The Effect of Sample Size on the Accuracy of Item Parameter and Ability Estimation in Polytomous Models Using Item Response Theory: A Simulation Study

Abstract

This study aimed to investigate the effect of sample size on the accuracy of estimating item parameters (difficulty, discrimination) and the ability parameter in polytomous models using Item Response Theory (IRT). A descriptive-analytical approach was adopted, and three different sample sizes (100, 500, and 1000 examinees) were generated following a normal distribution, with 20 items representing the test.

     The difficulty parameters (β) were set to range between (-3 and 3), the discrimination parameters (α) between (0.5 and 3), and the ability parameters (θ) for individuals between (-3 and 3). The study utilized three polytomous IRT models: the Graded Response Model (GRM), the Partial Credit Model (PCM), and the Nominal Response Model (NRM), which were selected due to their differing assumptions and estimation methods.

     A computer-based simulation was conducted using the WinGen program to generate artificial data, allowing precise control over data characteristics.

The findings revealed that the Graded Response Model (GRM) was the most accurate in estimating item parameters (difficulty, discrimination) and ability compared to the other models. Additionally, increasing the sample size improved estimation accuracy, as the computed values became closer to the true values. The study found no significant differences between the GRM and NRM in estimating the ability parameter, indicating that a larger sample size enhances estimation accuracy across all models.