Localized autocorrelation diagnostic statistic (LADS) for spatial models: Conceptualization, utilization, and computation

This paper proposes a regression diagnostic, the localized autocorrelation diagnostic statistic (LADS), that differs from traditional autocorrelation diagnostics in that: (1) it is concerned with localized occurrences of spatial autocorrelation; (2) each localized occurrence is assumed to result from a potentially distinct problem in model specification; and (3) problems are deduced post hoc from the particular geographic units implicated by the statistic. LADS ( N × N, E, C) is the probability that in a regression model with N spatial units, a contiguous block of C or more residuals among the E most extreme, same-signed residuals occurred by chance. LADS can help identify omitted independent variables, distinct regimes, and error heteroskedasticity. Two algorithms for the computation of LADS and various LADS( N, E, C)s for state-level models of the United States are provided.