The systematic collection of longitudinal data is very common in practice, making mixed models widely used. Most developments around these models focus on modeling the mean trajectory of repeated measurements, typically under the assumption of homoskedasticity. However, as data become increasingly rich through intensive collection over time, these models can become limiting and may introduce biases in analysis. In fact, such data are often heterogeneous, with the presence of outliers, heteroskedasticity, and asymmetry in the distribution of individual measurements. Therefore, ignoring these characteristics can lead to biased modeling results. In this work, we propose a mixed-effect distributional regression model based on the asymmetric Laplace distribution to: (1) address the presence of outliers, heteroskedasticity, and asymmetry in longitudinal measurements; (2) model the entire individual distribution of the heterogeneous longitudinal response over time, rather than just its conditional expectation; and (3) give a more comprehensive evaluation of the impact of covariates on the distribution of the responses through meaningful indicator. A Bayesian estimation procedure is presented. In order to choose between two distributional regression models, we also propose a new model selection criterion for longitudinal data. It measures the proximity between the individual distribution estimated by the model and the empirical individual distribution of the data over time, using a set of quantiles. The estimation procedure and the selection criterion are validated in a simulation study and the proposed model is compared to a distributional regression mixed model based on the Gaussian distribution and a location-scale linear quantile mixed model. Finally, the proposed model is applied to analyze blood pressure over time for hospitalized patients in the intensive care unit.

翻译：实践中系统性地收集纵向数据非常普遍，这使得混合模型得到广泛应用。围绕这些模型的大多数研究进展集中于对重复测量均值轨迹的建模，通常基于同方差性假设。然而，随着数据通过时间上的密集收集变得日益丰富，这些模型可能产生局限性，并在分析中引入偏差。实际上，此类数据常具有异质性，存在离群值、异方差性以及个体测量分布的非对称性。因此，忽略这些特征可能导致建模结果产生偏差。在本研究中，我们提出一种基于非对称拉普拉斯分布的混合效应分布回归模型，旨在：(1) 处理纵向测量中存在的离群值、异方差性与非对称性；(2) 对异质性纵向响应随时间变化的完整个体分布进行建模，而非仅对其条件期望建模；(3) 通过具有实际意义的指标，更全面地评估协变量对响应分布的影响。本文提出了贝叶斯估计流程。为在两种分布回归模型间进行选择，我们还针对纵向数据提出一种新的模型选择准则。该准则通过一组分位数，衡量模型估计的个体分布与数据随时间变化的经验个体分布之间的接近程度。估计流程与选择准则在模拟研究中得到验证，并将所提模型与基于高斯分布的分布回归混合模型以及位置-尺度线性分位数混合模型进行比较。最后，应用所提模型分析重症监护病房住院患者血压随时间的变化规律。