Multivariate Lattice Models for Spatial Environmental Data

Environmental problems often include data that are not only spatial in nature, but also multidimensional with several measurements recorded at each spatial location. One example is the assessment of environmental equity. Figure 1 show maps of St. James Parish, Louisiana, with counts of whites and minorities for each of the twenty census block groups overlaid with the location of the facilities listed in the United States Environmental Protection Agency’s Toxic Release Inventory (TRI). Considering the census block groups as an irregular lattice, the population counts by race represent the multivariate measurements. The goal of the study of environmental equity is to assess the association of these population counts with the impact of the TRI facilities. A wide spectrum of approaches have been used to study environmental equity, from basic descriptive summaries (General Accounting Office, 1983, and United Church of Christ, 1987) to far more sophisticated methods (Waller, et al., 1999, and Carlin and Xia, 1999). To study population counts by race in St. James Parish, Louisiana, we propose a hierarchical statistical model as follows. Let Yi1, . . . , Yip denote the observed counts at locations i = 1, . . . , n, specifically in this case the counts of whites and minorities in each block group. The data model is