This is a very basic question, but I am a bit confused with optim. I
want to get the MLEs using optim which could replace the newton-raphson
code I have below which also gives the MLEs. The function takes as input
a vector x denoting whether a respondent answered an item correctly
(x=1) or not (x=0). It also takes as input a vector b_vector, and these
are parameters of test items (Rasch estimates in this case)
For example, here is how my current function operates.
> rasch.max(c(1,1,0,0), c(-1,.5,0,1))
theta is about 0.14 , se 1.063972
I'm not quite sure how to accomplish the same thing using optim. Can
anyone offer a suggestion?
rasch.max <- function(x, b_vector){
p <- numeric(length(b_vector))
theta <- log(sum(x)/(length(x)/sum(x))) # This is a starting value
for theta
rasch <- function(theta,b) 1/ (1 + exp(b-theta))
old <- 0
updated <- 5
while(abs(old-updated) > .001){
old <- updated
for(k in seq(along=b_vector)) p[k] <- rasch(theta,b_vector[k])
first_deriv <- sum(x) - sum(p)
second_deriv <- sum((1-p)*-p)
change <- (first_deriv/second_deriv)
theta <- theta - change # This is the updated theta
updated <- change
}
cat('theta is about', round(theta,2), ', se', 1/sqrt(-second_deriv),
'\n')
}
Harold
> version
_
platform i386-pc-mingw32
arch i386
os mingw32
system i386, mingw32
status
major 2
minor 3.0
year 2006
month 04
day 24
svn rev 37909
language R
version.string Version 2.3.0 (2006-04-24)
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