Principal component analysis or PCA where can it be used for ecological data ??
Firstly one should run Kaiser-Mayer-Olkin measure of sampling along with Bartlett's Test of Sphericity to know whether PCA is applicable on a particular data set or not. Then the choice between orthogonal vs Oblique rotation methods to interpret the components. Varimax orthogonal rotation is no doubt one of the most popular widely used method. As explained by Dr. Irene, data must be collinear for PCA treatment/Varimax rotation. Otherwise alternative statistical treatments can also be used instead of PCA, like Linear Least Square Regression .
Best regards,
ABHIROOP Chowdhury
Please follow these links and pdf attachments.
https://www.researchgate.net/publication/215703214_Principal_component_analysis_development_of_a_multivariate_index_for_assessing_eutrophication_according_to_the_European_water_framework_directive_Ecol_Indic
http://link.springer.com/article/10.1007/BF00055215#page-1
http://link.springer.com/article/10.1007/BF00048872#page-1
https://www.researchgate.net/post/What_is_the_use_of_Principal_component_analysis_PCA_in_ecological_health_assessment_of_a_body_of_water_and_how_can_it_be_used
Article Principal component analysis: Development of a multivariate ...
Brief explanation taken from the "Past" software manual (link below):
"Principal components analysis (PCA) finds hypothetical variables (components) accounting for as much as possible of the variance in your multivariate data (Davis 1986, Harper 1999). These new variables are linear combinations of the original variables. PCA may be used for reduction of the data set to only two variables (the two first components), for plotting purposes. One might also hypothesize that the most important components are correlated with other underlying variables. For morphometric data, this might be size, while for ecological data it might be a physical gradient (e.g. temperature or depth). Bruton & Owen (1988) describe a typical morphometric application of PCA."
And an example in the paper linked below: we used PCA to compare the multi-elemental stoichiometric relations (concentrations of 11 elements) among species, sexes and developmental stages of xylophagous beetles (Fig. 2, Fig. 3).
http://folk.uio.no/ohammer/past/past3manual.pdf
Article How to Make a Beetle Out of Wood: Multi- Elemental Stoichiom...
Mike Palmer's ordination page is a valuable resource for understanding the different ordination type analyses, including PCA
http://ordination.okstate.edu/
also check out http://mb3is.megx.net/gustame, not only relevant for microbial data
Here is also some useful info with regards to PCA.
http://marcoplebani.com/pca/
PCA is a multivariate statistics method than effectively screen out meaningful components out of a large data set. It is a data reduction process. You may find this paper useful as here there is a detailed description of the process and how the same can be used for source apportionment of metal pollutants while evaluating its effect in a mangrove ecosystem.
https://www.researchgate.net/publication/301644037_Identification_of_metal_tolerant_plant_species_in_mangrove_ecosystem_by_using_community_study_and_multivariate_analysis_a_case_study_from_Indian_Sunderban
Article Identification of metal tolerant plant species in mangrove e...
The main principle has been explained by the answers above. Let me add some details I found useful:
- varimax rotation: it optimizes the correlation between variables and components (+/- factor loadings). You want to have either high or low (absolute) factor loadings, e.g a variable has either a strong effect on a component or a weak effect on the component.
Examine, whether you have an arch effect in your data. If your data are not scattered randomly in biplots, but form an arch, the components do have a non-linear relationships, eg. one of the assumptions of the PCA is violated.
kind regards
Irene
In the book:
Numerical ecology / Pierre Legendre and Louis Legendre
Amsterdam: Elsevier, 2003
you can find a good explanation for PCA and other multivariate techniques of ordination using ecological data.
Best regards,
Firstly one should run Kaiser-Mayer-Olkin measure of sampling along with Bartlett's Test of Sphericity to know whether PCA is applicable on a particular data set or not. Then the choice between orthogonal vs Oblique rotation methods to interpret the components. Varimax orthogonal rotation is no doubt one of the most popular widely used method. As explained by Dr. Irene, data must be collinear for PCA treatment/Varimax rotation. Otherwise alternative statistical treatments can also be used instead of PCA, like Linear Least Square Regression .
Best regards,
ABHIROOP Chowdhury
This two papers might help;PCA and dendogram(HCA) were applied on sediments collected in coastal area to deduce the human anthropogenic impact into the nearby Lagoon.
Cheers.
Hi Abesh,
pca is a multivariate technique particularly suitable for spatial data . I suggest you read my book that covers this topic .
Greetings
http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?ID=21599&Tipo=Libro&titolo=Factor+analysis+and+principal+component+analysis++
I hope this paper could help you
https://www.researchgate.net/publication/309463664_Environmental_Assessment_of_Heavy_Metal_Pollution_and_Human_Health_Risk
reagrds
Article Environmental Assessment of Heavy Metal Pollution and Human ...
My suggestion: https://www.researchgate.net/publication/319469038_New_Interpretation_of_Principal_Components_Analysis
Article New Interpretation of Principal Components Analysis
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