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

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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.