An investigation of three-matrix permutation tests |
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Authors: | Neal L Oden Robert R Sokal |
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Institution: | (1) Department of Preventive Medicine, Division of Epidemiology, Health Sciences Center, State Univeresity of New York, 11794-8036 Stony Brook, New York, USA;(2) Department of Ecology and Evolution, State University of New York, 11794-5245 Stony Brook, New York, USA |
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Abstract: | Several methods have recently been introduced for investigating relations between three interpoint proximity matricesA, B, C, each of which furnishes a different type of distance between the same objects. Smouse, Long, and Sokal (1986) investigate
the partial correlation betweenA andB conditional onC. Dow and Cheverud (1985) ask whethercorr (A, C), equalscorr (B, C). Manly (1986) investigates regression-like models for predicting one matrix as a function of others.
We have investigated rejection rates of these methods when their null hypotheses are true, but data are spatially autocorrelated
(SA). That is,A, andB are distance matrices from independent realizations of the same SA generating process, andC is a matrix of geographic connections.
SA causes all the models to be liberal because the hypothesis of equally likely row/column permutations invoked, by all these
methods, is untrue when data are SA. Consequently, we cannot unreservedly recommend the use of any of these methods with SA
data. However, if SA is weak, the Smouse-Long-Sokal method, used with a conservative critical value, is unlikely to reject
falsely. |
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Keywords: | Spatial autocorrelation Quadratic assignment Partial correlations Permutation tests Proximity matrices |
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