# [R] using mle2 for multinomial model optimization

Fri Feb 12 17:36:43 CET 2010

```Use "Nelder-Mead" as the method in optim.  This will give you the correct solution.

m1 <- mle2(mfun, start=svec, vecpar=TRUE, fixed=svec[1:(l-1)], method="Nelder")

Ravi.

____________________________________________________________________

Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619

----- Original Message -----
From: Benedikt Gehr <benedikt.gehr at ieu.uzh.ch>
Date: Friday, February 12, 2010 8:26 am
Subject: [R] using mle2 for multinomial model optimization
To: r-help at r-project.org

> Hi there
>  I'm trying to find the mle fo a multinomial model ->*L(N,h,S¦x)*.
> There
>  is only *N* I want to estimate, which is used in the number of
> successes
>  for the last cell probability. These successes are given by:
>  p^(N-x1-x2-...xi)
>   All the other parameters (i.e. h and S) I know from somewhere else.
>
>  Here is what I've tried to do so far for a imaginary data set:
>  #######################################################
>
>  cohort<-c(50,54,50)     #imaginary harvest numbers of a cohort
> harvested
>  over 3 years
>
>  l<-length(cohort)+1    #nr of cell probabilities
>  h<-c(0.2,0.3,1)         #harvest rates for the 3 diferent years
>  S<-c(0.9,0.8)         #survival rates
>
>  mfun <- function(d) {
>    S<-S            #survival rate
>    h<-h            #harvest rate
>    l<-length(d)
>      p<-rep(0,l)         #Cell probabilities
>      p[1]<-h[1]
>
>      prod<-(1-h[1])*S[1]
>      for (i in 2:(l-1)){
>          p[i]<-prod*h[i]
>          prod<-prod*(1-h[i])*S[i]
>
>      }
>     p[l]<-1-sum(p[-l])    #last cell probability
>    -dmultinom(exp(d),prob=p,log=TRUE)    #exp(d)->backtransform the estimates
>  }
>
>  c<-c(cohort,100)            #untransformed initial values for the
>  optimization,->100=N-x1-x2-x3
>  nvec<-c(rep("x",l-1),"N")     #names for the initial vector
>  nrs<-c(1:(l-1),1)            #nrs for the initial vector
>  svec = log(c)             #transformation of the data to avoid
>  constraints (x>0)
>  names(svec) <- paste(nvec,nrs,sep="")
>  parnames(mfun) <- names(svec)
>
>  m1 = mle2(mfun,start=svec,
>       vecpar=TRUE,fixed=svec[1:(l-1)]) #only estimate
>  "N-x1-x2-x3",everything else is fixed
>
>      coef(m1)
>  ############################################################################
>
>  The function "mfun" is working, however the mle2 won't work. How can
> I
>  fix this?
>
>  Thanks so much for your help
>
>  Beni
>
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>