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Fuzzy coding in constrained ordinations

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Abstract

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.

Suggested Citation

  • Michael Greenacre, 2012. "Fuzzy coding in constrained ordinations," Economics Working Papers 1325, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1325
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    1. Michael Greenacre, 2009. "Contribution biplots," Economics Working Papers 1162, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2011.
    2. Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
    3. Greenacre Michael, 2010. "Biplots in Practice," Books, Fundacion BBVA / BBVA Foundation, number 2011113, October.
    4. Nenadic, Oleg & Greenacre, Michael, 2007. "Correspondence Analysis in R, with Two- and Three-dimensional Graphics: The ca Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i03).
    5. Zerrin Asan & Michael Greenacre, 2008. "Biplots of fuzzy coded data," Economics Working Papers 1077, Department of Economics and Business, Universitat Pompeu Fabra.
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    Cited by:

    1. Michael Greenacre, 2014. "Size and shape in the measurement of multivariate proximity," Economics Working Papers 1444, Department of Economics and Business, Universitat Pompeu Fabra.

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    More about this item

    Keywords

    canonical correspondence analysis; crisp coding; dummy variables; fuzzy coding; redundancy analysis;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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