This study compared the precision of ability estimation on different types of item response theory models for mixed-format data. Participants in this study were 1625 Junior High School Students in Depok, Indonesia. The mixed-format test was used to measure the students' ability in mathematics. The test used consists of multiple-choice and constructed response. Multiple-choice items are scored dichotomously, whereas constructed response items are scored polytomously. Furthermore, the mixed response data were analyzed using combinations of item response theory models. This study used a combination of Multiple-Choice Model for dichotomous data and Graded response model for polytomous data (MCM+GRM). Analysis of this model combination has never been done simultaneously. Test response data were analysed using PARSCALE. Furthermore, the estimation results were compared with the estimation results from a combination of 3 Parameters Logistic Model and Generalized Partial Credit Model (3PLM+GPCM). There are two criteria evaluation for the level of estimation precision: Root Mean Squared Error (RMSE) and correlation method. Based on the results obtained, the estimated RMSE value for the MCM+GRM is smaller than the estimated RMSE value with the 3PLM+GPCM. Also, the results of the estimated ability with MCM+GRM produce higher correlation values than 3PLM+GPCM. So, it can be concluded that the level precision of the MCM+GRM model is higher than 3PLM+GPCM. Therefore, MCM+GRM is more recommended for estimating students' mathematical ability in mixed-format tests.