A test for robust detection of residual spatial autocorrelation with application to mortality rates in Sweden

Background: When analyzing data collected with a geographical dimension it is important to be able to test for spatial autocorrelation. The presence of spatial autocorrelation might unveil ignored explanatory variables or just be a factor necessary to consider when further analyzing the data.Objectives: The aim of this paper is to propose a new test that works well for detecting spatial autocorrelation, which is robust against heteroscedasticity and useful regardless of the underlying distribution. The new test is then used to investigate if the mortality rates in the aging Swedish population show spatial autocorrelation as an example of its use.Methods: We derive such a test assuming the mean function for the model is known and perform simulations for this case and for residuals to investigate its finite sample performance, especially how the nominal rejection size is kept.Results: In the simulations we show that our test works well if there is no heteroscedasticity and also under difficult situations such as heteroscedasticity with structure, given that sufficient number of observations are available. This study finds no autocorrelation of mortality rates in Swedish municipalities in the age group 64–75 in year 2006.