Fuzzy Coding in Constrained Ordinations

• Authors: Michael Greenacre.
• Keywords: canonical correspondence analysis , crisp coding , dummy variables , fuzzy coding , redundancy analysis
• JEL codes: C19, C88
• canonical correspondence analysis
• crisp coding
• dummy variables
• fuzzy coding
• redundancy analysis

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 we 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 ordinations is unified because all explanatory variables are measured at a categorical level.