Applications and Computational Issues Involving Generalized Linear and Mixed Models

涉及广义线性和混合模型的应用和计算问题

• 批准号: 0805865
• 负责人: James Booth
• 金额: $ 14.98万
• 依托单位: Cornell Univ - State: AWDS MADE PRIOR MAY 2010
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805865&HistoricalAwards=false
• 关键词: Applications; Computational; Issues; Involving; Generalized

The proposed research concerns theoretical and computational issues arising in the context of generalized linear and mixed effects models. A new multivariate model is suggested as a construct for analysis of covariance which provides a unified framework for adjusting treatment means in balanced and unbalanced design settings. Second, a new approximation for the number of contingency tables and tables of zeros and ones, meeting certain linear constraints, is proposed. This is relevant, for example, in determining the feasibility of exact conditional analysis of log-linear models. The approximation arises from a novel formulation of the problem in terms of a generalized linear model for geometric responses. The approximation is much more generally applicable, and appears to be far more accurate, than exiting competitors. Third, a practical fitting algorithm for a broad class of mixed effects models with analytically intractable likelihood functions is proposed. The approach involves an implementation of the Monte Carlo EM algorithm that uses a randomized spherical-radial integration rule at the E-step. Use of this integration rule reduces the required Monte Carlo sample size by two orders of magnitude in test cases.Statistical models are ubiquitous in almost all areas of modern research, including such diverse fields as agriculture, economics, medicine, and sociology. Advances in computing power enable statisticians to consider models and do calculations that were not feasible even a few years ago. This research targets three problems related to widely-used statistical models. The first concerns a technique for adjusting treatment means in designed experiments to account for observed covariates related to the response of interest. This is a classical problem with its roots in agricultural field trials. The technique has a long history dating back to the mid-20th century. It is somewhat surprising then that there is still disagreement on the correct way to make the adjustments, even in simple balanced experiments. An explanation is that the mathematical tools and computing power necessary for a complete solution were not available when the method was first developed. The second problem relates to the feasibility of exact statistical tests when data is sparse, and the standard approximations break down. Exact methods are used, for example, in medical studies testing for factors associated with various diseases. Finally, a new fitting algorithm is proposed for an important class of statistical models. Test cases suggest that the methods will significantly extend the range of models for which the computations are practically feasible.

拟议的研究涉及广义线性和混合效应模型背景下出现的理论和计算问题。建议使用一种新的多变量模型作为协方差分析的构造，该模型为在平衡和不平衡设计环境中调整治疗手段提供了统一的框架。其次，提出了满足某些线性约束的列联表以及零和一表的数量的新近似值。例如，这在确定对数线性模型的精确条件分析的可行性时是相关的。该近似值源自根据几何响应的广义线性模型对问题进行新颖的表述。与现有竞争对手相比，该近似值更普遍适用，并且似乎更准确。第三，提出了一种适用于具有分析上难以处理的似然函数的广泛混合效应模型的实用拟合算法。该方法涉及蒙特卡罗 EM 算法的实现，该算法在 E 步中使用随机球面-径向积分规则。使用这种积分规则可以将测试用例中所需的蒙特卡洛样本量减少两个数量级。统计模型在现代研究的几乎所有领域中无处不在，包括农业、经济学、医学和社会学等不同领域。计算能力的进步使统计学家能够考虑模型并进行几年前还不可行的计算。这项研究针对与广泛使用的统计模型相关的三个问题。第一个涉及在设计的实验中调整治疗手段的技术，以解释观察到的与感兴趣的反应相关的协变量。这是一个源于农业田间试验的经典问题。该技术有着悠久的历史，可以追溯到20世纪中叶。令人有些惊讶的是，即使在简单的平衡实验中，对于正确的调整方法仍然存在分歧。一种解释是，在该方法首次开发时，尚不具备完整解决方案所需的数学工具和计算能力。第二个问题涉及数据稀疏且标准近似值失效时精确统计检验的可行性。例如，在医学研究中使用精确的方法来测试与各种疾病相关的因素。最后，针对一类重要的统计模型提出了一种新的拟合算法。测试用例表明，这些方法将显着扩展计算实际上可行的模型范围。