sim.congeneric: 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

sim.congeneric(loads = c(0.8, 0.7, 0.6, 0.5),N = NULL,  err=NULL, short = TRUE, categorical=FALSE, low=-3,high=3)

Arguments

How many subjects to simulate. If NULL, return the population model

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 correlations, short=FALSE, report observed test scores as well as the implied pattern matrix

categorical

continuous or categorical (discrete) variables.

low

values less than low are forced to low

high

values greater than high are forced to high

Value

modelThe implied population correlation matrix if N=NULL or short=FALSE, otherwise the sample correlation matrix
patternThe pattern matrix implied by the loadings and error variances
rThe sample correlation matrix for long output
observeda matrix of test scores for n tests
latentThe latent trait and error scores

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. Mainly used for a discussion of reliability theory as well as factor score estimates.

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

References

Revelle, W. (in prep) An introduction to psychometric theory with applications in R. To be published by Springer. (working draft available at http://personality-project.org/r/book/

Examples

Run this code

test <- sim.congeneric(c(.9,.8,.7,.6))   #just the population matrix
test <- sim.congeneric(c(.9,.8,.7,.6),N=100)   # a sample correlation matrix
test <- sim.congeneric(short=FALSE, N=100)
round(cor(test$observed),2) # show  a congeneric correlation matrix
f1=fa(test$observed,scores=TRUE)
round(cor(f1$scores,test$latent),2)  #factor score estimates are correlated with but not equal to the factor scores
set.seed(42)
items <- sim.congeneric(N=500,short=FALSE,low=-2,high=2,categorical=TRUE) #500 responses to 4 discrete items
d4 <- irt.fa(items$observed)  #item response analysis of congeneric measures

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