Generalized linear models with zero-inflation and/or ever-dispersion with covariate measurement errors, methods for longitudinal and clustered data and finite mixture models

具有协变量测量误差的零膨胀和/或不断离散的广义线性模型、纵向和聚类数据的方法以及有限混合模型

• 批准号: 8593-2008
• 负责人: Paul, Sudhir
• 金额: $ 1.38万
• 依托单位: University of Windsor
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=497373
• 关键词: Generalized; linear; models; zero; inflation

Research will be pursued in a number of related areas in which I have been working in the last several years, such as: generalized linear models, count data, proportions and contingency tables with over/under dispersion, zero-inflated generalized linear models, correlated familial and survey data, survival models, longitudinal data analysis and finite mixture models. Research will also be pursued on inference procedures for generalized linear models, specifically for binomial and Poisson regression models with over dispersion and /or zero-inflation involving missing data, model misspecification and covariate measurement errors. Multivariate binary and Poisson (specifically bivariate Poisson) regression models will be studied. Goodness of fit tests and homogeneity testing has been and will be an important area of research. Epidemiological risk measures, such as, risk difference, risk ratio and relative risks for clustered correlated binary data will be studied and new procedures will be developed and compared. Methods for longitudinal Binary and Poisson data will be studied and new procedures involving GEEs will be developed and compared. Random effects, mixed effects models (GLMMs), and homogeneity testing will be studied in this context. Inference on the choice of variance function in semiparametric methodology, such as quasi-likelihood, extended quasi-likelihood, double extended quasi-likelihood will be studied. Inference procedures for the class of skew-normal ( a model providing specific departure from normality) distributions will be studied. Inference for common odds ratio in several 2x2 contingency tables will be studied. Inference procedures, that is, point and interval estimation and hypothesis testing procedures will be developed and evaluated. Tools, such as, maximum likelihood estimation, quasi-likelihood, extended quasi-likelihood, double extended quasi-likelihood, score tests, likelihood ratio tests and bootstrapp tests will be used and evaluated both theoretically and empirically. Rresearch results have and will have direct impact on varieties of fields of application, such as biology, Epidemiology, medical sciences and Engineering.

我将在过去几年中从事的许多相关领域进行研究，例如：广义线性模型、计数数据、比例和具有过度/不足离散度的列联表、零膨胀广义线性模型、相关家族和调查数据、生存模型、纵向数据分析和有限混合模型。还将对广义线性模型的推理程序进行研究，特别是针对具有过度分散和/或零膨胀（涉及缺失数据、模型错误指定和协变量测量误差）的二项式和泊松回归模型。将研究多元二元和泊松（特别是二元泊松）回归模型。拟合优度检验和同质性检验已经并将成为一个重要的研究领域。将研究流行病学风险度量，例如聚类相关二进制数据的风险差、风险比和相对风险，并将开发和比较新程序。将研究纵向二进制和泊松数据的方法，并将开发和比较涉及 GEE 的新程序。在此背景下将研究随机效应、混合效应模型 (GLMM) 和同质性测试。研究半参数方法中方差函数选择的推论，如拟似然、扩展拟似然、双扩展拟似然。将研究偏斜正态分布（提供特定偏离正态性的模型）类别的推理程序。将研究几个 2x2 列联表中常见比值比的推断。将开发和评估推理程序，即点估计和区间估计以及假设检验程序。将使用最大似然估计、拟似然、扩展拟似然、双扩展拟似然、得分检验、似然比检验和自举检验等工具，并在理论上和经验上进行评估。研究成果已经并将对生物学、流行病学、医学和工程学等各种应用领域产生直接影响。