2PLM下缺失数据处理方法及其比较

Missing Data Handling Methods Based on the 2PLM

项目反应理论(IRT)是用于客观测量的现代教育与心理测量理论之一,广泛用于缺失数据十分常见的大尺度测验分析。IRT中两参数逻辑斯蒂克模型(2PLM)下仅有完全随机缺失机制下缺失反应和缺失能力处理的EM算法。本研究推导2PLM下缺失反应忽略的EM算法,并提出随机缺失机制下缺失反应和缺失能力处理的EM算法和考虑能力估计和作答反应不确定性的多重借补法。研究显示:在各种缺失机制、缺失比例和测验设计下,缺失反应忽略的EM算法和多重借补法表现理想。

Missing data are encountered regularly by researchers in educational research. For example, many large-scale assessments are low- stakes surveys, which typically suffer from a substantial amount of missing data. The low-stakes nature of these surveys, as well as variations in the average performance across countries and other factors such as testing traditions, test design, time limits, intentional omission, have been discussed as contributing factors to the amount of omitted responses observed in these assessments. Researchers have shown that missing data may create problems in the estimation of item parameters and subject ability parameters in the item response theory （IRT） context. A number of missing data handling methods have been developed in the IRT framework. The methods are not only involving the response function imputation, but also including treating the missing items as not presented （NP）, incorrect （IN） or fract!onally correct （FR）, which can be carded out directly with the item parameter estimation software BILOG-MG. There have also been a number of algorithms in the context of data imputation. The current study described several approaches to deal with missing data in the two-parameter logistic model （2PLM）. Although the software BILOG-MG can handle the missing data, it is a commercial sottware. We needed to domestically develop an EM algorithm in which the missing responses were ignored, that is, to be treated as missing completely at random （MCAR）. MCAR, which can be thought of as having no systematic cause, is only one specific type of missing data. It is noted that Zhang, Xin, Zeng, and Sun have proposed an EM algorithm （denote it as ZS） to deal with missing data under MCAR with a huge computational burden when the percent of missing data is higher. When data are missing at random （MAR）, the probability of a value being missing is dependent on item response of the individual but not on the missing value itself. The estimation of item parameters and abilities may be influenced. However, to the best of our knowledge, there has been no work addressing the missing data under the assumption for MAR in 2PLM. We proposed an EM algorithm under MAR, denoted by EE. Following a general introduction of multiple imputing methods, which was based on the item response model, two new multiple imputing methods （EF and ER） were proposed by considering uncertainties of ability parameter estimates and missing item responses, compared against two original methods （PF and PR） proposed by Huisman and Molenaar, which were only based on item responses probability. Simulation studies were provided to demonstrate the accuracy of these methods with a sample size of 1000. Various percentages of missing data were simulated： 5%, 15%, 30%, 40% and 50%. Missing data were simulated according to three different types of underlying missing data mechanism, including MCAR, MAR, and missing not at random. Missing data were imputed by NP, ZS, IN, PR, PF, ER, EF, and EE. Simulation results suggested that new multiple imputing methods and NP method worked well in various conditions; the EM algorithm under MAR had similar performance compared with the NP, because the 2PLM had the advantage of invariance of model parameters.