OK, With this extra detail, a third solution follows, which may be closer in spirit to your application. It may or may not be faster than the other two, depending on the exact parameters used:
library(partitions) 1+blockparts(n=15,y=c(3,4,2,5,6)-1,include.fewer=T) (720 distinct solutions) rksh On 30 Aug 2006, at 15:49, Doran, Harold wrote: > 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 > > >>> >>> ______________________________________________ >>> R-help@stat.math.ethz.ch mailing list >>> 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. >> >> > > ______________________________________________ > R-help@stat.math.ethz.ch mailing list > 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. -- Robin Hankin Uncertainty Analyst National Oceanography Centre, Southampton European Way, Southampton SO14 3ZH, UK tel 023-8059-7743 ______________________________________________ R-help@stat.math.ethz.ch mailing list 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.