Title: An Estimation and Analysis Framework for the Rasch Model,
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.