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

我将在过去几年一直从事的一些相关领域进行研究，例如：广义线性模型，计数数据，比例和散度过高/过低的列联表，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。还将研究广义线性模型的推理程序，特别是具有过度分散和/或零膨胀的二项和泊松回归模型，涉及丢失数据，模型错误说明和协变量测量误差。多元二元和泊松（特别是二元泊松）回归模型将被研究。拟合优度检验和同质性检验已经并将成为重要的研究领域。将研究聚类相关二进制数据的风险差异、风险比和相对风险等流行病学风险度量，并开发和比较新的程序。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GEEs的新程序。随机效应、混合效应模型（glmm）和同质性检验将在此背景下进行研究。研究了半参数方法中拟似然、扩展拟似然、双扩展拟似然等方差函数选择的推理。我们将研究斜正态分布（偏离正态的模型）的推理过程。研究几种2x2列联表中共同优势比的推断。推理程序，即点和区间估计和假设检验程序将开发和评估。工具，如，最大似然估计，拟似然，扩展拟似然，双扩展拟似然，分数测试，似然比测试和bootstrap测试将被使用和评估理论和经验。研究成果已经并将直接影响到生物学、流行病学、医学和工程学等多个应用领域。

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.