Confounded Local Inference: Extending Local Moran Statistics to Handle Confounding

Local statistical analysis has long been of interest to social and environmental scientists who analyze geographic data. Research into local spatial statistics experienced a step-change in the mid-1990s, which provided a large class of local statistical methods and models. The local Moran statistic is one commonly used local indicator of spatial association, able to detect both areas of similarity and observations that are very dissimilar from their surroundings. From this, many further local statistics have been developed to characterize spatial clusters and outliers. These statistics have seen limited adoption because they do not sufficiently model the relationships involved in confounded spatial data, where the analyst seeks to understand the local spatial structure of a given outcome variable that is influenced by one or more additional factors. Recent innovations used to do joint multivariate local analysis also do not model this kind of conditional local structure in data. This article provides tools to rigorously characterize confounded local inference and a new and different class of multivariate conditional local Moran statistics that can account for confounding. To do this, we return to the Moran scatterplot as the critical tool for local Moran-style covariance statistics. Extending this concept, a new method is available directly from a “Moran-form” multiple regression. We show the empirical and theoretical properties of this statistic, show how some existing heuristic approaches arise naturally from this framework, and show how the use of conditional inference can change interpretations in an empirical analysis of rent and housing stock in a rapidly changing neighborhood.