R/item.sim.R

In frenchja/psych: Procedures for Psychological, Psychometric, and Personality Research

"item.sim" <-
function (nvar = 72 ,nsub = 500, 
    circum = FALSE, xloading =.6, yloading = .6, gloading=0, xbias=0,  ybias = 0,categorical=FALSE, low=-3,high=3,truncate=FALSE,cutpoint=0) 
	{ 
	avloading <- (xloading+yloading)/2
	
	errorweight <- sqrt(1-(avloading^2  + gloading^2))  #squared errors and true score weights add to 1
    g <- rnorm(nsub) 
	truex <- rnorm(nsub)* xloading  +xbias #generate normal true scores for x + xbias
	truey <- rnorm(nsub) * yloading + ybias #generate normal true scores for y + ybias

	if (circum)  #make a vector of radians (the whole way around the circle) if circumplex
	{radia <- seq(0,2*pi,len=nvar+1)  
      rad <- radia[which(radia<2*pi)]        #get rid of the last one
     } else   rad <- c(rep(0,nvar/4),rep(pi/2,nvar/4),rep(pi,nvar/4),rep(3*pi/2,nvar/4))  #simple structure 
        
	error<- matrix(rnorm(nsub*(nvar)),nsub)    #create normal error scores

	#true score matrix for each item reflects structure in radians
	trueitem <- outer(truex, cos(rad)) + outer(truey,sin(rad)) 

	item<- gloading * g +  trueitem  + errorweight*error   #observed item = true score + error score 
    if (categorical) {
        
    	item = round(item)       #round all items to nearest integer value
		item[(item<= low)] <- low     
		item[(item>high) ] <- high   
		}
	if (truncate) {item[item < cutpoint] <- 0  }
	return (item) 
	}