An Estimation and Analysis Framework for the Rasch Model

TL;DR

This paper introduces a novel linear MMSE estimator for the Rasch model, providing exact nonasymptotic error analysis and practical guidelines for data requirements, with demonstrated effectiveness on real-world datasets.

Contribution

It presents a new linear MMSE estimator for the Rasch model that allows for exact nonasymptotic error analysis and practical data guidelines, improving upon existing asymptotic guarantees.

Findings

The L-MMSE estimator achieves competitive predictive performance.

The framework offers precise error bounds and data requirements.

Effective on real-world collaborative filtering datasets.

Abstract

The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the available analytical performance guarantees are mostly asymptotic. This paper provides a framework that relies on a novel linear minimum mean-squared error (L-MMSE) estimator which enables an exact, nonasymptotic, and closed-form analysis of the parameter estimation error under the Rasch model. The proposed framework provides guidelines on the number of items and responses required to attain low estimation errors in tests or surveys. We furthermore demonstrate its efficacy on a number of real-world collaborative filtering datasets, which reveals that the proposed L-MMSE estimator performs on par with state-of-the-art nonlinear estimators in terms of predictive performance.