New Developments in Estimation, Selection and Applications for Mixed Models

混合模型估计、选择和应用的新进展

• 批准号: 0906661
• 负责人: Feifang Hu
• 金额: $ 11.65万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906661&HistoricalAwards=false
• 关键词: New; Developments; Estimation; Selection; Applications

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Correlated data are seen in diverse fields of sciences and humanities, ranging from computational biology and geology to health and social studies. However, modern correlated data frequently present additional complications such as high-dimensionality, nonlinearity and nongaussianity, for which more complex models are needed. Often times, these models require a large number of parameters, and the number of the parameters can increase with the sample size and can even be greater than the sample size. These pose significant challenges on both theoretical and computational fronts, as it is difficult to directly apply traditional likelihood techniques. This proposal aims to develop innovative statistical procedures and efficient computing algorithms for analyzing correlated data with complicated features using mixed models. The investigator focuses on three classes of mixed models: linear mixed models, nonlinear mixed models and generalized mixed models, and extends the concept of partial consistency and the nonconcave penalized least squares method to address several challenging issues in mixed model estimation and selection. In particular, the investigator 1) explores the concept of partial consistency in linear mixed models and develops a simple yet robust two-step estimation method; 2) develops penalized least squares methods to select fixed effects as well as the covariance and precision matrices of random effects; 3) formulates the nonlinear mixed model estimation and testing problems as model selection problems and develops a group selection method for nonlinear mixed models; 4) extends the proposed penalized least squares method to ultra-high dimensional variable selection; and 5) generalizes the proposed two-step estimation method and penalized least squares method to generalized linear mixed models. The research findings of this proposal will greatly broaden the applications of mixed models, especially in jointly modeling different types of data. For example, one can jointly model clinical and genomics data in a unified way where genomics data such as gene expressions are treated as random effects and explain the heterogeneity among groups while clinical data such as age, gender and blood pressure are treated as fixed effects and are of primary interest. Such a joint modeling approach allows one to account for the correlation among genes and to study genes or genetic pathways in a system way rather than traditional gene-by-gene way. Moreover, the research findings of this proposal will also shred light on analyzing high-dimensional and massive data. For example, by extending the concept of partial consistency to mixed models, one will have better understandings as how to explore the unique structure of high-dimensional data in order to extract valuable information to produce consistent, efficient and robust estimates for some parameters. In addition, the proposed methodologies will be introduced to researchers in other areas through interdisciplinary collaboration work, and will also be integrated into the investigator's educational activities by developing graduate and undergraduate curriculums and by training graduate students. Open source R and Matlab codes implementing the proposed methodologies will be made available to general public.

该奖项是根据2009年《美国复苏与再投资法》（公法111-5）资助的。 相关数据在科学和人文科学的不同领域中可以看到，从计算生物学和地质学到健康和社会研究。但是，现代相关数据经常呈现出其他并发症，例如高维，非线性和nongaussian，需要更复杂的模型。 通常，这些模型需要大量参数，并且参数的数量可以随样本量而增加，甚至可能大于样本量。 这些在理论和计算方面都构成了重大挑战，因为很难直接应用传统的可能性技术。 该建议旨在开发创新的统计程序和有效的计算算法，用于使用混合模型分析具有复杂特征的相关数据。研究者专注于三类混合模型：线性混合模型，非线性混合模型和广义混合模型，并扩展了部分一致性的概念和非concave的惩罚最小二乘方法，以解决混合模型估计和选择中的几个具有挑战性的问题。 特别是，研究者1）探讨了线性混合模型中部分一致性的概念，并开发了一种简单而强大的两步估计方法； 2）开发惩罚最小二乘方法，以选择固定效应以及随机效应的协方差和精确矩阵； 3）提出非线性混合模型估计和测试问题作为模型选择问题，并为非线性混合模型开发了组选择方法； 4）将提议的惩罚最小二乘法扩展到超高维变量选择； 5）将提出的两步估计方法概括为通用线性混合模型的最小二乘方法。该提案的研究结果将大大拓宽混合模型的应用，尤其是在共同建模不同类型的数据时。 例如，人们可以以统一的方式共同对临床和基因组学数据进行建模，其中基因组数据（例如基因表达）被视为随机效应并解释组之间的异质性，而临床数据（例如年龄，性别和血压）则被视为固定效应，并且具有主要兴趣。 这种联合建模方法使人们可以以系统方式而不是传统的基因方式来说明基因之间的相关性，并以系统的方式研究基因或遗传途径。 此外，该提案的研究结果还将阐明分析高维和大量数据。 例如，通过将部分一致性的概念扩展到混合模型，人们将对如何探索高维数据的独特结构，以便提取有价值的信息以为某些参数提供一致，高效且可靠的估计值。此外，拟议的方法将通过跨学科的合作工作向其他领域的研究人员介绍，还将通过开发研究生和本科课程和培训研究生，将其纳入研究人员的教育活动中。 实施该方法的开源R和MATLAB代码将提供给公众。