Conditional Independence and Dimensionality of Cognitive Diagnostic Models: a Test for Model Fit

Nonparametric cognitive diagnosis methods are useful in cognitive diagnosis modeling for calibration efficiency, especially when sample size is small or large, or the latent attributes are more complex. This article proposes the Mantel-Haenszel chi-squared statistic as an index for detecting the misspecification of latent attributes as well as testlet effects in nonparametric cognitive diagnosis methods. The proposed theoretical considerations are augmented by simulation studies conducted to assess the performance of the Mantel-Haenszel statistic under various conditions within the nonparametric diagnosis framework, with a special focus on situations were the set of latent abilities assumed to underlie the data was underspecified.