关键词: 个人拟合, 变点分析法, 迭代净化

Abstract: Back random responding (BRR) is a common form of aberrant responding in psychological and educational testing. It occurs when examinees respond normally during the earlier part of a test but shift to random or irregular responding in the later part. Such response behavior may contaminate item and person parameter estimation and threaten the validity of subsequent measurement inferences. Change point analysis (CPA) provides a useful framework for detecting this type of response change because it can identify not only whether an examinee shows aberrant responding but also where the abnormal change begins in the response sequence. However, most existing CPA applications assume known item parameters. In practical testing situations, item parameters are often unknown and must be estimated from response data that may already contain aberrant responses. Biased parameter estimation may therefore impair CPA performance, reduce statistical power, inflate Type I error rates, and weaken the accuracy of change-point localization. To address this issue, the present study incorporated an iterative purification procedure into the CPA framework. The procedure repeatedly identifies potentially aberrant responses, removes the suspected contaminated responses, and re-estimates item parameters, with the aim of reducing the influence of aberrant responses on parameter estimation and improving CPA performance under unknown-parameter conditions. This study combined simulation research with an empirical application. In the simulation study, both dichotomous and polytomous response data were generated under unidimensional item response theory models. Normal responses were generated using the two-parameter logistic model for dichotomous items and the graded response model for polytomous items, whereas back random responding was generated using a hybrid model with a latent change point. The manipulated factors included test length, the proportion of aberrant respondents, and the distribution of change-point locations. Three conventional CPA statistics, namely L_max, W_max, and S_max, were compared with their iterative-purification versions. The evaluation criteria included statistical power, Type I error rate, change-point localization accuracy, and item parameter recovery. In the empirical study, the proposed method was applied to a real questionnaire dataset to examine its practical utility in identifying potentially aberrant response patterns. The simulation results showed that, under unknown-parameter conditions, the performance of conventional CPA statistics deteriorated as the proportion of aberrant respondents increased. Specifically, statistical power decreased, Type I error rates tended to deviate from the nominal level, change-point localization became less accurate, and item parameter recovery worsened. After iterative purification was introduced, the three CPA statistics generally showed higher statistical power and more acceptable Type I error control. They also produced smaller change-point localization errors and improved item parameter recovery, as reflected by reduced bias and RMSE. These improvements were observed under both dichotomous and polytomous scoring conditions, with overall detection performance being more favorable for polytomous data. The empirical results further showed that the purified CPA statistics identified more potentially aberrant respondents than the conventional statistics. After removing respondents flagged by the CPA statistics, reliability indices of the scale increased to varying degrees, providing additional evidence for the practical value of the proposed approach in data quality control. In conclusion, incorporating iterative purification into the CPA framework is an effective strategy for detecting BRR when item parameters are unknown and response data may be contaminated. The proposed approach improves not only aberrant response detection but also change-point localization and item parameter recovery. This study extends iterative purification from traditional person-fit statistics to CPA-based methods and provides a useful tool for response quality assessment, aberrant response screening, and measurement diagnosis in psychological and educational testing.

Key words: person fit, change point analysis, iterative purification