Educational Sciences: Theory & Practice

ISSN: 2630-5984

Examination of Polytomous Items’ Psychometric Properties According to Nonparametric Item Response Theory Models in Different Test Conditions

Asiye Sengul Avsar
Department of Measurement and Evaluation in Education, Recep Tayyip Erdogan University, Rize Turkey
Ezel Tavsancil
Retired Lecturer from Department of Measurement and Evaluation in Education, Ankara University, Ankara Turkey


This study analysed polytomous items’ psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets—three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)—were generated by conducting 20 replications in 27 test conditions. Via simulated datasets, polytomous items’ psychometric properties were investigated through NIRT models, the Mokken Homogeneity Model (MHM) and the Kernel Smoothing Approach Model (KSAM). According to MHM analysis results, number of items, distribution of sample and sample-size factors affected items’ level of fit. As a result of scaling data according to MHM in this study’s test conditions, tests that generally fit MHM at weak and moderate levels, with high reliability, were achieved. According to KSAM analysis results, number of items, sample distribution and sample-size factors influenced item and test discrimination. Consequent to KSAM data analysis, tests that generally consisted of items with an acceptable discrimination level and with high reliability were achieved. In this study, producing H coefficients, through MHM, that were easy to interpret and providing, through KSAM, graphics with detailed information made it easier to examine complementary polytomous items’ psychometric properties.

Polytomous items, Nonparametric item response theory, Mokken homogeneity model, Kernel smoothing approach model, Simulation.