Analyzing the mean response of study subjects in psychological research is a standard, well-justified practice. However, theoretical arguments and empirical evidence also suggest that there is value in investigating other aspects of the distribution of such responses, such as their variability or skewness. A particular challenge that practitioners face is statistical modeling of associations between distributional features and other outcomes of interest. The most common approach is to perform estimation in two steps: distributional features are estimated first, and then those estimates are used as predictors for the relevant outcomes. Such an approach is most amenable to implementation in standard statistical software, but it ignores estimation error and can therefore lead to biased estimates and increased error rates. We introduce Distributional Feature Latent Variable Models (DFLVM), a general framework that represents between-person difference in distributional features as random intercepts. These intercepts can be simultaneously used as predictors for downstream outcomes and their associations estimated in a single estimation step. We compare the performance of our approach against two-step procedures in a simulation study and through a re-analysis of a real dataset.

翻译：分析心理研究中被试的均值响应是一种标准且合理的做法。然而，理论论证与实证证据均表明，探索响应分布的其他特征（如变异性或偏度）同样具有价值。研究者面临的一个特殊挑战是如何对分布特征与其他感兴趣结果之间的关联进行统计建模。最常见的方法是分两步进行估计：先估计分布特征，再将估计值用作相关结果的预测变量。这种方法最易于在标准统计软件中实现，但会忽略估计误差，从而可能导致有偏估计和错误率上升。我们提出分布特征潜变量模型（DFLVM）这一通用框架，将个体间在分布特征上的差异表示为随机截距。这些截距可同时用作下游结果的预测变量，并在单一估计步骤中估计其关联性。通过模拟研究与真实数据集的重分析，我们比较了该方法与两步骤程序的表现。