##	Simulate Responses according to the three-parameter
##	Normal Ogive or Logistic Model. J.-P. Fox, University of Twente, Augustus 2010. 

# normal ogive or logistic Model

# K: number of items  
# N: number of items 
# theta : latent variable
# beta : difficulty parameter	
# guess : guessing parameter


THREEPNO	<-	function(N,K)
	
{
	theta		<-	rnorm(N)
	theta		<- 	(theta - mean(theta))/sqrt(var(theta))
	alpha 		<- 	rnorm(K,mean=1,sd=.1)
	beta 	 	<-	rnorm(K,sd=.5)
	beta 	 	<-	beta - mean(beta)
	
	guess		<- runif(K,0,.25)
	par			<-	theta %*% matrix(alpha,nrow=1,ncol=K) - t( matrix(beta,nrow=K,ncol=N) )

	#Normit
	probs		<-	matrix(pnorm(par),ncol = K,nrow = N)	
	probs		<-     t(matrix(guess,ncol=N,nrow=K)) + (matrix(1,ncol=K,nrow=N)-t(matrix(guess,ncol=N,nrow=K)))*probs

	#Logit	 
	#probs		<-	matrix(1/(1+exp(-par)),ncol = K,nrow = N)	
	Y	        <-	matrix(runif(N*K),nrow = N, ncol = K)
	Y		<-	ifelse(Y < probs,1,0)
	return(list(Y,theta,alpha,beta,guess))
}