1*r)/(theta[3])^2)
> > return(G)
> > }
> >
> > and using numeric gradient and hessian matrix:
> >
> > a <- maxLik(loglik, start=c(40,50,2))
> > Warning messages:
> > 1: In log(theta[3]) : NaNs produced
> > 2: In log(theta[1] + theta[2]) : NaNs produced
> > 3: In log(theta[1]) : NaNs produced
> > 4: In log((T * (theta[1] + theta[2])) + (theta[1] * theta[2])) : NaNs
> > produced
> > 5: In log((C * (theta[1] + theta[2])) + (theta[1] * theta[2])) : NaNs
> > produced
> > 6: In log(theta[3]) : NaNs produced
> > 7: In log(theta[1] + theta[2]) : NaNs produced
> > and so on…..
> >
> > I don't know why I get these 50 warnings although:
> > 1- The inputs of the log() function are strictly positive.
> > 2- When I evaluated the log-likelihood fuction at the very begining it gave
> > me a number(which is -56.66) and not (NAN).
> >
> > I've also tried to:
> > 1- Reparamtrize my model using lamda(i)= log(theta(i)), for i=1,2,3, so
> > that it may solve the problem, but it didn't.
> > 2- I've used the comparederivitive() function, and the analytic and numeric
> > gradients were so close.
> >
> > Any help please?
> > Maram Salem
> >
> >         [[alternative HTML version deleted]]
> >
> > ______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> 
> 
> 
> --
> Arne Henningsen
> http://www.arne-henningsen.name


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