This paper presents a mixture item response tree (IRTree) model for extreme response style. Unlike traditional applications of single IRTree models, a mixture approach provides a way of representing the mixture of respondents following different underlying response processes (between individuals), as well as the uncertainty present at the individual level (within an individual). Simulation analyses reveal the potential of the mixture approach in identifying subgroups of respondents exhibiting response behavior reflective of different underlying response processes. Application to real data from the Students Like Learning Mathematics (SLM) scale of Trends in International Mathematics and Science Study (TIMSS) 2015 demonstrates the superior comparative fit of the mixture representation, as well as the consequences of applying the mixture on the estimation of content and response style traits. We argue that methodology applied to investigate response styles should attend to the inherent uncertainty of response style influence due to the likely influence of both response styles and the content trait on the selection of extreme response categories.

中文翻译：

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极端响应风格的混合 IRTree 模型：考虑响应过程的不确定性

本文提出了一种极端反应风格的混合项目反应树（IRTree）模型。与单一 IRTree 模型的传统应用不同，混合方法提供了一种方法来表示遵循不同的基本响应过程（个人之间）的受访者的混合，以及个人层面（个人内部）存在的不确定性。模拟分析揭示了混合方法在识别表现出反映不同潜在响应过程的响应行为的响应者子组方面的潜力。2015 年国际数学和科学研究趋势 (TIMSS) 的学生喜欢学习数学 (SLM) 量表应用于真实数据证明了混合表示的优越比较拟合，以及应用混合对内容和响应风格特征的估计的后果。我们认为，用于调查响应风格的方法应注意响应风格影响的固有不确定性，这是由于响应风格和内容特征都可能影响极端响应类别的选择。