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

# normal ogive or logistic Rasch Model

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


sim2PNO	<-	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)
	par			<-	theta %*% matrix(alpha,nrow=1,ncol=K) - 
							t( matrix(beta,nrow=K,ncol=N) )
	#Normit
	probs		<-	matrix(pnorm(par),ncol = K,nrow = N)	
	#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))
}

#Example
N	<- 1000
K	<- 20
sim		<-	sim2PNO(N,K)
Y		<- 	matrix(sim[[1]],ncol=K,nrow=N)
theta	<- 	matrix(sim[[2]],ncol=1,nrow=N)
alpha	<- 	matrix(sim[[3]],ncol=1,nrow=K)
beta 	<- 	matrix(sim[[4]],ncol=1,nrow=K)