Spatial autocorrelation in multi-scale land use models

Abstract

In several land use models statistical methods are being used to analyse spatial data. Land use drivers that best describe land use patterns quantitatively are often selected through (logistic) regression analysis. A problem using conventional statistical methods, like (logistic) regression, in spatial land use analysis is that these methods assume the data to be statistically independent. But, spatial land use data have the tendency to be dependent, a phenomenon known as spatial autocorrelation. Values over distance are more similar or less similar than expected for randomly associated pairs of observations. In this paper correlograms of the Moran’s I are used to describe spatial autocorrelation for a data set of Ecuador. Positive spatial autocorrelation was detected in both dependent and independent variables, and it is shown that the occurrence of spatial autocorrelation is highly dependent on the aggregation level. The residuals of the original regression model also show positive autocorrelation, which indicates that the standard multiple linear regression model cannot capture all spatial dependency in the land use data. To overcome this, mixed regressive–spatial autoregressive models, which incorporate both regression and spatial autocorrelation, were constructed. These models yield residuals without spatial autocorrelation and have a better goodness-of-fit. The mixed regressive–spatial autoregressive model is statistically sound in the presence of spatially dependent data, in contrast with the standard linear model which is not. By using spatial models a part of the variance is explained by neighbouring values. This is a way to incorporate spatial interactions that cannot be captured by the independent variables. These interactions are caused by unknown spatial processes such as social relations and market effects.