[R] maximizing the gamma likelihood

[Mark Leeds]

Thanks Xiaohui. I saw your solution a few days ago but only now realize what you're doing. It didn't at the time make sense to me to use the density from R directly. Now, I get it.  

The solution you get also make sense because the par[2] is ~ 1/par[1] which is what the analytical MLEs imply.  I had an error in my likelihood because
I left out a term which Haris Skiadis pointed out privately.  I fixed it ( but it still didn't converge ) and now I have something to shoot towards which will help me a lot to figuring out what's going so thanks very much.




-----Original Message-----
From: Xiaohui Chen [mailto:chenxh007 at gmail.com] 
Sent: Saturday, May 24, 2008 3:04 AM
To: markleeds at verizon.net
Cc: r-help at r-project.org
Subject: Re: [R] maximizing the gamma likelihood

Hi Mark,

As I said in earlier emails, you do NOT need to explicitly code the 
likelihood function for gamma distn. I just code you example as below:

vsamples<- c(14.7, 18.8, 14, 15.9, 9.7, 12.8)
gamma.nll <- function(par,data) 
-sum(dgamma(data,shape=par[1],scale=par[2],log=T))
optim(c(1,1),gamma.nll,data=vsamples,method='BFGS')
 >
$par
[1] 24.9327797 0.5743043

$value
[1] 14.72309


The mle is pretty robust to the starting values: if you change the 
initialization to c(10,10), the results would be
 >
$par
[1] 25.0285880 0.5721142

$value
[1] 14.72299

Anyway, for the standard distns, which R has implementation, you 
definitely don't have to do everything from scratch.

Xiaohui


markleeds at verizon.net 写道:
> for learning purposes and also to help someone, i used roger peng's 
> document to get the mle's of the gamma where the gamma is defined as
>
> f(y_i) = (1/gammafunction(shape)) * (scale^shape) * (y_i^(shape-1)) * 
> exp(-scale*y_i)
>
> ( i'm defining the scale as lambda rather than 1/lambda. various books 
> define it differently ).
>
> i found the likelihood to be n*shape*log(scale) + 
> (shape-1)*sum(log(y_i) - scale*sum(y_i)
> then i wrote below which is just roger peng's likelihood example but 
> using the gamma instead of the normal.
> I get estimates back but i separately found that the analytical mle of 
> the scale is equal to 1/ analytical mle(shape).
> and my estimates aren't consistent with that fact ? this leads me to 
> assume that my estimates are not correct.
>
> can anyone tell me what i'm doing wrong. maybe my starting values are 
> too far off ? thanks.
>
> make.negloglik <- function(data, fixed=c(FALSE,FALSE)) {
> op <- fixed
> function(p) {
> op[!fixed] <- p
> shape <- exp(op[1])
> scale <- exp(op[2])
> a <- length(data)*shape*log(scale)
> b <- (shape-1)*sum(log(data))
> c <- -1.0*scale*sum(data)
> -(a + b + c)
> }
> }
>
> vsamples<- c(14.7, 18.8, 14, 15.9, 9.7, 12.8)
> nLL <- make.negloglik(vsamples)
> temp <- optim(c(scale=1,shape=1), nLL, method="BFGS")[["par"]]
> estimates <- log(temp)
> print(estimates)
>
> check <- estimates[1]/mean(vsamples)
> print(check)
>
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