Deterministic Inputs, Noisy Mixed Modeling for Identifying Coexisting Condensation Rules

In cognitive diagnosis models, the condensation rule describes the logical relationship between the required attributes and the item response, reflecting an explicit assumption about the cognitive processes respondents engage in to solve problems. In practice, multiple condensation rules may apply to an item simultaneously, indicating that respondents should use multiple cognitive processes with different weights to identify the correct response. Coexisting condensation rules reflect the complexity of cognitive processes utilized in problem solving and that the cognitive processes respondents employ in determining item responses may be inconsistent with the expert-designed condensation rule. This study was conducted to evaluate the proposed deterministic input with a noisy mixed (DINMix) model to identify coexisting condensation rules and provide feedback for item revision to increase the validity of the measurement of cognitive processes. Two simulation studies were conducted to evaluate the psychometric properties of the proposed model. The simulation results indicate that the DINMix model can adaptively and accurately identify coexisting condensation rules, existing either simultaneously in an item or separately in multiple items. An empirical example was also analyzed to illustrate the applicability and advantages of the proposed model.