cacIRT (version 1.0)

recursive.raw: Recursive computation of conditional total score

Description

Returns probabilities of each possible total score conditional on theta

Usage

recursive.raw(theta, ip)

Arguments

theta

vector of ability estimates

ip

matrix of item parameters, columns assumed to be discrimination, difficulty, and guessing

Value

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function(theta, ip){
	
	ut <- theta
	if (is.null(dim(ip))) 
	        dim(ip) = c(1, 3)
	if(dim(ip)[2]==2)
		ip[,3]<-0        
	ni <- dim(ip)[1]
	nn <- length(ut)
	sc <- ni+1
	
			irf<-function(ip,x){
	   			
	   			if(dim(ip)[2]==2)
						ip[,3]<-0 
				ni = dim(ip)[1]		 
	    		f = (sapply(1:ni, function(i) {
	    			ip[i, 3] + (1 - ip[i, 3])/
	    			(1 + exp(-1.7*ip[i, 1] * (x-ip[i, 2])))}))
	    		r = list(x = x, f = f)
	    			return(r)}
	 	   
		Pjt <-  irf(ip,ut)$f
		Qjt <-  1-Pjt
		H <- apply(Qjt,1,prod)
		Zjt	<- Pjt/Qjt

	zm <- array(0, dim = c(nn, sc, ni))	
		zm[,1,] <- 1
		zm[,2,1] <- Zjt[,1]

	for(i in 2: ni){ # The recursive part, I have it set up as a matrix
			for(s in 2:sc){
				zm[,s,i] <- zm[,s,i-1] + Zjt[,i]*zm[,s-1,i-1]}}	
	
		out<- zm[,,ni]*H
				rownames(out) <- paste("theta = ",round(ut,3))
				colnames(out) <-paste("x = " , 0:ni)
	return(out)
	}