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en:expl_var [2019/02/26 23:20]
David Zelený [Is the value of explained variation too low?]
en:expl_var [2019/04/06 08:36] (current)
David Zelený [Adjusted R2]
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 <​imgcaption R2_adjR2|Comparison of variance explained in constrained ordination expressed by R2 and adjusted R2. The community data with one strong gradient were simulated using the library (simcom), with an increasing number of samples. The explanatory variables are randomly generated. R2 decreases with the number of samples in the dataset (left figure) and increases with the number of explanatory variables (although these are just randomly generated). Adjusted R2 is not influenced by these two dataset parameters.>​{{:​obrazky:​R2-vs-adjR2-simulcomm.png?​direct|}}</​imgcaption>​ <​imgcaption R2_adjR2|Comparison of variance explained in constrained ordination expressed by R2 and adjusted R2. The community data with one strong gradient were simulated using the library (simcom), with an increasing number of samples. The explanatory variables are randomly generated. R2 decreases with the number of samples in the dataset (left figure) and increases with the number of explanatory variables (although these are just randomly generated). Adjusted R2 is not influenced by these two dataset parameters.>​{{:​obrazky:​R2-vs-adjR2-simulcomm.png?​direct|}}</​imgcaption>​
  
-In the case of unimodal ordination methods, however, the values returned by Ezekiel’s formula are overestimated (and the dependence of variation on the number of samples and/or explanatory variables is not removed), and the R<​sup>​2</​sup>​ needs to be adjusted using the permutational method proposed by [[en:​references|Peres-Neto et al. (2006)]]. The principle of this permutation adjustment is based on using modified Ezekiel'​s formula to compare observed variation explained by the variables (R<​sup>​2</​sup>​) with expected (mean) variation the same number of variables would explain if they are random (<​m>​overline{R}^{2}_{perm}</​m>,​ <imgref perm_adjR2>​).+In the case of unimodal ordination methods, however, the values returned by Ezekiel’s formula are overestimated (and the dependence of variation on the number of samples and/or explanatory variables is not removed), and the R<​sup>​2</​sup>​ needs to be adjusted using the permutational method proposed by [[en:​references|Peres-Neto et al. (2006)]]. The principle of this permutation adjustment is based on using modified Ezekiel'​s formula to compare observed variation explained by the variables (R<​sup>​2</​sup>​) with expected (mean) variation the same number of variables would explain if they are random (<​m>​overline{R}^{2}_{perm}</​m>,​ <imgref perm_adjR2>​). Adjusted R<​sup>​2</​sup>​ calculated by the permutation method will slightly differ among calculations (these differences will be rather small if the number of permutations is set to be high).
  
 <​imgcaption perm_adjR2|>​{{:​obrazky:​adjR2_permutational_method.jpg?​direct|}}</​imgcaption>​ <​imgcaption perm_adjR2|>​{{:​obrazky:​adjR2_permutational_method.jpg?​direct|}}</​imgcaption>​
en/expl_var.txt · Last modified: 2019/04/06 08:36 by David Zelený