The non-response model in Knott et al. (1991, Statistician, 40, 217) can be represented as a tree model with one branch for response/non-response and another branch for correct/incorrect response, and each branch probability is characterized by an item response theory model. In the model, it is assumed that there is only one source of non-responses. However, in questionnaires or educational tests, non-responses might come from different sources, such as test speededness, inability to answer, lack of motivation, and sensitive questions. To better accommodate such more realistic underlying mechanisms, we propose a a tree model with four end nodes, not all distinct, for non-response modelling. The Laplace-approximated maximum likelihood estimation for the proposed model is suggested. The validation of the proposed estimation procedure and the advantage of the proposed model over traditional methods are demonstrated in simulations. For illustration, the methodologies are applied to data from the 2012 Programme for International Student Assessment (PISA). The analysis shows that the proposed tree model has a better fit to PISA data than other existing models, providing a useful tool to distinguish the sources of non-responses.

中文翻译：

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用于非响应建模的具有非完全不同端节点的项目响应树模型

Knott等人的无响应模型。(1991,统计学家, 40, 217) 可以表示为一个树模型，其中一个分支用于响应/不响应，另一个分支用于正确/不正确响应，每个分支概率由项目响应理论模型表征。在模型中，假设只有一个不答复来源。然而，在问卷或教育测试中，不回答可能来自不同的来源，例如测试速度、无法回答、缺乏动力和敏感问题。为了更好地适应这种更现实的底层机制，我们提出了一个具有四个末端节点的树模型，并非都是不同的，用于无响应建模。建议模型的拉普拉斯近似最大似然估计。所提出的估计程序的验证以及所提出的模型相对于传统方法的优势在模拟中得到了证明。例如，这些方法适用于 2012 年国际学生评估计划 (PISA) 的数据。分析表明，与其他现有模型相比，所提出的树模型更适合 PISA 数据，为区分不响应的来源提供了有用的工具。