extended · article · 2016

Critical Values for Yen’s <i>Q</i> ₃ : Identification of Local Dependence in the Rasch Model Using Residual Correlations

Karl Bang Christensen; Guido Makransky; Mike Horton; David Andrich

The assumption of local independence is central to all item response theory (IRT) models. Violations can lead to inflated estimates of reliability and problems with construct validity. For the most widely used fit statistic Q 3 , there are currently no well-documented suggestions of the critical values which should be used to indicate local dependence (LD), and for this reason, a variety of arbitrary rules of thumb are used. In this study, an empirical data example and Monte Carlo simulation were used to investigate the different factors that can influence the null distribution of residual correlations, with the objective of proposing guidelines that researchers and practitioners can follow when making decisions about LD during scale development and validation. A parametric bootstrapping procedure should be implemented in each separate situation to obtain the critical value of LD applica...