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This study aimed to examine unidimension assumption, local independency and parameter invariance and also compatibility of model at final examination in Islamic education subject by item response theory. Research Methodology used in this research is quantitative research with expose-facto approach. Data were collected by document study to the students’ response on multiple choices on Islamic education subject at XII grade of Senior High School in Gorontalo academic years 2016/2017 with 320 samples. Assumption test data analysis conducted by factor analysis by helping of SPSS version 24.0 software and compatibility statistic test of one item with model or goodness of fit statistic by using BILOGMG program version 3.0. The result shows that unidimension assumption testing gained information about fulfilled measurement model, because it is found many curves of eigen value from the output of total variance which explains the value of eigen in each component and explained variants and also the picture of scree-plot. The test of local independency assumption is automatically proven because the result of response data analysis from students is not unidimension. The appropriate model used to analyse the questions of Islamic education subject at final examination is 2 parameter logistic model (2PL). The assumption of 2PL parameter invariance testing shows that there is no estimation result of parameter variance at odd group and even groups. It means that parameter invariance of index discrimination (a) and difficulty index (b) is fulfilled. Keywords— Assumption testing; compatibility model; Item response theory

The Assumption Testing and Compatibility Model of Final Examination in Islamic Religious Education by Item Response Theory