# Re: [R] Create a vector from another vector

From: Dimitris Rizopoulos <dimitris.rizopoulos_at_med.kuleuven.be>
Date: Thu 31 Aug 2006 - 01:11:06 EST

maybe something like this could be of help:

```max.score <- c(3,4,3) # max score for each item
all.pats <- as.matrix(expand.grid(lapply(max.score, ":", 1)))
all.pats[rowSums(all.pats) == 5, ]

```

Best,
Dimitris

Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

```Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
http://www.student.kuleuven.be/~m0390867/dimitris.htm

```
• Original Message ----- From: "Doran, Harold" <HDoran@air.org> To: "Duncan Murdoch" <murdoch@stats.uwo.ca> Cc: <r-help@stat.math.ethz.ch> Sent: Wednesday, August 30, 2006 4:49 PM Subject: Re: [R] Create a vector from another vector

> 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 > x 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 > x1?
>
> 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))
>  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
>
>
> 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"
>
>
> Harold
>
>
>> >
>> > ______________________________________________
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>> > and provide commented, minimal, self-contained, reproducible
>> > code.
>>
>>
>
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