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en:pca

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en:pca [2019/02/25 20:56] David Zelený |
en:pca [2019/02/27 15:08] David Zelený [Important outputs to consider] |
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==== Important outputs to consider ==== | ==== Important outputs to consider ==== | ||

- | * Eigenvalues of individual axes, which represent the amount of variance given axis represents from the total variance (total inertia). One can calculate the proportion of variance explained by given axis as the axis eigenvalue divided by the total variance. If few main axes explain most of the variance, the ordination was successful (multidimensional information was successfully reduced to few main dimensions). | + | * Eigenvalues of individual axes, which represent the amount of variance given axis represents from the total variance (total inertia). One can calculate the proportion of variance explained by given axis as the axis eigenvalue divided by the total variance. If few main axes explain most of the variance, the ordination was successful (multidimensional information was successfully reduced to few main dimensions). You can plot a barplot with each eigenvalue as a bar to see how steadily/sharply the eigenvalues of higher axes decline. |

- | * Scores of samples and sites along ordination axes (this information is then used to draw the ordination diagram). | + | * Scores of samples and sites along ordination axes (this information is then used to draw the ordination diagram). Each PCA axis is a linear combination of all descriptors. |

- | * Factor loadings, also known as component loadings – correlation of the variable (species, descriptor) with individual PCA axes. If standardized, factor loadings can be compared between variables, and help interpret which descriptors are mostly associated with which PCA axis. | + | * Factor loadings, also known as component loadings – correlation of the variable (species, or generally descriptors) with individual PCA axes. If standardized, factor loadings can be compared between variables, and help interpret which descriptors are mostly associated with which PCA axis. |

* The correlation among variables is described by angles between variables vectors, not by the distance between the apices of the vectors. This is true only if the scaling of the ordination diagram is set to 2 (correlation biplot; see the note about scaling below). | * The correlation among variables is described by angles between variables vectors, not by the distance between the apices of the vectors. This is true only if the scaling of the ordination diagram is set to 2 (correlation biplot; see the note about scaling below). | ||

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==== The circle of equilibrium contribution ==== | ==== The circle of equilibrium contribution ==== | ||

- | The circle sometimes projected onto ordination diagram to estimate the importance of individual species/descriptors/variables. The radius is calculated as √(//d/////p//), where //d// is the number of displayed PCA axes (usually //d// = 2) and //p// is the number of variables (columns in the dataset). The arrow of the same length as the circle radius contributes equally to all axes in PCA; arrows longer than circle radius make a higher contribution than average and can be interpreted with confidence (in the context of given number of ordination axes, here two, <imgref pca_circle_eq_contrib>). | + | The circle sometimes projected onto ordination diagram to estimate the importance of individual species/descriptors/variables. The radius is calculated as √(//d/////p//), where //d// is the number of displayed PCA axes (usually //d// = 2) and //p// is the number of variables (columns in the dataset). The descriptor with a vector of the same length as the circle radius contributes equally to all axes in PCA; vectors extending the circle radius make a higher contribution than average to the current display and can be interpreted with confidence (in the context of given number of ordination axes, here two, <imgref pca_circle_eq_contrib>). |

<imgcaption pca_circle_eq_contrib|Circle of equilibrium contribution projected onto PCA ordination diagram. PCA based on wetland water chemistry dataset.>{{obrazky:pca_circle_of_eq_contrib.jpg |}}</imgcaption> | <imgcaption pca_circle_eq_contrib|Circle of equilibrium contribution projected onto PCA ordination diagram. PCA based on wetland water chemistry dataset.>{{obrazky:pca_circle_of_eq_contrib.jpg |}}</imgcaption> | ||

en/pca.txt · Last modified: 2020/03/29 10:52 by David Zelený