Confirmatory factor analysis : a brief introduction and critique

One of the routes to construct validation of a test is predicting the test's factor structure based on the theory that guided its construction, followed by testing it. The method of choice for such testing is often confirmatory factor analysis (CFA). In CFA, the predicted factor structure of a number of observed variables is translated into the complete covariance matrix over these variables. Next, this matrix is adjusted to the actual covariance matrix, and subsequently compared with it. The discrepancy between the two, the "goodness of fit" (GOF), is expressed by a number of indices. An assessment of how well the predicted factor structure is corroborated by the sample data, and whether it could be generalized to the population, is often based on the values of these indices. This brief and selective review discusses the CFA procedure, the associated indices of goodness of fit and the reliability of the latter. Much doubt surrounds the GOF indices, and thus an alternative approach is briefly explained.