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.

Spatio-temporal aspects of the environmental factors affecting water quality in boreal rivers

“…Spatial dependency and therefore SAC (Dormann et al 2007) is a common statistical property in geographical phenomena. SAC is positive when subjects close to each other are more similar than subjects far away (Overmars et al 2003). The presence of SAC in model residuals may increase the rates of type I error (Dormann et al 2007), which can lead to flawed results.…”

Potential Range Expansion of Japanese Honeysuckle (Lonicera japonica Thunb.) in Southern U.S. Forestlands

“…Drawing on the literature on plant invasions, we selected a set of possible variables for plots within our study area directly from the traditional FIA dataset (Table 1). In addition, we used plot Universal Transverse Mercator (UTM) coordinates, x for distance east and y for distance north of the UTM origin, to test for spatial autocorrelation effects across plots, employing Moran's I index [54]. We also used the same dataset to compute Shannon's index of tree species diversity, H s , for each plot [49,50]:…”

Determinants of species richness patterns in the Netherlands across multiple taxonomic groups

“…Positive autocorrelation in the residuals of the regression model at small distances would then suggest that certain explanatory variables are missed in the analysis (Diniz-Filho et al 2003). In order to test whether our model residuals show spatial autocorrelation we used Moran's I values (Diniz-Filho et al 2003; Overmars et al 2003). We calculated Moran's I values of the residuals of the species richness models at 7 different distance classes with a lag size of 5 km using SAM software (Rangel et al 2006).…”