AI 中文总结
该研究将决策树整合到带协变量的潜在类别分析框架中，解决了传统logistic模型处理协变量复杂交互时的缺陷，提出了可解释的新方法并给出实际示例，旨在推动相关应用研究发展。
AI 中文摘要
我们提出了一种将决策树拟合到潜在类别的新方法。潜在类别分析的方法论文献此前一直聚焦于给定协变量下类别归属的logistic模型，该模型在协变量存在复杂交互作用时存在重要缺陷：logistic模型易因遗漏某些交互项而设定错误，且纳入高阶交互项后解释的复杂性会迅速增加。我们提出的方法将决策树建模直接整合到潜在类别分析框架中，以易于解释的树模型来建模协变量效应，该树模型可引导使用者通过预测变量的组合得出最终的条件分类。该新方法不需要带协变量的潜在类别模型采用任何非传统假设，基于成熟的模型估计程序，且可在现有软件中轻松实现。在本文中，我们聚焦于针对二值协变量的决策树，阐述了所提出的方法，描述了两种树剪枝策略，并提供了一个实际数据示例。重要的扩展方向包括：通过开发更高级的预测变量内部分割程序，将该方法推广到多分类和连续协变量；以及开发和评估替代的树剪枝策略。本研究的最终目标是在潜在类别分析方法论文献中开启一条新的研究方向，并通过一种新的数据分析工具推动应用研究的进展。
英文摘要
We propose a novel methodology for fitting decision trees to latent classes. The latent class analysis methodological literature has previously been focusing on logistic models of class membership given covariates, which has important drawbacks in the presence of complex interactions between covariates: logistic models are easily misspecified by omitting some interaction terms and complexity of interpretation increases rapidly with inclusion of higher-order interaction terms. Our proposed approach directly integrates decision tree modeling into the latent class analysis framework to model the covariate effects as an easily interpretable tree leading the eye through combinations of predictors to a final conditional classification. The novel methodology does not require any non-traditional assumptions for latent class models with covariates, is based on well-established routines of model estimation, and can be readily implemented in existing software. In the present paper, we focus on decision trees for binary covariates. We present the proposed approach, describe two tree pruning strategies, and provide a real-data illustration. Important extensions include generalizing the approach to multinomial and continuous covariates by developing more advanced within-predictor splitting procedures, and developing and evaluating alternative tree pruning strategies. The ultimate aim of this work is to initiate a novel research line in the latent class analysis methodological literature, and to facilitate the advancement of applied research via a novel data analytical tool.
