Advancing Statistical Models for Complex and Correlated Data

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In small area estimation (SAE), policy decisions regarding the allocation of resources to sub-groups of a population depend on reliable predictors of their underlying parameters. However, in some sub-groups, called small areas due to small sample sizes relative to the population, the information needed for reliable prediction is typically not available. Consequently, survey (or administrative) data on a coarser scale is used to predict the characteristics of small areas. Mixed models are mainly used to borrow information from alternative sources (e.g., previous surveys, administrative and census data sets) to provide a reliable prediction. Such predictions have many applications, e.g. in disease mapping the main objective is to find reliable rates of disease such as cancer in small areas. It also has other applications in agriculture, economics, policymaking, and allocation of funds. Over the next 5 years, I will continue to develop new and original models in the context of SAE. My plan is to work on 10 projects dealing with non--ignorable missing covariates; quantile responses; robust statistics; measurement error in covariates in longitudinal data; non-parametric responses in the class of generalized linear mixed models. In spatial statistics, I am pursuing research on the analysis of disease rates over space and time. In general, these spatio--temporal models fall under the umbrella of mixed models. The spatio--temporal models are mainly used in disease mapping to provide a reliable estimate of the underlying disease risk by borrowing strength from neighboring geographic sub-regions. The idea behind developments on spatial and spatio--temporal modeling of disease rates is essential to model variations in true rates and better separate systematic variability from random noise, a component that usually overshadows crude rate maps. Over the next 5 years, I will continue to develop new and original spatial and temporal models in my research program. My plan is to work on 9 projects dealing with maximum likelihood estimation (MLE) for complex spatio--temporal models of point- referenced datasets; robust version of the mixture of spatial or spatio--temporal models; MLE for joint modeling of two or more relevant diseases; non--ignorable missing covariates; measurement error in covariates, a robust mixture of health outcome, and multiple health outcomes in the context of the individual- or area -level infectious disease statistical models. Ignoring proper modeling of data applications (as explained above) may lead to wrong conclusions that can have clear policy implications in survey sampling and public health. These developments will also enable researchers in the statistical sciences to engage in more reliable fitting and evaluation of their hypothesized models which are important to report reliable results to the public and policy-makers for better planning to ultimately help people. I expect to train 13 HQP in the next five years.