The Linear Logistic Test Model (LLTM) as the methodological foundation of item generating rules for a new verbal reasoning test

Based on the demand for new verbal reasoning tests to enrich psychological test inventory, a pilot version of a new test was analysed: the 'Family Relation Reasoning Test' (FRRT; Poinstingl, Kubinger, Skoda & Schechtner, forthcoming), in which several basic cognitive operations (logical rules) have been embedded/implemented. Given family relationships of varying complexity embedded in short stories, testees had to logically conclude the correct relationship between two individuals within a family. Using empirical data, the linear logistic test model (LLTM; Fischer, 1972), a special case of the Rasch model, was used to test the construct validity of the test: The hypothetically assumed basic cognitive operations had to explain the Rasch model's item difficulty parameters. After being shaped in LLTM's matrices of weights ((qij)), none of these operations were corroborated by means of the Andersen's Likelihood Ratio Test.