Using Cognitive Diagnostic Models to Evaluate the Two-Process Theory of Matrix Reasoning

Area of Science:

• Cognitive psychology
• Psychometrics
• Educational assessment

Background:

• Figural matrices assess reasoning ability, with performance linked to correspondence finding (induction) and goal management (working memory).
• Cognitive theory posits item characteristics (change rules, design principles) interact multiplicatively to influence figural matrix difficulty.

Purpose of the Study:

• To test the multiplicative effect hypothesis on item difficulty in figural matrices.
• To compare additive and multiplicative cognitive diagnostic models for understanding item parameter reconstruction.

Main Methods:

• Administered a 26-item figural matrix test to 633 high-ability individuals.
• Applied Linear Logistic Test Model (LLTM) and Least Square Distance Method (LSDM) to item parameters.
• Utilized Rasch and 2PL item parameter estimation techniques.

Main Results:

• Contrary to the hypothesis, the additive LLTM model demonstrated superior item parameter reconstruction compared to the LSDM with multiplicative effects.
• Findings suggest change rules and design principles independently contribute to figural matrix difficulty.
• Correspondence finding is primarily linked to design principles, while change rules impact goal management demands.

Conclusions:

• The additive model better explains item difficulty, challenging the multiplicative effect hypothesis.
• Item components, particularly phenomenological representations, are crucial for understanding figural matrix solution processes.
• Results have implications for refining cognitive theories and improving the construction of figural matrix items.