circ.sim {psych}R Documentation

Generate simulated data structures for circumplex or simple structure

Description

Rotations of factor analysis and principal components analysis solutions typically try to represent correlation matrices as simple structured. An alternative structure, appealing to some, is a circumplex structure where the variables are uniformly spaced on the perimeter of a circle in a two dimensional space. Generating these data is straightforward, and is useful for exploring alternative solutions to affect and personality structure.

Usage

circ.sim(nvar = 72, nsub = 500, circum = TRUE, xloading = 0.6, yloading = 0.6, gloading = 0, xbias = 0, ybias = 0, categorical = FALSE, low = -3, high = 3, truncate = FALSE, cutpoint = 0)

Arguments

nvar Number of variables to simulate
nsub Number of subjects to simulate
circum circum=TRUE is circumplex structure, FALSE is simple structure
xloading the average loading on the first dimension
yloading Average loading on the second dimension
gloading Average loading on a general factor (default=0)
xbias To introduce skew, how far off center is the first dimension
ybias To introduce skew on the second dimension
categorical continuous or categorical variables.
low values less than low are forced to low
high values greater than high are forced to high
truncate Change all values less than cutpoint to cutpoint.
cutpoint What is the cutpoint

Details

This simulation was originally developed to compare the effect of skew on the measurement of affect (see Rafaeli and Revelle, 2005). It has been extended to allow for a general simulation of affect or personality items with either a simple structure or a circumplex structure. Items can be continuous normally distributed, or broken down into n categories (e.g, -2, -1, 0, 1, 2). Items can be distorted by limiting them to these ranges, even though the items have a mean of (e.g., 1).

Value

A data matrix of (nsub) subjects by (nvar) variables.

Author(s)

William Revelle

References

Variations of a routine used in Rafaeli and Revelle, 2006; Rafaeli, E. & Revelle, W. (2006). A premature consensus: Are happiness and sadness truly opposite affects? Motivation and Emotion.

Acton, G. S. and Revelle, W. (2004) Evaluation of Ten Psychometric Criteria for Circumplex Structure. Methods of Psychological Research Online, Vol. 9, No. 1 http://www.dgps.de/fachgruppen/methoden/mpr-online/issue22/mpr110_10.pdf

See Also

See Also the implementation in this to generate numerous simulations. circ.simulation, circ.tests

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--    or do  help(data=index)  for the standard data sets.
circ.data <- circ.sim(nvar=8,nsub=200)
round(cor(circ.data),2)

## The function is currently defined as
function (nvar = 72 ,nsub = 500, 
    circum = TRUE, 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 <- rep(seq(0,3*pi/2,len=4),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) 
        }

[Package psych version 1.0-18 Index]