The importance of regional models in assessing canine cancer incidences in Switzerland.

Fitting canine cancer incidences through a conventional regression model assumes constant statistical relationships across the study area in estimating the model coefficients. However, it is often more realistic to consider that these relationships may vary over space. Such a condition, known as spatial non-stationarity, implies that the model coefficients need to be estimated locally. In these kinds of local models, the geographic scale, or spatial extent, employed for coefficient estimation may also have a pervasive influence. This is because important variations in the local model coefficients across geographic scales may impact the understanding of local relationships. In this study, we fitted canine cancer incidences across Swiss municipal units through multiple regional models. We computed diagnostic summaries across the different regional models, and contrasted them with the diagnostics of the conventional regression model, using value-by-alpha maps and scalograms. The results of this comparative assessment enabled us to identify variations in the goodness-of-fit and coefficient estimates. We detected spatially non-stationary relationships, in particular, for the variables related to biological risk factors. These variations in the model coefficients were more important at small geographic scales, making a case for the need to model canine cancer incidences locally in contrast to more conventional global approaches. However, we contend that prior to undertaking local modeling efforts, a deeper understanding of the effects of geographic scale is needed to better characterize and identify local model relationships.