Robust Bayesian growth curve modelling using conditional medians
Robust Bayesian growth curve modelling using conditional medians
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DOI：
10.1111/bmsp.12216
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发表时间：
2020-09-14
影响因子：
2.6
通讯作者：
Zhou, Jianhui
中科院分区：
文献类型：
--
作者：
Tong, Xin;Zhang, Tonghao;Zhou, Jianhui
增长曲线模型已被广泛用于分析社会和行为科学的纵向数据。虽然具有正态假设的增长曲线模型相对容易估计，但实际数据很少是正态的。不考虑非正态数据可能导致不可靠的模型估计和误导性的统计推断。在这项工作中，我们提出了一个强大的方法，使用条件中位数的增长曲线建模，是不太敏感的离群观测。贝叶斯方法应用于模型估计和推断。在已有的基于非对称拉普拉斯分布的贝叶斯分位数回归研究的基础上，本文利用非对称拉普拉斯分布将中值增长曲线模型的估计问题转化为变换模型的极大似然估计问题。蒙特卡洛模拟研究已经进行了评估所提出的方法与数据包含离群值或杠杆观测的数值性能。结果表明，所提出的方法比传统的增长曲线模型产生更准确和有效的参数估计。我们说明了我们的强大的方法，使用条件中位数的基础上，从弗吉尼亚州认知老化项目的真实的数据集的应用。
Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non-normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project.