Application of Latent Class Multidimensional Item Response Theory (LCMIRT) on investigating cognitive dimensions and clustering math test items: A case study of the math test of national Konkur of physics and mathematics

Math skills include different content and cognitive processes domains which indicate the complexity of math skill and its latent traits. Until now, Study of these complexities has been done through traditional data analysis or subjective methods. Therefore, present research studied cognitive dimensions and latent variables of the math test of national university entrance examination through the application of Latent Class Multidimensional Item Response Theory (LCMIRT). In doing so, the math test data of national examinations in 2008, 2011 and 2015 were studied. Results showed that the math test, as a high stakes test in the national university entrance examination, encompasses a set of multidimensional cognitive traits. Results of the unified parallel analysis method showed that the tests do not fit with the unidimensional model and adding additional dimensions can significantly improve model fit. Moreover, cognitive domains of comprehension, problem solving and reasoning were recognized as three essential constructs which account for math skills and give more detailed information about items quality in clustering and analysis of the test items. This property of LCMIRT, in comparison with other approaches, increases the number of cognitive sub-clusters. At last, it is recommended that LCMIRT models are considered in constructing and analyzing educational and psychological tests, in order to more validly detect latent cognitive skills of the tests.