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en:rda_cca [2019/02/10 09:40]
David Zelený [Canonical correspondence analysis (CCA)]
en:rda_cca [2019/02/25 20:56]
David Zelený
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-====== Ordination analysis ======+Section: [[en:​ordination]]
 ===== RDA, tb-RDA, CCA & db-RDA (constrained ordination) ===== ===== RDA, tb-RDA, CCA & db-RDA (constrained ordination) =====
  
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 Unimodal constrained ordination method, related to correspondence analysis (CA), with an algorithm derived from redundancy analysis (RDA). The algorithm of RDA is modified in the way that instead of raw species composition data, the set of regressions is done on the <​m>​overline{Q}</​m>​ matrix, and the weighted multiple regression is used instead of simple multiple regression, where weights are row sums, i.e. the sums of species abundances in individual samples. The requirement for input data is the same as for correspondence analysis - the data must be non-negative integers or presences-absences. Unimodal constrained ordination method, related to correspondence analysis (CA), with an algorithm derived from redundancy analysis (RDA). The algorithm of RDA is modified in the way that instead of raw species composition data, the set of regressions is done on the <​m>​overline{Q}</​m>​ matrix, and the weighted multiple regression is used instead of simple multiple regression, where weights are row sums, i.e. the sums of species abundances in individual samples. The requirement for input data is the same as for correspondence analysis - the data must be non-negative integers or presences-absences.
  
-Note that CCA calculates **two sets of sample scores**: LC scores, and WA scores. **LC scores** are linear combinations of the columns in the environmental matrix, while **WA scores** are weighted averages of the species scores. Default plotting of ordination diagrams differ between programs; e.g. in R (library //vegan//), the samples in CCA ordination plots are using WA scores, while in CANOCO 5 they are plotted using LC scores. Use of each scoring method has its proponents and opponents. ​Some (e.g. ter Braak, one of two CANOCO 5 authors) that LC scores are more meaningful, since they are not influenced by species composition;​ others (e.g. McCune, author of PC-ORD) that WA scores are better, because they are resistant against the noise in the species composition data. FIXME The difference when plotted onto the ordination diagram is rather obvious when explanatory (environmental) variables are factors with several levels, or quantitative variables with evenly spaced values (<imgref cca-lc-wa-scores>​). Remember to report which scores you have chosen to display, whether LC or WA. +Note that CCA calculates **two sets of sample scores**: LC scores, and WA scores. **LC scores** are linear combinations of the columns in the environmental matrix, while **WA scores** are weighted averages of the species scores. Default plotting of ordination diagrams differ between programs; e.g. in R (library //vegan//), the samples in CCA ordination plots are using WA scores, while in CANOCO 5 they are plotted using LC scores. Use of each scoring method has its proponents and opponents. The difference when plotted onto the ordination diagram is rather obvious when explanatory (environmental) variables are factors with several levels, or quantitative variables with evenly spaced values (<imgref cca-lc-wa-scores>​). Remember to report which scores you have chosen to display, whether LC or WA. 
  
-<​imgcaption cca-lc-wa-scores|Difference between WA and LC scores in CCA. The upper row of figures is CCA calculated using dune data with a factor (Management with four levels) as an explanatory variable. The lower row of figures is CCA calculated using vltava data with quantitative variable (cover of tree and shrub layer, E32) as explanatory;​ the values in E32 were rounded into nearest tens (ie it contains values like 20, 30, 40, ...). Left column are WA scores, right LC scores. In the Figure (b), the sample scores are all hidden behind the centroids of the management factor. Note that species scores (red plus symbols) are not influenced by the choice of sample scores.>​{{:​obrazky:​cca-lc-wc-scores.png?​direct|}}</​imgcaption>​+<​imgcaption cca-lc-wa-scores|Difference between WA and LC scores in CCA. The upper row of figures is CCA calculated using dune data with a factor (Management with four levels) as an explanatory variable. The lower row of figures is CCA calculated using vltava data with quantitative variable (cover of tree and shrub layer, E32) as explanatory;​ the values in E32 were rounded into nearest tens (ie it contains values like 20, 30, 40, ...). Diagrams in the left column are using WA scores, ​those in the right column are using LC scores. In Figure (b), the sample scores are all hidden behind the centroids of the management factor. Note that species scores (red plus symbols) are not influenced by the choice of sample scores.>​{{:​obrazky:​cca-lc-wc-scores.png?​direct|}}</​imgcaption>​
  
  
en/rda_cca.txt · Last modified: 2019/02/25 20:56 by David Zelený