The effect of Maximum Likelihood Estimation Methods and the Logistic Model on the Bias of Item Parametres Values and the Ability of Individuals

Abstract

The current research aims to compare the estimation of Item parameters and the ability of individuals according to the estimation method and the logistic model using the bias indices (BAIS) and (Akaiki), as indicators of bias estimates. Therefore, the researcher used the experimental method according to the repeated measurements design, where he applied the research tool consisting of Robert Thorndike's abstract intelligence test based on the ability to process words and symbols and how to deal with them. The test was applied to a sample of (1072) adults, male and female, obtained from students at the University of Salahaddin/Erbil. In order to analyze the data obtained, the researcher resorted to three of the binary gradual models of the Item response theory. After ensuring that the data generated from the three logistic models (Rasch, Lord, Birnbaum) matched, the (Bilog–MG3) program was used to estimate the Item parameters (difficulty, discrimination, guessing) according to the aforementioned models.

The researcher used both the joint maximum likelihood and marginal likelihood methods to estimate the Item parameters. After that, the researcher made a comparison in estimating the Item parameters according to the estimation method and the logistic model using the bias index (BAIS). It became clear to him that estimating the Item parameters according to the joint maximum likelihood method is less deviant from the average of the parameters, which indicates that this method is less biased than estimating the parameters according to the marginal maximum likelihood method. This indicates that the joint likelihood method is more accurate in estimating the difficulty, discrimination and estimation parameters according to the Birnbaum model, followed by the Lord model, then the Rasch model, and according to the specificity of the model in estimating the parameters, compared to the marginal likelihood method. After estimating the ability parameters according to the three logistic models, a comparison was made to estimate the ability according to the bias index for the joint maximum and marginal odds methods according to the Birnbaum model, which was less than the arithmetic mean values ​​for the Lord model as well as for the Rasch model, which indicates the superiority of the Birnbaum model over the other two models in reducing the bias in estimating the ability of individuals, followed by the Lord model and then the Rasch model.The results of calculating bias according to Akaike Information Criterion were consistent with the results obtained according to the bias index (BAIS). Based on the results reached by the current research, the researcher recommended using the Birnbaum model and according to the joint maximum likelihood method in estimating the Item parameters and the ability of individuals, in order to avoid bias in the estimates and obtain more accurate results in the estimation. The researcher also suggested conducting more studies such as comparing the graded models of the Item response theory in revealing the most accurate and least biased model in estimating the Item parameters and individuals.