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

TL;DR

This paper introduces a new unbiased estimator for the average ability in three-parameter logistic models, combining item response theory with small area estimation, and demonstrates its superior performance through simulations and real data application.

Contribution

The paper presents a novel unbiased estimator for the average ability in three-parameter logistic models, integrating item response theory with small area estimation in the presence of missing data.

Findings

Our estimator has substantially lower standard errors than the Horvitz-Thompson estimator.

Simulation results show improved accuracy over existing methods.

Application to PISA data confirms the estimator's practical effectiveness.

Abstract

We propose a novel methodology relating item response theory methods with small area estimation strategies in the presence of missing data. Specifically, we propose an unbiased estimator for the average ability parameter of three-parameter logistic models. Thus, we carry out an extensive simulation study in order to compare our estimator with the well-known Horvitz-Thompson estimator. According to our experiments with synthetic data, our proposal has substantial lower standard errors than its competitor. In addition, we perform an actual application by considering the Mathematics results of the 2015 Program for International Student Assessment (PISA), and also, compare our results with previous analyses. Our findings strongly suggest that our methodology is a high competitive alternative for generating compelling official statistics.