Diagnostics for mixture regression models: applications to public health

在许多公共卫生研究中，经常使用有限混合回归模型来分析来自异质人群的数据。当基本假设似乎被违反时，评估参数估计的稳定性和统计推断的有效性是很重要的，但文献中缺乏适当的诊断。本研究旨在发展有效的诊断方法，以评估混合回归模型的充分性和伴随检验统计量的敏感性。所制定的方法将使保健专业人员能够专注于实质性问题，并从相关和过度分散的结果中得出准确和有效的结论。在存在异常观测的情况下，影响诊断可以深入了解异质性的来源和明显的过度分散，同时适应由于纵向研究设计或嵌套数据结构而产生的固有相关性。该研究的意义在于其科学的新颖性和实际应用的广泛性。公共卫生将在国家和国际上受益。对于激励并与本研究相关的实证研究，健康结果的评估在预防和控制复发性尿路感染、医院战略规划以及中风后护理和康复管理方面具有重要意义。此外，对老年人身体活动干预的适当评估与预防跌倒和减少久坐老年人的肌肉骨骼疾病有关。

In many public health studies, finite mixture regression models are often used to analyse data arising from heterogeneous populations. It is important to assess the stability of parameter estimates and the validity of statistical inferences when the underlying assumptions appear to be violated, but appropriate diagnostics are lacking in the literature. This research aims to develop effective diagnostic methods for assessing the adequacy of mixture regression models and the sensitivity of accompanying test statistics. The methodology developed will enable health care professionals to focus on substantive issues and to draw accurate and valid conclusions inferred from correlated and over-dispersed outcomes. In the presence of anomalous observations, the influence diagnostics can provide insights into the source of heterogeneity and the apparent over-dispersion, while accommodating the inherent correlation due to the longitudinal study design or nested data structure. Significance of the research lies in its scientific novelty and the breadth of its practical applications. The benefits to public health will accrue both nationally and internationally. For the empirical studies that motivated and are linked to this research, evaluation of health outcomes has significant implications in the prevention and control of recurrent urinary tract infections, hospital strategic planning, and post-stroke care and rehabilitation management. Moreover, appropriate assessment of a physical activity intervention for older adults is pertinent to falls prevention and reduction of musculoskeletal disorders among sedentary seniors.