Quantile regression for longitudinal data using the asymmetric Laplace distribution
Quantile regression for longitudinal data using the asymmetric Laplace distribution
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DOI：
10.1093/biostatistics/kxj039
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发表时间：
2007-01-01
期刊：
影响因子：
2.1
通讯作者：
Bottai, Matteo
中科院分区：
文献类型：
--
作者：
Geraci, Marco;Bottai, Matteo
在纵向研究中，对同一个体的测量在不同时间重复进行。通常，主要目标是描述响应随时间的变化以及影响变化的因素。这些因素不仅会影响位置，而且会更普遍地影响响应随时间的分布形状。例如，为了对人口分布的形状进行推断，如果分布不是近似高斯分布，那么广泛流行的混合效应回归将是不够的。我们提出了一种新的线性模型的分位数回归（QR），其中包括随机效应，以占同一主题的连续观察之间的依赖性。QR的概念与响应变量的条件分布的稳健分析同义。我们提出了一个基于似然的方法来估计的回归分位数，使用非对称的拉普拉斯密度。在一个模拟研究中，所提出的方法有优势的QR估计的均方误差，当与考虑惩罚固定效应的方法相比。按照我们的策略，个体效应的接近最佳程度的收缩是由数据及其可能性自动选择的。此外，我们的模型似乎是一个强大的替代均值回归与随机效应时，响应的条件分布的位置参数是感兴趣的。我们将我们的模型应用于一个真实的数据集，该数据集由女性自我报告的分娩疼痛测量值随时间的推移反复进行，其分布的特点是偏态，并通过似然比统计来评估参数的意义。
In longitudinal studies, measurements of the same individuals are taken repeatedly through time. Often, the primary goal is to characterize the change in response over time and the factors that influence change. Factors can affect not only the location but also more generally the shape of the distribution of the response over time. To make inference about the shape of a population distribution, the widely popular mixed-effects regression, for example, would be inadequate, if the distribution is not approximately Gaussian. We propose a novel linear model for quantile regression (QR) that includes random effects in order to account for the dependence between serial observations on the same subject. The notion of QR is synonymous with robust analysis of the conditional distribution of the response variable. We present a likelihood-based approach to the estimation of the regression quantiles that uses the asymmetric Laplace density. In a simulation study, the proposed method had an advantage in terms of mean squared error of the QR estimator, when compared with the approach that considers penalized fixed effects. Following our strategy, a nearly optimal degree of shrinkage of the individual effects is automatically selected by the data and their likelihood. Also, our model appears to be a robust alternative to the mean regression with random effects when the location parameter of the conditional distribution of the response is of interest. We apply our model to a real data set which consists of self-reported amount of labor pain measurements taken on women repeatedly over time, whose distribution is characterized by skewness, and the significance of the parameters is evaluated by the likelihood ratio statistic.