# Robust estimation of the latent trait in graded response models

## TL;DR

This paper introduces a new method to improve the accuracy of psychological assessments by reducing the impact of careless or incorrect responses in surveys with multiple-choice items.

## Contribution

A novel robust estimator for the graded response model is proposed to handle response disturbances in Likert-type items.

## Key findings

- The robust estimator significantly reduces bias in latent trait estimates under various conditions.
- Stable standard errors were observed, indicating reliable performance of the estimator.
- Application to real data from the Big Five Inventory-2 demonstrates practical utility.

## Abstract

Aberrant responses (e.g., careless responses, miskeyed items, etc.) often contaminate psychological assessments and surveys. Previous robust estimators for dichotomous IRT models have produced more accurate latent trait estimates with data containing response disturbances. However, for widely used Likert-type items with three or more response categories, a robust estimator for estimating latent traits does not exist. We propose a robust estimator for the graded response model (GRM) that can be applied to Likert-type items. Two weighting mechanisms for downweighting “suspicious” responses are considered: the Huber and the bisquare weight functions. Simulations reveal the estimator reduces bias for various test lengths, numbers of response categories, and types of response disturbances. The reduction in bias and stable standard errors suggests that the robust estimator for the GRM is effective in counteracting the harmful effects of response disturbances and providing more accurate scores on psychological assessments. The robust estimator is then applied to data from the Big Five Inventory-2 (Ober et al., 2021) to demonstrate its use. Potential applications and implications are discussed.