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Traditionally, teachers evaluate students’ abilities via their total test scores. Recently, cognitive diagnostic models (CDMs) have begun to provide information about the presence or absence of students’ skills or misconceptions. Nevertheless, CDMs are typically applied to tests with multiple-choice (MC) items, which provide less diagnostic information than constructed-response (CR) items. This paper introduces new CDMs for tests with both MC and CR items, and illustrates how to use them to analyse MC and CR data, and thus, identify students’ skills and misconceptions in a mathematics domain. Analyses of real data, the responses of 497 sixth-grade students randomly selected from four Taiwanese primary schools to eight direct proportion items, were conducted to demonstrate the application of the new models. The results show that the new models can better determine students’ skills and misconceptions, in that they have higher inter-rater agreement rates than traditional CDMs. [ABSTRACT FROM AUTHOR]

By analysing the test data of 1029 British secondary school students’ performance on 20 Programme for International Student Assessment English reading items through the generalised deterministic input, noisy ‘and’ gate (G-DINA) model, the study conducted two investigations on exploring the relationships among the five reading comprehension skills defined by six English language experts. Skill groups, skill types and conflicting relationship were discovered in the investigation about the relationship among reading comprehension skills as part of the cognitive structure of the examinees, which provided insights into the sequence of reading skill training. The investigation about the relationship among reading comprehension skills in the problem-solving process, conducted at the item level, conceptualised skill relationship patterns as strategies for solving items. The study also demonstrated that saturated G-DINA model catered to the characteristics of reading comprehension skills and could be applied to tests involving highly interactive and hierarchical skills. [ABSTRACT FROM AUTHOR]