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.
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).