ABSTRACT
This chapter considers parametric covariance structures for models typically used for areal data. Spatial dependence in these models is specified indirectly through a spatial weights matrix, which may be modeled parsimoniously using only one or a few parameters and may be row-standardized so that the weights of each site's neighbors sum to one. The covariance matrices that result from combining a spatial weights matrix with a simultaneous autoregressive (SAR), conditional autoregressive (CAR), or spatial moving average (SMA) model are derived. These models and some variants, and the relationships between them, are reviewed. Relationships between the spatial weights and marginal correlations of the observations are also explored.
