Jointly Modeling Omitted and Not-Reached Items in Time-Limit Tests: A Survival Analysis Approach

Item response theory models are widely used and play an important role in psychological measurement and educational assessment. In its practical application, missing data is unavoidable, especially the not-reached and omitted items. For such missingness, if not handled properly, a biased parameter estimation would be derived, leading to an inaccurate estimation of examinees. To address this issue, this paper develops a joint model allowing for missing responses resulting from not-reached and omitted items. The proposed model simultaneously incorporates responses, response time, and omission time, using a survival analysis framework. Under the proposed model, the missing mechanism of not-reached items (NRIs) is interpreted by the right censoring of potential response times for examinees’ first NRIs. Furthermore, the missing mechanism of omitted items is explained by the competing relationship between response time and omission time. The simulation study confirms the consistent recovery of the proposed method. In addition, the comparison of the proposed method and alternative methods showed that only the method accounting for both missing patterns could recover model parameters well. An empirical study based on the Program for International Student Assessment 2015 Science Test was further conducted.