Introduction to Ordination Techniques
the relevance of different types of data and measurement-scales: (e.g. presence/absence, abundance, biomass, counts, ratio-scales, interval-scales)
the different implicit models that underly what superficially may seem to be similar kinds of display but which are to be interpreted differently (e.g. through distance angle or asymmetry)
the distinction between a two-way table and a multivariate sample (units x variables).
Against this background the following methods are briefly described - Principal Component Analysis; Duality, Q and R-mode Analysis; Principal Coordinates Analysis; Classical Scaling; Metric Scaling via Stress and Sstress; Multidimensional Unfolding; Non-metric Multidimensional Scaling; the effects of closure; Horseshoes; Multiplicative Models; Asymmetry Analysis; Canonical Analysis; Correspondence Analysis; Multiple Correspondence Analysis; Comparison of Ordinations; Orthogonal Procrustes Analysis; Generalised Procrustes Analysis; Individual Differences Scaling and other three-way methods.
The more important methods, not discussed in greater detail elsewhere in t h i s volume, are illustrated by examples and the provenance of suitable software is given.
KeywordsBiomass Migration Covariance Geochemistry Lime
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- Alvey, N. G, C. F. Banfield, R. I. Baxter, J. C. Gower, W. J. Krzanowski, P. W. Lane, P. K. Leech, J. A. Nelder, R. W. Payne, K. M. Phelps, C. E. Rogers, G. J. S. Ross, H. R. Simpson, A. D. Todd, G. Tunnicliffe- Wilson, R. W. M. Wedderburn, R. P. White, and G. N. Wilkinson. 1983. Genstat a general statistical program. Numerical Algorithms Group. Oxford.Google Scholar
- Chayes, F. 1971. Ratio correlation. A manual for s t u d e n t s of petrology and geochemistry. University Press. Chicago.Google Scholar
- Digby, P. G. N., and J. C. Gower. 1981. Ordination between- and within-groups applied to soil classification, p. 63–75. In: D. F. Merriam [ed.] Down to earth statistics: Solutions looking for geological problems. Syracuse University Geological Contributions.Google Scholar
- Digby, P. G. N., and R. Kempton. 1986. Multivariate analysis of ecological communities. Chapman and Hall. London (in the press).Google Scholar
- Gifi, A. 1981. Nonlinear multivariate analysis. Department of Data Theory, Faculty of Social Sciences, University of Leiden, Middelstegracht 14, 2312 TW Leiden, The Netherlands.Google Scholar
- Gittins, R. 1984. Canonical analysis. Springer Verlag. Berlin.Google Scholar
- Gower, J. C. 1971b. Statistical methods of comparing different multivariate analyses of the same data. p. 138–149. In: J. R. Hodson, D. G. Kendall and P. Tautu [eds] Mathematics in the archeological and historical sciences. University Press. Edinburgh.Google Scholar
- Gower, J. C. 1977. The analysis of asymmetry and orthogonality, p. 109–123. In: J. Barra et al. [eds.] Recent developments in statistics. North Holland. Amsterdam.Google Scholar
- Gower, J. C. 1980. Problems in interpreting asymmetrical chemical relationships. p. 399–409. In F. Bisby, J. C. Vaughan and C. A. Wright [eds.] Chemosystematics: principles and practice. Academic Press. New York.Google Scholar
- Gower, J. C. 1984a. Multivariate Analysis: ordination multidimensonal scaling and allied topics, p. 727–781. In E. H. Lloyd [ed.] Handbook of applicable mathematics Vol. V I: Statistics. J. Wiley and Sons. Chichester.Google Scholar
- Gower, J. C. 1984b. Multidimensional scaling displays, p. 592–601. In H. G. Law, C. W. Snyder, J. Mattie and R. P. McDonald [eds.] Research methods formulti-mode data analysis. Praeger. New York.Google Scholar
- Green, P.J. 1981. Peeling bivariate data. p. 3-19. In V. Barnett [ed.] Interpreting multivariate data. J. Wiley and Sons. Chichester.Google Scholar
- Greenacre, M. J. 1984. Theory and applications of correspondence analysis. Academic Press. London.Google Scholar
- Heiser, W., and J. de Leeuw. 1979. How to use SMACOF-1. A program for metric multidimensional scaling, p. 1-63. Department of Datatheory. Faculty of Social Sciences, University of Leiden, Middelstegracht 14, 2312 TW Leiden, The Netherlands.Google Scholar
- Kruskal, J.B., and M. Wish. 1978. Multidimensional scaling. Sage University papers on quantitative applications in the social sciences. Series No. 07 - 911, Sage Publications. Beverley Hills and London.Google Scholar
- Law, H. G., Snyder, C. W. Jr., J. A. Hattie, and R. P. McDonald. 1984. Research methods for multimode data analysis. Praeger. New York.Google Scholar
- Lebart, L., A. Morineau, and K. M. Warwick. 1984. Multivariate descriptive statistical analysis. J.Wiley & Sons. New York.Google Scholar
- de Leeuw, J. 1984. The Gifi system of non-linear multivariate analysis. In E. Diday et al. [ed.] Data analysis and informatics I V, North Holland. Amsterdam.Google Scholar
- Legendre, L., and P. Legendre. 1983. Numerical ecology. Elsevier Scientific Publishing Co. Amsterdam.Google Scholar
- Sammon, J. W. 1969. A non-linear mapping for data structure analysis, I.E.E.E. Transactions on Computers 18: 401–409.Google Scholar
- Shepard, R.N., and J. D. Carroll. 1966. Parametric representation of non-linear data structures, p. 561–592. In P. R. Krishnaiah [ed.]. Multivariate analysis. Academic Press. New York.Google Scholar
- Sibson, R. 1979. Studies in the robustness of multidimensional scaling: purturbational analysis of classical scaling. J. Roy. Statist. Soc. B 41: 217–229.Google Scholar
- Takane, Y., F. Young, and J. de Leeuw. 1977. Nonmetric individual differences scaling: an alternating least squares method with optimal scaling features. Psychometrika 42: 7–68.Google Scholar