Diagnostics for appropriate model form

Studies of spatially varying parameter estimates obtained in the calibration of various types of local statistical models are commonplace. The variation in such estimates is typically explained in terms of spatially varying processes. This paper highlights that an alternative explanation for spatially varying parameter estimates, in terms of non-linearity, should be examined prior to relating such variation to spatially varying processes. This can be achieved by a simple screening procedure which is described and demonstrated and which can easily be applied to the results of any local model. The problem is highlighted, and the solution demonstrated, with a set of simulated data and then with a real-world data set. The paper also highlights the obverse situation whereby the inappropriate application of a GAM produces spurious nonlinear results when the real relationships are linear but spatially varying.