Local Dependence Diagnostics in IRT Modeling of Binary Data

Abstract

Local dependence (LD) for binary IRT models can be diagnosed using Chen and Thissen’s bivariate X² statistic and the score test statistics proposed by Glas and Suárez-Falcón, and Liu and Thissen. Alternatively, LD can be assessed using general purpose statistics such as bivariate residuals or Maydeu-Olivares and Joe’s M _r statistic. The authors introduce a new general statistic for assessing the source of model misfit, R₂, and compare its performance to the above statistics using a simulation study. Results suggest that the bivariate and trivariate X² statistics have unacceptable Type I error rates. As for the remaining statistics, if their computation involves the information matrix (bivariate residuals and score tests), they show good power; if not (M _r and R₂), they lack power. Of course, the performance of the bivariate residuals and score tests depends on how the information matrix is approximated.