期刊
ECOLOGY
卷 94, 期 11, 页码 2381-2391出版社
WILEY
DOI: 10.1890/12-1899.1
关键词
linear regression; Moran's eigenvector maps; multivariate ordination; oribatid mite species data set; spatial analysis; spatial autocorrelation; spatial filtering; spatial structure of ecological data; statistical hypothesis testing
类别
资金
- National Sciences and Engineering Council of Canada
The linear regression model, with its numerous extensions including multivariate ordination, is fundamental to quantitative research in many disciplines. However, spatial or temporal structure in the data may invalidate the regression assumption of independent residuals. Spatial structure at any spatial scale can be modeled flexibly based on a set of uncorrelated component patterns (e.g., Moran's eigenvector maps, MEM) that is derived from the spatial relationships between sampling locations as defined in a spatial weight matrix. Spatial filtering thus addresses spatial autocorrelation in the residuals by adding such component patterns (spatial eigenvectors) as predictors to the regression model. However, space is not an ecologically meaningful predictor, and commonly used tests for selecting significant component patterns do not take into account the specific nature of these variables. This paper proposes spatial component regression (SCR) as a new way of integrating the linear regression model with Moran's eigenvector maps. In its unconditioned form, SCR decomposes the relationship between response and predictors by component patterns, whereas conditioned SCR provides an alternative method of spatial filtering, taking into account the statistical properties of component patterns in the design of statistical hypothesis tests. Application to the well-known multivariate mite data set illustrates how SCR may be used to condition for significant residual spatial structure and to identify additional predictors associated with residual spatial structure. Finally, I argue that all variance is spatially structured, hence spatial independence is best characterized by a lack of excess variance at any spatial scale, i.e., spatial white noise.
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