Testing the Local Independence Assumption of the Rasch Model With Q 3-Based Nonparametric Model Tests

Abstract

Local independence is a central assumption of commonly used item response theory models. Violations of this assumption are usually tested using test statistics based on item pairs. This study presents two quasi-exact tests based on the $Q_3$ statistic for testing the hypothesis of local independence in the Rasch model. The proposed tests do not require the estimation of item parameters and can also be applied to small data sets. The authors evaluate the tests with three simulation studies. Their results indicate that the quasi-exact tests hold their alpha level under the Rasch model and have higher power against different forms of local dependence than several alternative parametric and nonparametric model tests for local independence.

Keywords: IRT model fit; Rasch model; local independence.