Modeling and predicting common factors in multivariate spatial health-statistics data

Multivariate spatially referenced data are commonly seen in public health research. There are usually two kinds of correlations seen in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two kinds of correlations both are caused by a common spatially correlated underlying factor. Under this hypothesis, a common spatial factor model is developed under a normal assumption for the data, and the parameters are estimated with the maximum likelihood method. Our main goal is to determine which variables share similar structures and predict the common spatial factor underlying these variables, and provide a map which may be used to identify the spatial trends or clusters of high and low values of the common spatial factor. The model is applied to the county level disease-specific mortality rates in Minnesota to find whether there exists a common spatially-varying factor underlying the diseases throughout the state.;The common spatial factor model is then generalized to accommodate more types of data such as Poisson and Binary data and more spatial common factors. The generalized common spatial factor model is set up under the Bayesian framework, the parameters are estimated using Markov chain Monte Carlo method with appropriate constraints on the model to ensure identifiability. This model is applied to Minnesota county level cancer mortality data and binary heavy metal soil pollution data.;When predicting the common factor in frequentist method, we treat the estimated parameters as the truth and ignore the variability of the parameter estimators, thus the prediction error is usually underestimated, and the coverage probability of the prediction interval usually is lower than the nominal. This underestimation is also commonly seen in general spatial kriging. To address this issue, we propose two parametric bootstrap methods to incorporate the variability of the parameter estimators. A simulation study is performed to evaluate the coverage probability of these methods. Finally, we apply the bootstrap methods to a real data set and compare the results with those from naive (i.e., treating estimated parameters as truth) and Bayesian methods.