Tests of geographical correlation with adjustment for explanatory variables: an application to dyspnoea in the elderly.

We propose a test of correlation of the residuals in generalized linear models which is a generalization of the spatial autocorrelation test based on Moran's I. It allows adjustment for sizes of geographical areas and for explanatory variables. A formula is given to compute the weights according to the alternative hypothesis. We compare inference using the distribution in the model and using the permutation distribution. A simulation study showed that the model-based test may be very conservative and this leads to a loss of power compared to the permutation test or to the model-based test with correction for estimated parameters. As this latter is intractable for very large samples when the model includes explanatory variables, we recommend the use of the permutation test. The permutation test is used to study geographical correlation of dyspnoea in the elderly.