Hi Madan,
You are trying to find the MLE of a binary mixture distribution. So, there are
constraints on the parameters, as you have indicated. The nlm() function
cannot handle constraints. I would recommend one of the following functions
(not necessarily in any order), all of which can handle box-constraints:
1. optim(), with method="L-BFGS-B")
2. nlminb()
3. spg() in package "BB"
4. Write an EM algorithm; this automatically imposes all the required
constraints, and is guaranteed to converge (to a local maximum).
John Nash and I are writing a package called "optimx", which contains a
function called optimx() that integrates all the different optimization
functions for smooth nonlinear problems. Thsi would make it extremely easy for
you to do steps (1) - (3) above, using a single call to optimx(). Let me know
if you are interested.
Hope this helps,
Ravi.
____________________________________________________________________
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University
Ph. (410) 502-2619
email: rvarad...@jhmi.edu
----- Original Message -----
From: Madan Gopal Kundu <madan.ku...@ranbaxy.com>
Date: Wednesday, July 1, 2009 9:25 am
Subject: [R] Difficulty in calculating MLE through NLM
To: r-help <r-h...@stat.math.ethz.ch>
> Hi R-friends,
>
> Attached is the SAS XPORT file that I have imported into R using
> following code
> library(foreign)
> mydata<-read.xport("C:\\ctf.xpt")
> print(mydata)
>
> I am trying to maximize logL in order to find Maximum Likelihood
> Estimate (MLE) of 5 parameters (alpha1, beta1, alpha2, beta2, p) using
> NLM function in R as follows.
>
> # Defining Log likelihood - In the function it is noted as logL
> > library(stats)
> > loglike1<- function(x)
> + {
> + alpha1<-x[1]
> + beta1<-x[2]
> + alpha2<-x[3]
> + beta2<-x[4]
> + p<-x[5]
> + n<- mydata[3]
> + e<-mydata[4]
> + f1<-
> ((1+beta1/e)^(-n))*((1+e/beta1)^(-alpha1))*gamma(alpha1+n)/(gamma(n+1)*gamma(alpha1))
> + f2<-
> ((1+beta2/e)^(-n))*((1+e/beta2)^(-alpha2))*gamma(alpha2+n)/(gamma(n+1)*gamma(alpha2))
> + logL=sum(log(p*f1+(1-p)*f2))
> + logL<- -logL
> + }
>
> # Supplying starting parameter values
> > theta<-c(.2041,.0582, 1.4150, 1.8380,0.0969)
>
> # Calculating MLE using NLM function
> > result<- nlm(loglike1, theta, hessian=TRUE, print.level=1)
>
> Now the problem is, this is not working as there is no improvement in
> final parameter estimate over starting values and NLM just stops just
> after 1 iteration with gradient value of all the 5 parameters as zero.
> I have tried other set of starting values, but then also I am getting
> final parameter estimates similar to starting values and iteration
> stops just after one step. When I check for warnings, R displays
> following kind of warnings:
>
> * NA/Inf replaced by maximum positive value
> * value out of range in 'gammafn'
>
> Please suggest what I should do. I am expecting the final MLE of
> alpha1, alpha2, beta1 and beta2 greater than 0 and P should lie
> between 0 to 1.
>
> Thanks & Regards,
> Madan Gopal Kundu
> Biostatistician, CDM, MACR, Ranbaxy Labs. Ltd.
> Tel(O): +91 (0) 1245194045 - Mobile: +91 (0) 9868788406
>
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