Choice of MIRT Model for Analysis of Higher Mathematics Tests

Abstract

Purpose. This study aims to identify the most appropriate MIRT model for evaluating higher mathematics tests, with a focus on polytomous models without decomposition into dichotomous components. Methods. The empirical data were obtained from a calculus test administered to 120 students at Igor Sikorsky Kyiv Polytechnic Institute. The test included 20 dichotomous and polytomous items with up to 12 response categories. The study was conducted in two stages. First, Exploratory Factor Analysis (EFA) was applied using multiple criteria (CD, EMPKC, HULL, MAP, NEVALSGT1, RAWPAR, SESCREE, SMT) to determine the latent dimensionality. Second, Confirmatory Factor Analysis (CFA) was used to estimate and compare nine MIRT models (GPCM, GRM, NRM) in one-, two-, and three-dimensional specifications. Model fit was evaluated using AIC, BIC, RMSEA, CFI, and TLI indices. Results. The EFA results showed partial inconsistency across methods: most criteria supported a two-dimensional structure, whereas some suggested higher dimensionality. The CFA results indicated that the two-dimensional GPCM model (GPCM2) provided the best fit according to the information criteria. Analysis of factor loadings, as well as checks for monotonicity and local independence, confirmed the overall adequacy of the model while identifying several misfitting items. The findings demonstrate that unidimensional models are insufficient to capture the structure of mathematical knowledge, whereas higher-dimensional models introduce parameter redundancy without substantial improvement in model fit. Conclusions. The results support the effectiveness of a multi-stage approach to MIRT model selection. The two-dimensional GPCM model is the most appropriate for analyzing polytomous mathematics test items. Two relatively independent latent dimensions were identified, corresponding to key components of calculus competence: differential and integral calculus.