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Activity Number: 253
Type: Contributed
Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
Sponsor: SSC
Abstract - #310093
Title: A Valid Parametric Test of Significance for the Average R2 in Redundancy Analysis with Spatial Data
Author(s): Pierre Dutilleul*+ and Bernard Pelletier
Companies: McGill University, Macdonald Campus and McGill University, Macdonald Campus
Keywords: Auto- and cross-correlations ; coefficients of determination ; heteroscedasticity ; modified F-test
Abstract:

Let Y (nxp) and X (nxq) with n>q+1 be two tables of 2-D spatial, continuous quantitative data collected in the same n sampling locations at a given time, with the purpose of explaining the p Y-variables by the q X-variables in a redundancy analysis. Under multivariate normality and first-order stationarity, we developed a parametric test of significance for the average R2 in this context. Our modified F-test takes into account the heteroscedasticity and cross-correlations of the Ys, in addition to the spatial autocorrelation of the Y- and X-variables. We present a proof for its construction, including an approximate distribution for the test statistic. The validity of variants of the testing procedure, which differ in the modeling of the heteroscedasticity, cross-correlations and autocorrelation mentioned above for the model-based ones, is assessed in an extensive simulation study with 156 scenarios, including the type and size of the sampling grid, the number of Ys and the sign and strength of the correlations between Xs. The proposed modified F-test is shown to be generally valid. Comparison is made with the modified F-test used in multiple correlation analysis with spatial data.


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