# FFD
ffd.fake <- function(J, K, mu.a.true, x1.true, x2.true, x3.true, f.true, sigma.item.true, sigma.id.true, sigma.y.true){
	item <- rep(1:K, J)                            # item
	id   <- rep(1:J, each=K)                       # subject
	cond <- rep(c(1,2,3,4,5,6,7,8,  2,3,4,5,6,7,8,1, 3,4,5,6,7,8,1,2, 4,5,6,7,8,1,2,3,
		          5,6,7,8,1,2,3,4,  6,7,8,1,2,3,4,5, 7,8,1,2,3,4,5,6, 8,1,2,3,4,5,6,7), J*K/64)
	f <- ifelse(cond<=4, -.5, .5)             # frequency

	x1 <- rep(0,J*K)
	x2 <- rep(0,J*K)
	x3 <- rep(0,J*K)

	x1[cond==2 | cond==6] <-   .5
	x1[cond==3 | cond==7] <-  -.5   
 	x2[cond==1 | cond==5] <-  -.5
	x2[cond==4 | cond==8] <-   .5
	x3[ (cond==1 | cond==4) | (cond==5 | cond==8) ] <- -.25
	x3[ (cond==2 | cond==3) | (cond==6 | cond==7) ] <- .25

    # hyperparameters for ffd
	mu.a.true #<-   228
	f.true   #<-     7
	x1.true  #<-     7
	x2.true  #<-     7
	x3.true  #<-	    7
	sigma.item.true #<- 16
	sigma.id.true   #<- 25
	sigma.y.true    #<- 65
	print(f.true)

	# person- and item level parameters
	a.id.true <- rnorm(J, 0, sigma.id.true)
	a.item.true <- rnorm(K, 0, sigma.item.true)

	# data
	y <- rnorm(J*K, log(mu.a.true) + f*log(1+f.true/mu.a.true) + x1*log(1+x1.true/mu.a.true)+ x2*log(1+x2.true/mu.a.true) + x3*log(1+x3.true/mu.a.true) + 
	                   a.id.true[id] + a.item.true[item],
				 sigma.y.true)
	y <- exp(y)
#y <- data.frame(y, f, x1, x2, x3, id, item)	

return(data.frame(y, f, x1, x2, x3, id, item))
}