Robust and Interpretable Bayesian Quantile Longitudinal Analysis in Social and Behavioral Sciences

该研究项目将开发统计技术，以解决社会和行为科学应用研究人员在纵向研究中面临的鲁棒性和可解释性挑战。纵向研究帮助我们理解行为的变化。虽然纵向研究在社会和行为科学中越来越受欢迎，但它经常面临方法上的挑战。该项目将为纵向数据分析文献提供创新方法。该研究将扩大纵向分析在数据分布偏离正态分布、缺失值频繁存在、样本量小、数据稀疏和不规则等领域的应用范围。该项目有可能为具有不同特点的主题确定不同的有效干预措施，从而可能使少数群体受益。将开发免费的开放源码软件，以便技术上复杂的方法可以由实质性研究人员随时实施。该项目还将为下一代统计学家和心理学家提供培训机会。与纵向数据相关的问题包括处理非正态和/或缺失数据、小样本量、大测量误差、高维变量选择和总体异质性。本计画将借由发展贝氏分位数成长曲线模型策略来解决这些问题。该方法不对条件均值的变化建模，而是对条件分位数的变化建模，避免了一般数据的分布假设。研究人员将使用非对称拉普拉斯分布将估计分位数增长曲线模型的问题转换为获得转换模型的最大似然估计量的问题，以便可以方便地应用计算强大的贝叶斯方法，并可以灵活地处理缺失数据。将通过惩罚函数主成分分析对总体变化轨迹的自然形态施加限制。这种方法将为应用研究人员提供实用和可解释的估计增长轨迹。新方法将足够强大，使研究人员能够对收集的数据进行有效，可解释和强大的分析，而不管数据分布如何。此外，由于该方法适用于小样本，因此可以减少社会和行为科学中的重现性问题。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will develop statistical techniques that address robustness and interpretability challenges in longitudinal studies for applied researchers in the social and behavioral sciences. Longitudinal studies help us understand changes in behavior. Although longitudinal research has gained popularity in social and behavioral sciences, it often faces methodological challenges. This project will contribute innovative methods to the longitudinal data analysis literature. The research will increase the scope of applications of longitudinal analysis to areas where data distributions deviate from normality, missing values frequently exist, sample size is small, and data are sparse and irregular. The project has the potential to identify different effective interventions for subjects with different characteristics, potentially benefiting minority groups. Free open-source software will be developed so that technically sophisticated methods can be readily implemented by substantive researchers. The project also will provide training opportunities for the next generation of statisticians and psychologists.Problems associated with longitudinal data include the handling of non-normal and/or missing data, small sample sizes, large measurement errors, high-dimensional variable selection, and population heterogeneity. This project will address these problems by developing a Bayesian quantile growth curve modeling strategy. Instead of modeling the change of conditional means, the new approach will model the change of conditional quantiles, which avoids the distributional assumption of data in general. The investigators will use the Asymmetric Laplace distribution to convert the problem of estimating a quantile growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model so that computationally powerful Bayesian methods can be applied conveniently and missing data can be flexibly addressed. Constraints on the natural shape of the overall change trajectory will be imposed through penalized functional principal component analysis. This approach will yield practical and interpretable estimated growth trajectories for applied researchers. The new methodology will be powerful enough to allow researchers to conduct valid, interpretable, and robust analyses of collected data regardless of the data distribution. In addition, because the method will work well for small-sized samples, the reproducibility problem in social and behavioral sciences may be reduced.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.