Identification of Optimal Equating Method in Multidimensional Tests

Equating is one of the most important issues in educational measurement, violation of the assumptions of which results in serious challenges in it. In multidimensional tests, the use of unidimensional equating methods causes bias in results. Therefore, the purpose of this study was to identify the optimal equating methods in multidimensional tests. Six equating methods consisting of unidimensional and multidimensional methods was compared with each other. The equipercentile method was considered as the criterion for comparing the other methods in terms of being robust against the unidimensionality assumption. The statistical population consisted of all the candidates in Mathematics’ entrance exam in the years 2017 and 2018. Mathematics’ exam data of 5,000 people from both years were selected for equating. Test dimensions were determined using NOHARM and MPLUS software, the ltm package was used to estimate the unidimensional parameters and the mirt package in the R software was used to estimate the multidimensional parameters. IRT unidimensional observed score and true score equating conduct with PIE program and equipercentile equating was performed using R equate package. The mirt, mvnorm, and MASS packages in R software were also used for multidimensional equating.  The results showed that the most optimal method for multidimensional tests equating was FULL MIRT observed score equating,and then the unidimensionalized MIRT observed score equating is the appropriate method and that using unidimensional methods of the observed score and true score are not efficient in such conditions. Therefore, it is recommended that FULL MIRT observed score methods are used in equating tests with multidimensional structure.