A Comparative Study on the Detection Efficacy of CUSUM and CPA in Multidimensional Tests

Cumulative summation (CUSUM) and change point analysis (CPA) procedures are the two most widely used methods for flagging aberrant item responses, yet their relative merits have been examined almost exclusively in unidimensional settings. This study evaluated five person-fit statistics (PFSs) that have demonstrated strong detection power in earlier research: the CUSUM-based ( $C_i^T,C_i^{LARD}$ ), and the CPA-based ( $L_{\max },W_{\max },R_{\max }$ ), in multidimensional testing scenarios. In addition, the Wald statistic was derived to a new form for multidimensional tests, which is much different from the unidimensional version. Both a simulation experiment and a case study were conducted to assess the performance of these PFSs in detecting back random response (BRR). Results showed that inter-dimensional ability correlation influenced detection rates, and this effect diminished as test length increased. Across all conditions, the newly proposed $W_{\max }$ statistic achieved higher average detection efficiency than its competitors and exhibited the greatest stability.