Acharyya Satwik, Pati Debdeep, Sun Shumei, Bandyopadhyay Dipankar
Department of Biostatistics, University of Michigan, Ann Arbor, MI, USA.
Department of Statistics, Texas A&M University, College Station, TX, USA.
J Appl Stat. 2023 Feb 7;51(6):1023-1040. doi: 10.1080/02664763.2023.2173156. eCollection 2024.
Beta distributions are commonly used to model proportion valued response variables, often encountered in longitudinal studies. In this article, we develop semi-parametric Beta regression models for proportion valued responses, where the aggregate covariate effect is summarized and flexibly modeled, using a interpretable monotone time-varying single index transform of a linear combination of the potential covariates. We utilize the potential of single index models, which are effective dimension reduction tools and accommodate link function misspecification in generalized linear mixed models. Our Bayesian methodology incorporates the missing-at-random feature of the proportion response and utilize Hamiltonian Monte Carlo sampling to conduct inference. We explore finite-sample frequentist properties of our estimates and assess the robustness via detailed simulation studies. Finally, we illustrate our methodology via application to a motivating longitudinal dataset on obesity research recording proportion body fat.
贝塔分布通常用于对纵向研究中经常遇到的比例值响应变量进行建模。在本文中，我们为比例值响应开发了半参数贝塔回归模型，其中使用潜在协变量线性组合的可解释单调时变单指标变换来汇总和灵活建模总体协变量效应。我们利用单指标模型的潜力，这些模型是有效的降维工具，并能适应广义线性混合模型中的链接函数误设。我们的贝叶斯方法纳入了比例响应的随机缺失特征，并利用哈密顿蒙特卡罗采样进行推断。我们探索了估计量的有限样本频率性质，并通过详细的模拟研究评估了稳健性。最后，我们通过将方法应用于一个关于肥胖研究的激励性纵向数据集（记录体脂比例）来说明我们的方法。
