Collaborative Research: Prediction and Model Selection for New Challenging Problems with Complex Data+

混合模型预测，即基于一类被称为混合效应模型的统计模型的预测，具有相当长的历史。传统的应用领域包括遗传学、农业、教育和调查。如今，除了传统领域之外，商业和健康科学等领域也出现了新的和具有挑战性的问题，混合模型预测方法可能适用于这些领域，但如果没有进一步的方法和计算发展，就不会出现这种问题。其中一些问题发生在兴趣是在学科水平，如个性化医疗，或（小）亚人口水平，如小社区，而不是在大人口水平。在这种情况下，通过识别新主题所属的类，可以在预测准确性方面取得实质性的进展。当在数据不完整或缺失的情况下应用现有的模型搜索策略时，在以预测为主要兴趣的模型搜索或选择中，以及在基于模型搜索或选择的结果进行统计推断时，会出现其他具有挑战性的问题。本合作研究项目旨在解决复杂数据情况下的预测和模型选择的挑战性问题，例如数据不完整或缺失，以及由于存在随机效应而导致的数据相关。在这个合作研究项目中，pi开发了一种新的统计方法，称为分类混合模型预测，以确定主题类别。这样，新主题与训练数据中对应同一类的随机效应相关联，从而可以使用混合模型预测方法进行最佳预测。此外，pi开发了一种最近提出的方法，称为E-MS算法，用于在存在不完整或缺失数据的情况下进行模型选择。pi还提出了一种称为预测模型选择的想法，方法是推导出一种缺乏拟合的预测度量，并将这种度量与最近开发的一种称为fence方法的模型选择策略相结合。最后，在模型选择后，pi开发了一种统一的Jackknife方法来准确评估混合模型分析中的不确定性。将为这些新方法建立理论，并通过广泛的蒙特卡罗模拟研究它们的性能和潜在收益。这些新方法将在R语言/环境中实现，用于统计计算和图形。将通过与专家的一系列密切合作，在若干应用中应用和检验所制定的所有方法，这些专家将提供获取数据的机会，并在解释和传播调查结果方面提供指导。应用领域包括遗传学、健康和医学、农业、教育、商业和经济。该研究项目还将促进涉及弱势群体的教学、培训和学习，并在我们的机构之间建立研究网络。

Mixed model prediction, that is, prediction based on a class of statistical models known as mixed effects models, has a fairly long history. The traditional fields of applications have included genetics, agriculture, education, and surveys. Nowadays, new and challenging problems have emerged from such fields as business and health sciences, in addition to the traditional fields, to which methods of mixed model prediction are potentially applicable, but not without further methodology and computational developments. Some of these problems occur when interest is at subject level, such as personalized medicine, or (small) sub-population level, such as small communities, rather than at large population level. In such cases, it is possible to make substantial gains in prediction accuracy by identifying a class that a new subject belongs to. Other challenging problems occur when applying existing model search strategies in situations of incomplete or missing data, in model search or selection when prediction is of primary interest, and in making statistical inference based on the result of model search or selection. This collaborative research project aims at solving these challenging problems in prediction and model selection in situations of complex data, such as incomplete or missing data, and data that are correlated due to presence of random effects.In this collaborative research project the PIs develop a novel statistical method, called classified mixed model prediction, to identify the subject class. This way, the new subject is associated with a random effect corresponding to the same class in the training data, so that the mixed model prediction method can be used to make the best prediction. Furthermore, the PIs develop a recently proposed method, called E-MS algorithm, for model selection in the presence of incomplete or missing data. The PIs also develop an idea called predictive model selection by deriving a predictive measure of lack-of-fit, and combining this measure with a recently developed class of strategies of model selection, called the fence methods. Finally, the PIs develop a unified Jackknife method to accurately assess uncertainty in mixed model analysis after model selection. Theories will be established for these new methods, and their performance and potential gains through extensive Monte-Carlo simulations will be studied. The new methods will be implemented in the R language/environment for statistical computing and graphics. All of the developed methodologies will be applied and tested in a number of applications via a series of close collaborations with experts who will provide access to the data and also guidance in interpretation and dissemination of findings. The fields of applications include genetics, health and medicine, agriculture, education, business and economy. The research project will also promote teaching, training and learning that involve under-represented groups, and build research networks between our institutions.