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The main purpose of the study was to investigate the superiority of scoring by utilizing the combination of MCM/GPCM model in comparison to 3PLM/GRM model within a mixed-item format of Mathematics tests. To achieve the purpose, the impact of two scoring models was investigated based on the test length, the sample size, and the M-C item proportion within the mixed-item format test and the investigation was conducted on the aspects of: (1) estimation of ability and item parameters, (2) optimalization of TIF, (3) standard error rates, and (4) model fitness on the data. The investigation made use of simulated data that was generated based on fixed effects factorial design 2 x 3 x 3 x 3 and 5 replications resulting in 270 data sets. The data were analyzed by means of fixed effect MANOVA on Root Mean Square Error (RMSE) of the ability and RMSE and Root Mean Square Deviation (RNSD) of the itemparameters in order to identify the significant main effects at level of a = .05; on the other hand, the interaction effects were incorporated into the error term for statistical testing. The -2LL statistics were also used in order to evaluate the moel fitness on the data set. The results of the study show that the combination of MCM/GPCM model provide higher accurate estimation than that of 3PLM/GRM model. In addition, the test information given by the combination of MCM/GPCM model is three times hhigher than that of 3PLM/GRM model although the test information cannot offer a solid conclusion in relation to the sample size and the M-C item proportion on each test length which provides the optimal score of thest information. Finally, the differences of fit statistics between the two models of scoring determine the position of MCM/GPCM model rather than that of 3PLM/GRM model.

Estimation of ability and item parameters in mathematics testing by using the combination of 3PLM/ GRM and MCM/ GPCM scoring model