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

Abstract

In recent years, statistical methods have been developed that include spatial considerations, for example, those that incorporate data with georeferencing. The descriptive part of geographical information systems currently provides many visualization and analysis tools; however, in terms of analysis, these systems are still quite limited, therefore, ignorance of these limitations may result in data with spatial effects being treated with conventional statistical methods for non-spatial use, which can certainly invalidate the excellent work of data capture with advanced tools such as those that are used daily 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 easy to apply in other designs with the development of the design matrix, its reparameterization and the choice of the respective weight matrix. This may cause users to reconsider the traditional method of analysis and incorporate some appropriate analysis methodology to address spatial effects present in data or in outputs from the modeling process.