An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation
An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation
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DOI：
10.1007/s11336-019-09683-4
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发表时间：
2019-12-01
期刊：
影响因子：
3
通讯作者：
Culpepper, Steven Andrew
中科院分区：
文献类型：
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作者：
Culpepper, Steven Andrew
诊断模型(DM)为研究人员和从业者提供了将受访者分类为实质性相关类别的工具。DMS被广泛应用于二元反应数据；然而，二元反应模型不适用于教育、心理和行为研究人员收集的大量有序数据。先前的研究开发了验证性有序DM，需要专家知识来指定潜在结构。本文介绍了一种探索性的有序数据挖掘方法。特别是，我们提出了一种探索性序数DM，它使用累积概率链接和贝叶斯变量选择技术来揭示潜在结构。进一步，我们讨论了具有二元属性的结构多项式混合模型的新的可辨识性条件。我们在蒙特卡罗模拟研究中提供了从中等样本到大样本的准确参数恢复的证据。我们应用该模型对来自1998-1999幼儿园班级学习方法和自我描述问卷的12个题目进行了检验，并报告了8个班级的三属性解决方案，以描述教师和家长评分的潜在结构。简而言之，所开发的方法有助于发展有序的DM，并扩大了它们的适用性，以更普遍地解决社会科学中的理论和实质性问题。
Diagnostic models (DMs) provide researchers and practitioners with tools to classify respondents into substantively relevant classes. DMs are widely applied to binary response data; however, binary response models are not applicable to the wealth of ordinal data collected by educational, psychological, and behavioral researchers. Prior research developed confirmatory ordinal DMs that require expert knowledge to specify the underlying structure. This paper introduces an exploratory DM for ordinal data. In particular, we present an exploratory ordinal DM, which uses a cumulative probit link along with Bayesian variable selection techniques to uncover the latent structure. Furthermore, we discuss new identifiability conditions for structured multinomial mixture models with binary attributes. We provide evidence of accurate parameter recovery in a Monte Carlo simulation study across moderate to large sample sizes. We apply the model to twelve items from the public-use, Early Childhood Longitudinal Study, Kindergarten Class of 1998-1999 approaches to learning and self-description questionnaire and report evidence to support a three-attribute solution with eight classes to describe the latent structure underlying the teacher and parent ratings. In short, the developed methodology contributes to the development of ordinal DMs and broadens their applicability to address theoretical and substantive issues more generally across the social sciences.