congeneric.sim: Simulate a congeneric data set

Description

Classical Test Theory (CTT) considers four or more tests to be congenerically equivalent if all tests may be expressed in terms of one factor and a residual error. Parallel tests are the special case where (usually two) tests have equal factor loadings. Tau equivalent tests have equal factor loadings but may have unequal errors. Congeneric tests may differ in both factor loading and error variances.

Usage

congeneric.sim(N = 1000, loads = c(0.8, 0.7, 0.6, 0.5), err=NULL, short = TRUE)

Arguments

How many subjects to simulate

loads

A vector of factor loadings for the tests

err

A vector of error variances -- if NULL then error = 1 - loading 2

short

short=TRUE: Just give the test scores, short=FALSE, report observed test scores as well as the implied pattern matrix

Value

observeda matrix of test scores for n tests
patternThe pattern matrix implied by the loadings and error variances

Details

When constructing examples for reliability analysis, it is convenient to simulate congeneric data structures. These are the most simple of item structures, having just one factor.

The implied covariance matrix is just pattern %*% t(pattern).

Examples

Run this code

#test <- congeneric.sim()


## The function is currently defined as

function(N = 1000, loads = c(0.8, 0.7, 0.6, 0.5),err=NULL, short=TRUE) { 
 n <- length(loads) 
loading <- matrix(loads, nrow = n) 
error <- diag(1, nrow = n) 
if (!is.null(err)) {diag(error) <- err} else {
 diag(error) <- sqrt(1 - loading^2) }
pattern <- cbind(loading, error) 
colnames(pattern) <- c("theta", paste("e", seq(1:n), sep = "")) 
rownames(pattern) <- c(paste("V", seq(1:n), sep = "")) 
latent <- matrix(rnorm(N * (n + 1)), ncol = (n + 1)) 
observed <- latentif (short) {return(observed)}  else result <- list(observed=observed,pattern=pattern)
 return(result)
}