Analysis of the Latin Square Task with linear logistic test models

The Latin Square Task (LST) was developed by Birney, Halford, and Andrews [Birney, D. P., Halford, G. S., & Andrews, G. (2006). Measuring the influence of cognitive complexity on relational reasoning: The development of the Latin Square Task. Educational and Psychological Measurement, 66, 146–171.] and represents a non-domain specific, language-free operationalization of Relational Complexity (RC-)Theory. The current study investigates the basic cognitive parameters and structure of LST as defined by RC-Theory, using IRT-based linear logistic test models (LLTM). 850 German school students completed 26 systematically designed LST items. Results support the notion of Rasch-scalability. LLTM analyses reveal that both operation complexity and number of operations affect item difficulty. It is shown how LLTM and its variants can provide substantial insights into cognitive solution processes and composition of item difficulty in relational reasoning in order to make item construction more efficient.

Research highlights
► The Latin Square Task is an appropriate operationalization of RC-Theory.
► Rule-based design and item construction of LST can be regarded successful.
► Basic design parameters are stable difficulty-affecting factors.
► The LLTM provides flexible possibilities to analyze items from rule-based design.