An application of the Hybrid model to a state competency test in mathematics

The present study models a procedure to extract instructional information from a minimal competency test in mathematics, using Yamamoto's (1989) Hybrid model (a combination of latent class models (LCM) and an item response theory model (IRT)). This procedure is applied to the data of 1600 ninth grade students from three inner-city schools, who took the June 1991 examination of the New York State Regents Competency Test (RCT) in mathematics. The test is examined in terms of mathematical content and cognitive processes proposed by the National Council of Teachers of Mathematics (NCTM). Two analyses were made: a two parameter with 14 latent classes Hybrid model was compared to a two parameter IRT model in terms of fit. Next, the classes identified by the Hybrid model were compared with the classes identified by a sub-score method, using Cohen's coefficient of agreement to assess if the same students were being identified by each method. Nine teachers with a minimum of 10 years experience evaluated the latent class groupings of items obtained from the Hybrid model to determine instructional relevance. The Hybrid model provided a better fit then the IRT model (...