Abstract
Scientists often use factor analysis to reduce the number of dimensions needed to meaningfully describe the variation of species' abundances at a set of sample locations. Their assessments of appropriateness and adequacy of a factor solution for explaining observed geographic variation are limited to subjective considerations of numerical results and maps. Spatial autocorrelation analysis of the factor solution can be used to test the sufficiency of results objectively. This approach provides one way for investigators to determine how many factors should be retained and to evaluate the performance of those factors as descriptors of the spatial pattern.
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Blackman, A. and Somayajulu, B. L. K., 1966, Pacific Pleistocene cores: Faunal analyses and geochronology: Science, v. 154, p. 886–889.
Brubaker, L. B., 1980, Spatial patterns of tree growth anomalies in the Pacific Northwest: Ecology, v. 61, p. 798–807.
Cattell, R. B., 1978, The Scientific use of factor analysis in behavioral and life sciences: Plenum Press, New York, 618 p.
Cliff, A. D. and Ord, J. K., 1973, Spatial autocorrelation: Pion Press, Ltd., London, 175 p.
Cliff, A. D. and Ord, J. K., 1981, Spatial processes: Models and applications: Pion Press, Ltd., London, 266 p.
Crain, I. K. and Bhattacharyya, B. K., 1967, Treatment of non-equispaced two-dimensional data with a digital computer: Geoexploration, v. 5, p. 173–194.
Crawford, C. B. and Koopman, P., 1973, A note on Horn's test for the number of factors in factor analysis: Mutlivar. Behav. Res., v. 8, p. 117–125.
Davis, J. C. 1973, Statistics and data analysis in geology: John Wiley & Sons, New York, 550 p.
Davis, R. E., 1976, Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean: J. Phys. Oceanog., v. 6, p. 249–266.
Davis, R. E., 1978, Predictability of sea level pressure over the North Pacific Ocean: J. Phys. Oceanog., v. 8, p. 233–246.
Fritts, H. C., Blasing, T. J., Hayden, B. P., and Kutzbach, J. E., 1971, New techniques for specifying tree-growth and climate relationships and for reconstructing anomalies in paleoclimate: J. Appl. Met., v. 10, p. 845–864.
Geary, R. C., 1954, The contiguity ratio and statistical mapping: The incorporated statistician, v. 5, p. 115–145.
Goodman, D., 1979, Applications of eigenvector analysis in the resolution of spectral pattern in spatial and temporal ecological sequences;in Patil, G. P. and Rosenzweig, M. L. (Eds.), Contemporary quantitative ecology and related econometrics: International Co-operative Publishing House, Fairland, Maryland, p. 139–155.
Harman, H. H., 1976, Modern factor analysis: The university of Chicago Press, Chicago, Illinois, 487 p.
Harshman, R. A. and Reddon, J. R., 1984, Deciding the number of factors by comparing real with random data: A serious flaw and some possible corrections: submitted to Psychometrika.
Horn, J. L., 1965, A rationale and test for the number of factors in factor analysis: Psychometrika, v. 30, p. 179–185.
Imbrie, J., van Donk, J., and Kipp, N. G., 1973, Paleoclimatic investigation of a late Pleistocene Caribbean deep-sea core: Comparison of isotopic and faunal methods: Quat. Res., v. 3, p. 10–37.
Imbrie, J. and Kipp, N. G., 1971, A new micropaleontological method for quantitative paleoclimatology: Application to a late Pleistocene Caribbean core;in Turekian, K. K. (Ed.), The late cenozoic glacial ages: Yale University Press, New Haven, p. 71–181.
Joreskog, K. G., Klovan, J. E., and Reyment, R. A., 1976, Geological factor analysis: Elsevier Press, Amsterdam, 178 p.
Jumars, P. A., Thistle, D., and Jones, M. L., 1977, Detecting two-dimensional spatial structure in biological data: Oecologia (Berl.), v. 28, p. 109–123.
Kaiser, H. F., 1960, The application of electronic computers to factor analysis: Ed. Psych. Meas., v. 20, p. 141–151.
Kipp, N. G., 1976, New transfer function for estimating past sea-surface conditions from seabed distribution of planktonic Foraminiferal assemblages in the North Atlantic;in Cline, R. M. and Hays, J. D. (Eds.), Investigation of late quaternary paleoceanography and paleoclimatology: Geol. Soc. Amer. Mem., v. 145, p. 3–41.
Lorenz, E. N., 1956, Empirical orthogonal functions and statistical weather predication: Scientific report no. 1, statistical forecasting project: Department of Meteorology, MIT, Cambridge, Massachusetts, 49 p.
Moran, P. A. P., 1950, Notes on continuous stochastic phenomena: Biometrika, v. 37, p. 17–23.
Mulaik, S. A., 1972, The foundations of factor analysis: McGraw-Hill, New York, 453 p.
Oden, N. L., 1984, Assessing the significance of a spatial correlogram: Geogr. Anal., v. 16, p. 1–16.
Overland, J. E. and Preisendorfer, R. W., 1982, A significance test for principal components applied to cyclone climatology: Mon. Weath. Rev., v. 110, p. 1–4.
Rummel, R. J., 1970, Applied factor analysis: Northwestern University Press, Evanston, Illinois, 617 p.
Sokal, R. R., 1979, Ecological parameters inferred from spatial correlograms;in Patil, G. and Rosenzweig, M. L. (Eds.), International Co-operative Publishing House, Fairland, Maryland, p. 167–196.
Sokal, R. R., Bird, J., and Riska, B., 1980, Geographic variation inPemphigus populicaulis (Insecta: Aphididae) in eastern North America: Biol. J. Linn. Soc., v. 14, p. 163–200.
Sokal, R. R. and Oden, N. L., 1978a, Spatial autocorrelation in biology, I, Methodology: Biol. J. Linn. Soc., v. 10, p. 199–228.
Sokal, R. R. and Oden, N. L., 1978b, Spatial autocorrelation in biology. 2. Some biological implications and four applications of evolutionary and ecological interest: Biol. J. Linn. Soc., v. 10, p. 229–249.
Sokal, R. R. and Riska, B., 1981, Geographic variation inPemphigus populitransversus (Insecta: Aphididae): Biol. J. Linn. Soc., v. 15, p. 201–233.
Walsh, J. E. and Richman, M. E., 1981, Seasonality in the associations between surface temperatures over the United States and the north Pacific Ocean: Mon. Weath. Rev., v. 109, p. 767–783.
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Wartenberg, D. Spatial autocorrelation as a criterion for retaining factors in ordinations of geographic data. Mathematical Geology 17, 665–682 (1985). https://doi.org/10.1007/BF01031609
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DOI: https://doi.org/10.1007/BF01031609