Models and Methods - The COSAN Model

This section begins with a brief description of the McDonald's COSAN model. Let S be a population variance-covariance matrix for a set of manifest variables. The COSAN model (McDonald, 1978) holds if S may be expressed as

S = F1F2...FkPFk¢ ...F2¢ F1¢ (8)

where P is symmetric and Gramian, and any of the elements of any F matrix or P may be constrained under the model to be a function of the others, or to be specified numerical values. As a powerful additional option, any square F matrix may be specified to be the inverse of a patterned matrix. This "patterned inverse" option is critical for applications to path analysis. A COSAN model with k F matrices is referred to as "a COSAN model of order k."

Obvious special cases are: Orthogonal and oblique common factor models, confirmatory factor models, and patterned covariance matrices.

McDonald's COSAN model is a powerful and original approach which offers many benefits to the prospective tester of covariance structure models. Testing and estimation for the model were implemented in a computer program called, aptly enough, COSAN (See Fraser and McDonald, 1988 for details on a recent version of this program, which has been available since 1978).

In 1978, J. J. McArdle proposed some simple rules for translating any path diagram directly to a structural model. In collaboration with McDonald, he proposed an approach which yielded a model directly testable with the COSAN computer program.