The gradient test and its finite sample size properties in a conditional maximum likelihood and psychometric modeling context

Abstract

In asymptotic theory, the gradient test proposed by Terrell is a recent likelihood-based hypothesis testing approach which can be considered as an alternative to the well-established trinity of likelihood ratio, Rao score, and Wald tests. The gradient test has not yet entered into the mainstream of applied statistics. This is particularly true for the psychometric context. This research discusses a novel application of the gradient test within the conditional maximum likelihood and the Rasch modeling framework. It also investigates some of its finite sample size properties and compares it with the classical trinity of chi square tests by conducting an extensive Monte Carlo study. The results confirm that the gradient test has its pros and cons.