Application of improved Moran?s I in the evaluation of urban spatial development

Modeling spatial autocorrelation is widely done in fields like geology, population biology, and social economy. A commonly used statistics is Moran's I, where we distinguish between global and local Moran's I. The traditional form of Moran's I is applicable only if the number of observations equals unity in each spatial unit. If the number of spatial units is small, however, this traditional form does not obey the characteristics of a spatial distribution and may not show significance appropriately. This paper presents two methods to improve upon this. It adjusts the improved formulas to be suited for situations where the number of observations of each spatial unit deviates from one. As compared with the traditional form of Moran's I, the spatial distribution expressed by the improved Moran's I is shown to be more reliable. As an application, this research explores the relation of the spatial development of urban districts where we consider the transfer of urban vehicles. The observations show that those can be well analyzed as a stationary process. We conclude that the improved Moran's I improves the accuracy of the characteristics a spatial distribution.(c) 2023 Elsevier B.V. All rights reserved.