Applying Bi-factor Multidimensional Item-response Theory Model for Dimensionality and Differential items Functioning Analysis on Testlet-Based Tests

The present study has been done with the purpose of investigating the dimensionality and differential item functioning of the testlet-based test of Iran's PIRLS 2011. In order to analyze the dimensionality, graded response and bi-factor item-response theory models were used with full-information maximum likelihood estimation method and to analyze the differential item functioning multiple-group bi-factor model of Cai et al (2011) was applied. The results of the dimensionality investigation showed that the bi-factor model is better fitted to the data than the graded response model both in Iran's total sample and in boy and girl groups. The results of testlets effect variance showed that effects of second factors on Iranian student's performance in two testlet related to literal comprehension, has caused dimensionality in Iran's PIRLS testlets. The results showed that there was no significant difference in average student's performance of the boy and girl in general latent trait of reading comprehension, but the difference between the average reading proficiency of the boy and the girl in three literal and three informational testlet in favor of girls was significant. The result of differential items functioning based on the bifactor model showed that many items have an uniform and non-uniform differential item functioning, and boys in multiple-choice items and girls in constructed response items have better performances. In general, the results showed that in Iran's PIRLS 2011 testlets, the traits related to the two literal comprehension testlets were differently perceived between boy and girl students, and these two testlet had more local item dependence among girls than boys. Also, the results indicated a difference between the performance of Iranian boy and girl students in the mixed items format test of PIRLS.