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CCA: canonical axes and the length/ strength of the explanatory gradients
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I performed CCA on a taxa-sample matrix using 8 explanatory variables. They say that the length of the vectors that represent the explanatory variables in your triplot visualization is proportional to its impact on the taxonomic variance. However, since various of my explanatory variables have a similar length, I prefer to calculate their length using the CCA score list above visual estimation.
The problem: I calculated the root of the sum of squares of all 8 CCA scores of the explanatory variables. However, it turns out that the lengths of the explanatory variables equal the root of the sum of squares of only CCA scores of the first two (canonical) axes in the graph. As a result, I have two vectors in my graph of which the smallest is almost half of the bigger one, while in reality, when I calculate their length by taking the square root of the sum of the squares of their CCA scores (over al 8 canonical axes):
enter image description here
enter image description here
Precip -0,1315 0,074613 -0,00788 -0,40556 0,077369 0,144983 0,021653 -0,04012
Open area -0,23588 0,144588 0,18441 -0,09637 -0,01802 0,174098 -0,25398 -0,02785
0,465282326 0,151190429
0,464494416 0,276666081
Left values: length of resp. Open area and Precip over all 8 (canonical) dimensions.
Right values: length of resp. Open area and Precip over the first 2 (canonical) dimensions.
That seems strange: the lengths of the vectors actually only represents the impact of the explanatory variables over the first two (strongest) canonical axes it seems. As a result the impact given to precipitation is much smaller as when all 8 dimensions are included.
Serge Mooijman
analysis vector-analysis
asked Aug 2 at 14:54
Serge
11
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I performed CCA on a taxa-sample matrix using 8 explanatory variables. They say that the length of the vectors that represent the explanatory variables in your triplot visualization is proportional to its impact on the taxonomic variance. However, since various of my explanatory variables have a similar length, I prefer to calculate their length using the CCA score list above visual estimation.
The problem: I calculated the root of the sum of squares of all 8 CCA scores of the explanatory variables. However, it turns out that the lengths of the explanatory variables equal the root of the sum of squares of only CCA scores of the first two (canonical) axes in the graph. As a result, I have two vectors in my graph of which the smallest is almost half of the bigger one, while in reality, when I calculate their length by taking the square root of the sum of the squares of their CCA scores (over al 8 canonical axes):
enter image description here
enter image description here
Precip -0,1315 0,074613 -0,00788 -0,40556 0,077369 0,144983 0,021653 -0,04012
Open area -0,23588 0,144588 0,18441 -0,09637 -0,01802 0,174098 -0,25398 -0,02785
0,465282326 0,151190429
0,464494416 0,276666081
Left values: length of resp. Open area and Precip over all 8 (canonical) dimensions.
Right values: length of resp. Open area and Precip over the first 2 (canonical) dimensions.
That seems strange: the lengths of the vectors actually only represents the impact of the explanatory variables over the first two (strongest) canonical axes it seems. As a result the impact given to precipitation is much smaller as when all 8 dimensions are included.
Serge Mooijman
analysis vector-analysis
asked Aug 2 at 14:54
Serge
11
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 2 at 14:57
add a comment |Â
up vote
0
down vote
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up vote
0
down vote
favorite
I performed CCA on a taxa-sample matrix using 8 explanatory variables. They say that the length of the vectors that represent the explanatory variables in your triplot visualization is proportional to its impact on the taxonomic variance. However, since various of my explanatory variables have a similar length, I prefer to calculate their length using the CCA score list above visual estimation.
The problem: I calculated the root of the sum of squares of all 8 CCA scores of the explanatory variables. However, it turns out that the lengths of the explanatory variables equal the root of the sum of squares of only CCA scores of the first two (canonical) axes in the graph. As a result, I have two vectors in my graph of which the smallest is almost half of the bigger one, while in reality, when I calculate their length by taking the square root of the sum of the squares of their CCA scores (over al 8 canonical axes):
enter image description here
enter image description here
Precip -0,1315 0,074613 -0,00788 -0,40556 0,077369 0,144983 0,021653 -0,04012
Open area -0,23588 0,144588 0,18441 -0,09637 -0,01802 0,174098 -0,25398 -0,02785
0,465282326 0,151190429
0,464494416 0,276666081
Left values: length of resp. Open area and Precip over all 8 (canonical) dimensions.
Right values: length of resp. Open area and Precip over the first 2 (canonical) dimensions.
That seems strange: the lengths of the vectors actually only represents the impact of the explanatory variables over the first two (strongest) canonical axes it seems. As a result the impact given to precipitation is much smaller as when all 8 dimensions are included.
Serge Mooijman
analysis vector-analysis
asked Aug 2 at 14:54
Serge
11
I performed CCA on a taxa-sample matrix using 8 explanatory variables. They say that the length of the vectors that represent the explanatory variables in your triplot visualization is proportional to its impact on the taxonomic variance. However, since various of my explanatory variables have a similar length, I prefer to calculate their length using the CCA score list above visual estimation.
The problem: I calculated the root of the sum of squares of all 8 CCA scores of the explanatory variables. However, it turns out that the lengths of the explanatory variables equal the root of the sum of squares of only CCA scores of the first two (canonical) axes in the graph. As a result, I have two vectors in my graph of which the smallest is almost half of the bigger one, while in reality, when I calculate their length by taking the square root of the sum of the squares of their CCA scores (over al 8 canonical axes):
enter image description here
enter image description here
Precip -0,1315 0,074613 -0,00788 -0,40556 0,077369 0,144983 0,021653 -0,04012
Open area -0,23588 0,144588 0,18441 -0,09637 -0,01802 0,174098 -0,25398 -0,02785
0,465282326 0,151190429
0,464494416 0,276666081
Left values: length of resp. Open area and Precip over all 8 (canonical) dimensions.
Right values: length of resp. Open area and Precip over the first 2 (canonical) dimensions.
That seems strange: the lengths of the vectors actually only represents the impact of the explanatory variables over the first two (strongest) canonical axes it seems. As a result the impact given to precipitation is much smaller as when all 8 dimensions are included.
Serge Mooijman
analysis vector-analysis
asked Aug 2 at 14:54
Serge
11
edited Aug 2 at 14:58
asked Aug 2 at 14:54
Serge
11
asked Aug 2 at 14:54
Serge
11
asked Aug 2 at 14:54
Serge
11
11
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 2 at 14:57
add a comment |Â
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 2 at 14:57
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 2 at 14:57
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 2 at 14:57
add a comment |Â
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Aug 2 at 14:57