# [R] Est. Component Size with AIC/BIC under Gamma Distribution

From: Edward Wijaya <ewijaya_at_gmail.com>
Date: Fri, 23 May 2008 15:40:56 +0900

Dear all,

I am trying to model number of samples from a given series. The series are modelled according Gamma function.

In order to estimate the # samples, I use BIC/AIC with MLE (computed from dgamma function).

Here is the code I have.

__BEGIN__ mlogl <- function( x_func, theta_func, samp) {

# computing log_likelihood
return( - sum(dgamma(samp, shape = x_func, scale=theta_func, log = TRUE)))
}

find_bic <- function(mll,smpl,k) {

```      bic <- (-2 * mll) + (k * log(length(smpl)))
bic
```

}

find_aic <- function(mll,smpl,k) {

```      aic <- (-2 * mll) + (k * 2)
aic

```

}

mlogl_process <- function(smpl,error,start ) {

# EM algorithm to estimate max loglikelihood     thetalast <- 0
thetacurrent <- start
theta <- start
difference <- start
thetaprocess <- start
best <- 0

while (difference > error) {

```        mlogl_out <- nlm(mlogl, mean(smpl),  theta_func=thetacurrent, samp=smpl)
theta <- mlogl_out\$estimate
thetalast <- thetacurrent
thetacurrent <- theta
difference <- abs(thetalast - thetacurrent)

# E-STEP
new_maxlogl <- nlm(mlogl, mean(smpl),  theta_func=theta,  samp=smpl)

# M-STEP
if (new_maxlogl\$minimum > best) {
best <- new_maxlogl\$minimum

}
```

}
best
}

# main program

# my samples
vsamples<- c(14.7, 18.8, 14, 15.9, 9.7, 12.8)

# initialize
start_ <- 300
error_ <- 0.001
thetastart <- 1
k <- 5

# compute AIC/BIC for k component

for (nofc in 1:k {
cat("k = ", nofc, "\n")
maxlogl <- -(mlogl_process(vsamples,error_,thetastart))   bic_k <- find_bic(maxlogl,vsamples,nofc)   aic_k <- find_aic(maxlogl,vsamples,nofc)   cat("BIC = ", bic_k, " - AIC = ", aic_k, "- MLL= ", maxlogl,"\n")
}

__ END__ We finally expect to choose K with the smallest AIC/BIC value.

However, the problem I have is that the AIC/BIC value is always on the increase.

Can anybody advice what's wrong with my above approach?

Regards,
Edward

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