Introducing multiple factor analysis (MFA) as a diagnostic taxonomic tool complementing principal component analysis (PCA)

Multiple factor analysis (MFA) is introduced as a diagnostic tool for taxonomy and discussed using examples from the herpetological literature. Its methodology and output are compared and contrasted to the more often used principal component analysis (PCA). The most significant difference between MFA and PCA is that the former can more appropriately integrate numeric (meristic and/or morphometric) and categorical characters (e.g., big-small, blue-red, striped-banded, keeled-smooth, etc.) in the analysis, thus creating a nearly total-evidence morphological output. MFA emphasizes the diagnostic utility of categorical characters in a statistically defensible landscape as opposed to their often-anecdotal treatment or complete omission in species diagnoses, usually owing to their variability. PCA is most informative when only a single numeric data type (e.g., morphometric or meristic) is analyzed. Using PCA to analyze different data types separately and comparing the results, one can determine which data type and which of their variables (traits/characters) bear most heavily on the differentiation among the operational taxonomic units (OTUs [i.e., populations or species]) and, in some cases, their biological significance. If more than one data type is used in a PCA, the output may be biased by the data type with the largest amount of variation or statistical variance. Also discussed is the necessity of using a non-parametric permutation of analysis of variance (PERMANOVA)-or a similar analysis-as a robust, statistically defensible method for assessing the significance of OTU plot positions as opposed to subjective visual interpretations.