Random effects modeling of longitudinal and spatial data with and without zero-inflation.

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My proposed research is mainly focusing on random effect modeling of longitudinally, spatially and spatiotemporally correlated skewed data occurring in medical, health, ecological, environmental and biological studies. To be specific, we model data that are observed over time (time series), on many individuals over time (longitudinal), over space/location (e.g. spatial), over space and time (e.g. spatiotemporal). My research interest lies in the following three areas.******First, I would continue working on random effect modeling of the longitudinal skewed data with particular interest in zero-inflated data. In longitudinal count data, responses collected over time frequently suffer the presence of excessive zero. In the literature, two-part model (also known as delta-gamma approach) is commonly used to model longitudinal skewed data, where the presence-absence and the positive responses are modeled separately. As this type of separate modeling of breaking between zero and non-zero values presents unnatural discontinuity in density function, it destroys the serial correlation structures commonly present in the longitudinal data. To overcome this problem, I propose to incorporate distribution-free random effects into the flexible class of Tweedie generalized linear models to model various types of zero-inflated longitudinal skewed responses. ******Second, I will extend methodologies proposed in the previous research area to spatial and spatiotemporal skewed datadata. My focus will be to develop the methodology to handle the data where response observed overtime at different spatial locations which are nested within other spatial locations for skewed continuous, semi-continuous and count data. I propose to develop Tweedie mixed models considering two levels of spatial random effects, which can also accommodate various flexible spatiotemporal correlation structures. ******Third, I will focus on joint modeling of mixed types of spatiotemporal data including count, continuous and semi-continuous data where responses are jointly collected along with various covariates for number of years from ecological districts which are nested within ecological regions. Failure to take appropriate account of this joint modeling phenomenon of the data set can lead to biased estimation of the regression parameters. Joint modeling has received increasing attention in the recent years due to the fact that it may increase statistical efficiency by using all of the data simultaneously in a single model. In the literature there are few approaches available to model longitudinal and survival data jointly. To the best of our knowledge there is nothing available to model spatiotemporal data jointly including count, continuous and semi-continuous data. I propose to develop a Tweedie mixed model based computationally simpler approach to jointly model count, continuous and semi-continuous data in an integral way. **