A simulation study on the hybrid nature of Tango's index

Since the early 1990s, there has been an increasing interest in statistical methods for detecting global spatial clustering in data sets. Tango's index is one of the most widely used spatial statistics for assessing whether spatially distributed disease rates are independent or clustered. Interestingly, this statistic can be partitioned into the sum of two terms: one term is similar to the usual chi-square statistic, being based on deviation patterns between the observed and expected values, and the other term, similar to Moran's I, is able to detect the proximity of similar values. In this paper, we examine this hybrid nature of Tango's index. The goal is to evaluate the possibility of distinguishing the spatial sources of clustering: lack of fit or spatial autocorrelation. To comply with the aims of the work, a simulation study is performed, by which examples of patterns driving the goodness-of-fit and spatial autocorrelation components of the statistic are provided. As for the latter aspect, it is worth noting that inducing spatial association among count data without adding lack of fit is not an easy task. In this respect, the overlapping sums method is adopted. The main findings of the simulation experiment are illustrated and a comparison with a previous research on this topic is also highlighted.