Re: [R] Create a vector from another vector

From: Doran, Harold <HDoran_at_air.org>
Date: Thu 31 Aug 2006 - 00:49:56 EST


Hi Duncan

Here is a bit more detail, this is a bit tough to explain, sorry for not being clear. Ordering is not important because the vector I am creating is used as a sufficient statistic in an optimization routine to get some MLEs. So, any combination of the vector that sums to X is OK. But, the condition that x2[i] <= x[i] must be maintained. So, the example below would not work because x2[1] > x[1] as you note below.

> I don't think it's really clear what you mean by "ordering is
> not important". Would
>
> x2 <- c(6,5,2,4,2)
> be acceptable (a re-ordering of your first two examples),
> even though x2[1] > x1[1]?

To be concrete, the following is the optimization function. This is a psychometric problem where the goal is to get the MLE for a test taker conditional on their response pattern (i.e., number of points on the test) and the item parameters.

pcm.max3 <- function(score, d){

    pcm <- function(theta, d, score)
exp(sum(theta-d[1:score]))/sum(exp(cumsum(theta-d)))

    opt <- function(theta) -sum(log(mapply(pcm, d, theta = theta, score= score )))

    start_val <- log(sum(score-1)/(length(score-1)/sum(score-1)))     out <- optim(start_val, opt, method = "BFGS", hessian = TRUE)     cat('theta is about', round(out$par, 2), ', se', 1/sqrt(out$hes),'\n')
  }

Suppose we have a three item test. I store the item parameters in a list as

items <- list(c(0,.5,1), c(0,1), c(0, -1, .5, 1))

We can get the total possible number correct as

(x <- sapply(items, length))
[1] 3 2 4

But, you cannot actually get the MLE for this because the likelihood is unbounded in this case.

So, let's say the student scored in the following categories for each item:

x2 <- c(3,1,4)

By x2[i] <= x[i], I mean that there are 3 possible categories for item 1 above. So, a student can only score in categories 1,2 or 3. He cannot score in category 4. This is why the condition that x2[i] <= x[i] is critical.

But, because total score is a sufficient statistic, (i.e., "ordering is not important") we could either vector in the function pcm.

x3 <- c(3,2,3)

Using the function

pcm.max3(x2, items)
pcm.max3(x3, items)

Gives the same MLE.

But, the vector

X_bad <- c(4,1,3)

Would not work. You can see that the elements of this vector actually serve as indices denoting which category a test taker scored in for each item in the list "items"

I hope this is helpful and appreciate your time.

Harold

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu Aug 31 08:53:46 2006

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