Missing responses generally exist in educational and psychological assessments. The statistical inference will lead to serious deviation if the missing responses are not properly modeled in the framework of non-ignorable missing mechanism. In this current study, it is studied whether the different missing mechanism (ignorable missing and non-ignorable missing) models are appropriate to analyze the missing response data from the perspective of parameter estimation and model assessment. In addition, a highly effective Bayesian sampling algorithm based on auxiliary variables is used to estimate the complex models. Compared with the traditional marginal likelihood method and other Bayesian algorithms, the advantages of the new algorithm are discussed in detail. Based on the Markov Chain Monte carlo samples from the posterior distributions, the deviance information criterion (DIC) and the logarithm of the pseudomarignal likelihood (LPML) are employed to compare the different missing mechanism models. Four simulation studies are conducted and a detailed analysis of PISA science data is carried out to further illustrate the proposed methodology.

在教育和心理评估中通常缺少答复。如果在不可忽略的缺失机制框架中未正确建模缺失响应，则统计推断将导致严重偏差。在本研究中，从参数估计和模型评估的角度研究了不同的缺失机制（可忽略缺失和不可忽略缺失）模型是否适合分析缺失响应数据。此外，基于辅助变量的高效贝叶斯采样算法用于估计复杂模型。与传统的边缘似然法和其他贝叶斯算法相比，详细讨论了新算法的优点。根据后验分布的马尔可夫链蒙特卡罗样本，偏差信息准则（DIC）和伪海洋可能性的对数（LPML）用于比较不同的缺失机制模型。进行了四次模拟研究，并对PISA科学数据进行了详细分析，以进一步说明所提出的方法。