Fitting the normal-ogive factor analytic model to scores on tests

This article (a) describes how McDonald's nonlinear factor analytic approach to the normal ogive curve can be used to factor analyse total test scores, (b) discusses the conditions in which this model is more appropriate than the widely used linear model, and (c) illustrates the applicability of both models using an empirical example. The rationale for the described procedure is that the test scores are simple sums of binary item responses whose item characteristic curves are adequately represented by normal ogives. The results obtained in the empirical example are meaningful and informative, and agree with the results obtained at the item level.