Geri Anasayfa

Detay


Comparison of 1PL, 2PL, 3PL and 4 PL item response theory models

Abstract
In this study model-data fit studies were conducted for 1PLM, 2PLM, 3PLM and 4PLM, accuracy of item and ability parameter estimation was compared, and item and test information functions were provided. To be able to compare models on these issue, 2012 SBS (high school entrance exam) Turkish subtest were taken from Ministry of Education. The study group was comprised by 1500 examinee. Before the analysis of research problems, the assumptions of IRT were checked. First, the data were checked for unidimensionality with EFA based upon tetrachoric correlation matrix, and it appeared essentially unidimensional. Then, all pairs of items were checked for local independence using Yen’s Q3. None of the pairwise residual correlations for all 4 models were greater than .20 in absolute value, which showed that local dependence did not appear to be a problem. The item and ability parameters were provided the property of invariance. In terms of model-data fit, it was found that 4PLM was the best fitting model of all. The items were calibrated with all related models using MML in R Studio. The standard errors for most of the item parameters were reasonably small. This showed that the item parameters were estimated with good accuracy. The abilities (θ) were estimated for each individual examinee with all 4 models using maximum likelihood estimation. The standard errors of ability estimate were compared using Analysis of Variance for the degree of estimation accuracy. It was found that the estimation with 4PLM had smaller standard errors than the other 3 models, and the abilities were most precisely estimated with 4PLM. In addition, the most information was provided by 4PLM for the related test. All the models provided more information on the theta interval -1 and 0 than the other θ levels.

Keywords
Item Response Theory, 4 Parameter Logistic Model, Accuracy of Estimation, Information Functions