An Estimation and Analysis Framework for the Rasch Model

Andrew Lan, Mung Chiang, Christoph Studer
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:2883-2891, 2018.

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 associated 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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v80-lan18a, title = {An Estimation and Analysis Framework for the {R}asch Model}, author = {Lan, Andrew and Chiang, Mung and Studer, Christoph}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {2883--2891}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/lan18a/lan18a.pdf}, url = {http://proceedings.mlr.press/v80/lan18a.html}, 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 associated 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.} }
Endnote
%0 Conference Paper %T An Estimation and Analysis Framework for the Rasch Model %A Andrew Lan %A Mung Chiang %A Christoph Studer %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-lan18a %I PMLR %P 2883--2891 %U http://proceedings.mlr.press/v80/lan18a.html %V 80 %X 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 associated 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.
APA
Lan, A., Chiang, M. & Studer, C.. (2018). An Estimation and Analysis Framework for the Rasch Model. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:2883-2891 Available from http://proceedings.mlr.press/v80/lan18a.html.

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