Geraci Marco, Bottai Matteo
Department of Epidemiology and Biostatistics, University of South Carolina, 800 Sumter Street, Columbia, SC 29208, USA.
Biostatistics. 2007 Jan;8(1):140-54. doi: 10.1093/biostatistics/kxj039. Epub 2006 Apr 24.
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.
在纵向研究中，对同一组个体随时间进行反复测量。通常，主要目标是描述随时间变化的反应特征以及影响变化的因素。这些因素不仅会影响反应分布的位置，更普遍地会影响其随时间变化的分布形状。例如，如果分布不是近似高斯分布，那么广泛使用的混合效应回归对于推断总体分布的形状就会不够充分。我们提出了一种用于分位数回归（QR）的新型线性模型，该模型包含随机效应，以考虑同一受试者连续观测值之间的相关性。QR的概念与对响应变量条件分布的稳健分析同义。我们提出了一种基于似然的方法来估计回归分位数，该方法使用非对称拉普拉斯密度。在一项模拟研究中，与考虑惩罚固定效应的方法相比，所提出的方法在QR估计器的均方误差方面具有优势。按照我们的策略，数据及其似然性会自动选择个体效应的近乎最优的收缩程度。此外，当关注响应条件分布的位置参数时，我们的模型似乎是具有随机效应的均值回归的稳健替代方法。我们将我们的模型应用于一个真实数据集，该数据集由女性随时间反复自我报告的劳动疼痛测量量组成，其分布具有偏态性，并且通过似然比统计量评估参数的显著性。
