![]() ![]() ![]() ![]() The Hierarchical Diagnostic Classification Model (HDCM) reflects on the sequences of the presentation of the essential materials and attributes to answer the items of a test correctly. A data set from the Trends in International Mathematics and Science Study 2007 mathematics assessment is analyzed as an illustration. Simulation studies are conducted to examine the Type I error and power of the hypothesis tests under varied conditions. This study aims to evaluate whether several hypothesis tests, namely, the Wald test using various variance–covariance matrices, the likelihood ratio (LR) test, and the LR test using approximated parameters, can be used to select the appropriate CDMs for each task of graded response items. If the CDM specified for each task is not in accordance with the underlying cognitive processes, the validity of the inference could be questionable. Although a host of dichotomous CDMs with different condensation rules can be used to parameterize the success probability of each task, specifying the most appropriate one remains challenging. The sequential generalized deterministic input noisy “and” gate model is a general cognitive diagnosis model (CDM) for graded response items of this type. Each task could involve different attributes, and those required attributes may be “condensed” in various ways to produce the responses. Solving a constructed-response item usually requires successfully performing a sequence of tasks. ![]()
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