Comparison among cognitive diagnostic models for the TIMSS 2007 fourth grade mathematics assessment

A variety of cognitive diagnostic models (CDMs) have been developed in recent years to help with the diagnostic assessment and evaluation of students. Each model makes different assumptions about the relationship between students' achievement and skills, which makes it important to empirically investigate which CDMs better fit the actual data. In this study, we examined this question by comparatively fitting representative CDMs to the Trends in International Mathematics and Science Study (TIMSS) 2007 assessment data across seven countries. The following two major findings emerged. First, in accordance with former studies, CDMs had a better fit than did the item response theory models. Second, main effects models generally had a better fit than other parsimonious or the saturated models. Related to the second finding, the fit of the traditional parsimonious models such as the DINA and DINO models were not optimal. The empirical educational implications of these findings are discussed.