Interchangeability between factor analysis, logistic IRT, and normal ogive IRT.

Abstract

In existing studies, it has been argued that factor analysis (FA) is equivalent to item response theory (IRT) and that IRT models that use different functions (i.e., logistic and normal ogive) are also interchangeable. However, these arguments have weak links. The proof of equivalence between FA and normal ogive IRT assumes a normal distribution. The interchangeability between the logistic and normal ogive IRT models depends on a scaling constant, but few scholars have examined whether the usual values of 1.7 or 1.702 maximize interchangeability. This study addresses these issues through Monte Carlo simulations. First, the FA model produces almost identical results to those of the normal ogive model even under severe nonnormality. Second, no single scaling constant maximizes the interchangeability between logistic and normal ogive models. Instead, users should choose different scaling constants depending on their purpose in using a model and the number of response categories (i.e., dichotomous or polytomous). Third, the interchangeability between logistic and normal ogive models is determined by several conditions. The interchangeability is high if the data are dichotomous or if the latent variables follow a symmetric distribution, and vice versa. In summary, the interchangeability between FA and normal ogive models is greater than expected, but that between logistic and normal ogive models is not.