Small area estimation using multiple imputation in three-parameter logistic models

This article presents a new method that combines item response theory techniques with small-area estimation approaches to handle missing data. We propose an unbiased estimator for the average skill parameter of three-parameter logistic models using plausible values as the imputation method for missing data. We conduct a thorough simulation study to compare our estimator with the Horvitz-Thompson estimator in complex sampling. Synthetic data experiments demonstrate that our proposal has lower standard errors than its competitor. Additionally, we apply our method to the results in mathematics of the 2015 Program for International Student Assessment and compare our findings with previous studies. These findings indicate that our method is a competitive alternative for generating accurate official statistics.