The effect of spatial lag on modeling geomatic covariates using analysis of variance

Abstract

Abstract In recent years, statistical methods involving spatial considerations have been developed, for example, those incorporating data with some type of georeferencing. The descriptive part of geographic information systems currently provides many visualization and analytic tools; however, the latter is still quite limited. In this sense, research of a spatial nature is seen as combining non-spatial statistical methods for inferential treatment that can certainly invalidate the excellent capture work with advanced tools such as those observed every day in the geomatic context. This prompted the current document, drawing attention to how geomatic information analyzed with statistical methods that imply independence in modeled observations can be invalid. The Moran index is compared with a proposal for a spatial lag coefficient in the context of experimental design so that users of variance analysis do not apply this well-known procedure in a ritualistic way, perhaps revising some assumptions and perhaps ignoring more important ones. The distortion of the p value generated from the analysis of variance is clear in the presence of spatial dependence. In this case it is associated with the lag or spatial overlap. The methodology is simple to adopt in other experimental designs with the simple consideration of the design matrix and its reparameterization and the choice of the appropriate weight matrix. This will allow users to reconsider the traditional method of analysis and incorporate some methodology to support spatial dependency structures.