Local Dependence Diagnostics in IRT Modeling of Binary Data
LiuY. & Maydeu-Olivares A.
Local independence is a basic assumption ofIRT. Researchers have developed several global indices to assess the localdependence between items, which include Q3 statistic, bivariate X2 statistic,bivariate residuals, and Mr statistics. In this study, the authors introduced a new statistics (i.e., the score test statistics) for assessing the source of model misfit and compared with the existing statistic.
(1) Yen’s Q3 statistic: the correlation between the residual for two items.
(2) Peasons’ X2 statistic:
(3) Glas & Suarez-Falcon: thresholdshift model in which a shift parameter is added into the 2PL model
(4) Liu & Thissen: a bifactor LD modelin which a second latent variable is added into the 2PL model (similar to testlet model)
(5) Maydeu-Olivares & Joe: standardized bivariate/trivariate residuals
(6) Liu & Thissen: sum-score-based bivariate statistic.
The simulations were conducted. It was found that the bivariate and trivariate X2 statistics have inflated Type I error. Forthe remaining statistics, they showed good power when the information matrix was involved in computation and otherwise when the information is not involved.
Comments:
1. It is a difficult paper for me.
2. A global statistic for assessing local dependence is attractive but is not easy. Such as a global statistic for assessing multidimensionality.
3. Whether the statistics will be differentfor polytomous items.