Investigating the Use of the Variogram for Lattice Data

The standard tool used in the analysis of geostatistical data is the variogram. When the variogram is applied to lattice data, most commonly the data associated with each region are assumed to have been observed and arbitrarily assigned at the center or centroid of the region. Distances between centroids are then used to develop the spatial covariance structure through the variogram function directly. This arbitrariness of assigning the data to the centroid causes concern because the spatial structure estimated by the variogram depends heavily on the distances between observations. This article investigates what happens to the estimation of the variogram when each lattice value is, in fact, placed randomly within its associated region. We examine the effect that this randomly placed location has on the empirical variogram, the fitted theoretical variogram, and testing for the existence of spatial correlation. Both a regular lattice and an irregular lattice are used for demonstration. In particular, county level summaries of standardized mortality rates for lung, pancreas, and stomach cancer are investigated to see how placing data points randomly throughout the county affects the estimation of the variogram.

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