Comparison of Item Response Theory parameter estimations according to classical and bayesian approaches in different simulation conditions

The purpose of this research is to compare the ability and item parameter estimations of Item Response Theory (IRT) according to the Classical and Bayesian approaches in different simulation conditions. For this purpose, normal, skewed left, skewed right, leptokurtic, platykurtic five different type including the distribution sample size, item count (test length), and estimated parameters of the model depending on the number of cases of classical maximum likelihood method and the Bayesian method to differentiation according to the differences in ability and item parameters and the RMSE value were investigated. Monte Carlo Simulation technique was used to generate the data. According to this; by keeping the estimation methods constant, simulation conditions were created by manipulating the sample size, item count and parameters of the model in different types of distribution. Prior distribution (normal, skewed left, skewed right, leptokurtic, platykurtic), item count (10, 20, 40), sample size (100, 500, 1000), model parameters (2 PL, 3 PL) and 5x3x3x2=90 simulation conditions were carried out with 100 replications. The R program was used to generate the data, estimate the parameters and draw the graphs. The unidimensionality, local independence and model-data fit analyzes of the data produced according to the simulation conditions were made according to the assumptions of the IRT. Also, statistical and logical validity checks were made for the simulation data. In each of the simulation conditions, the differences in the RMSE values in the ability and item parameter estimations of the IRT according to the maximum likelihood and Bayesian approaches were examined. Mixed model ANOVA analysis was performed to determine the differentiations. Accordingly, it was observed that there were significant differences in the RMSE values of both ability and item parameters between classical (maximum likelihood) and Bayesian estimations in data with normal, left skewed, right skewed, leptokurtic or platykurtic a priori ability distribution. The a priori ability distribution type, number of items and estimation method were significant in the differentiation of the estimated ability parameter and RMSE values in the 2 PL model. The a priori ability distribution type and the number of items were significant in the differences in the ability parameter and RMSE values estimated in the 3 PL model. While a priori ability distribution type, sample size and estimation method created significant differences in the RMSE values of the item discrimination parameter estimated in the 2PL model, none of conditions created a significant difference in the RMSE values of the item difficulty parameter. A priori ability distribution type, sample size and estimation method created significant differences in the item discrimination RMSE values predicted in the 3PL model. Prior ability distribution and estimation method created significant differentiation in the RMSE values of the lower asymptote parameter. However, none of the conditions created a significant difference in the RMSE values of item difficulty parameters. Significant conditions for ability and item parameters are in favor of Bayes estimation method when the a priori ability distribution is skewed to the left and right, the sample size is smaller and the number of items decreases. Bayesian estimation method estimates lower error values than classical maximum likelihood method. Accordingly, as the a priori ability distribution moves away from the normal distribution, as the sample gets smaller and the number of items decreases, it is recommended to use the Bayesian method in the estimation of ability and item parameters.