### A Latent Factor Model with a Nonnegative Component with Application to Cheating Detection in Educational Testing

Statistics Seminar

3rd May 2019, 3:00 pm – 3:45 pm

Main Maths Building, SM3

In this talk, we introduce a new family of latent factor models, which add non-negative constraints on some latent factors and the corresponding loading parameters. This model is motivated by an application to cheating detection in educational testing, where a subset of examinees may have cheated in the exam on a subset of leaked test items. The goal is to detect both cheating examinees and leaked items based on item response data. The proposed model captures normal item response behavior using an unconstrained latent factor component and captures the cheating behavior using a non-negative latent factor component. Thanks to the latent variable modeling formulation, marginal false discovery rate (mFDR) and marginal false non-discovery rate (mFNR) can be defined for the detection of cheating examinees and compromised items, respectively. They can be estimated from data under an empirical Bayes framework. The proposed model is applied to a real data example and successfully recovers the cheating examinees and leaked items that have been flagged by the testing program. Finally, extensions are discussed, including (1) the incorporation of response time, and (2) the general theory for the decomposition of a non-sparse low rank matrix and a sparse low rank matrix.

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