This article introduces a flexible modelling strategy to extend the familiar mixed-effects models for analysing longitudinal responses in the multivariate setting. By initiating a flexible multivariate multimodal distribution, this strategy relaxes the imposed normality assumption of related random-effects. We use copulas to construct a multimodal form of elliptical distributions. It can deal with the multimodality of responses and the non-linearity of dependence structure. Moreover, the proposed model can flexibly accommodate clustered subject-effects for multiple longitudinal measurements. It is much useful when several subpopulations exist but cannot be directly identifiable. Since the implied marginal distribution is not in the closed form, to approximate the associated likelihood functions, we suggest a computational methodology based on the Gauss–Hermite quadrature that consequently enables us to implement standard optimization techniques. We conduct a simulation study to highlight the main properties of the theoretical part and make a comparison with regular mixture distributions. Results confirm that the new strategy deserves to receive attention in practice. We illustrate the usefulness of our model by the analysis of a real-life dataset taken from a low back pain study.

本文介绍了一种灵活的建模策略，以扩展熟悉的混合效应模型，以分析多元设置中的纵向响应。通过启动灵活的多元多峰分布，该策略可以放宽相关随机效应的正态性假设。我们使用copulas构造椭圆分布的多峰形式。它可以处理响应的多模态和依赖结构的非线性。此外，所提出的模型可以灵活地适应用于多个纵向测量的聚类主题效果。当存在几个子群体但无法直接识别时，它非常有用。由于隐含的边际分布不是封闭形式，因此为了近似关联的似然函数，我们建议一种基于高斯-赫尔姆正交的计算方法，从而使我们能够实施标准的优化技术。我们进行了仿真研究，以突出理论部分的主要特性，并与常规混合物分布进行比较。结果证实了新策略在实践中值得引起关注。我们通过对来自腰背痛研究的真实数据集的分析来说明我们模型的有效性。