Estimation of a cluster-based correlation model for familial-spatial and spatial-temporal continuous data

Abstract

The study of data collected from geographical regions is called spatial data analysis, and the study of these data over time is called spatial-temporal data analysis. Recently, the analysis of spatial and spatial-temporal data has been of interest to researchers in the fields of epidemiology, biology, forestry, agriculture, and geography. In the analysis of spatial data, locations within a user-specified distance are usually considered to constitute a cluster. Responses obtained from neighbouring locations are likely to be correlated due to the effect of latent variables at each location. Many authors have used a linear mixed effects regression model to analyze continuous/Gaussian spatial data under a variety of assumptions between and within clusters. Previous studies have focused on the single observation studies obtained from each location (Mariathas and Sutradhar (2016)). The intent of this research is to consider an extension to multivariate data collected at each location that we refer to as familial-spatial data. Thus, aside from the correlation between responses from neighbouring locations, we also consider the effect of the familial correlation between the multivariate responses collected at the same location. We then develop a familial-spatial cluster-based correlation model for the data and propose methods for estimating the model parameters. Furthermore, we extend the cluster-based correlation idea of Mariathas and Sutradhar (2016) to develop models to spatial-temporal data. Intensive simulation studies are applied to assess the performance of the models.