Overcoming trends in irregularly spaced locations by regional polish - exemplified by estimation of the range of influence between Salmonella Dublin-seropositive cattle herds

The aim of the study was to develop a procedure to remove spatial trends in irregularly spaced data, with trends partly due to regional differences. Median polish is often used on regularly spaced (lattice) data where column and row medians are removed. For irregularly spaced data a low-resolution map of the spatial locations is often used where data locations are assigned to the nearest lattice node followed by median polish. In this study regional polish was developed. The inverse distance weighted median was calculated based on observations from locations in the neighbourhood of the actual observation. The regional polish residual is obtained as the difference between the observed value and the weighted median. The regional polish procedure was applied to Salmonella Dublin data showing strong regional trends. Estimation of the range of influence between cattle herds with positive S. Dublin herd status was considerably improved with a stable parameter estimate and reduced standard error.