1 / 83

Multivariate Description

Multivariate Description. What Technique?. a) Rotate the Variable Space. Raw Data. Linear Regression. Two Regressions. Principal Components. Gulls Variables. Scree Plot. Output. > summary(gulls.pca2) Importance of components:

jermaine-aguilar
Download Presentation

Multivariate Description

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multivariate Description

  2. What Technique?

  3. a) Rotate the Variable Space

  4. Raw Data

  5. Linear Regression

  6. Two Regressions

  7. Principal Components

  8. Gulls Variables

  9. Scree Plot

  10. Output > summary(gulls.pca2) Importance of components: Comp.1 Comp.2 Comp.3 Standard deviation 1.8133342 0.52544623 0.47501980 Proportion of Variance 0.8243224 0.06921464 0.05656722 Cumulative Proportion 0.8243224 0.89353703 0.95010425 > gulls.pca2$loadings Loadings: Comp.1 Comp.2 Comp.3 Comp.4Weight -0.505 -0.343 0.285 0.739Wing -0.490 0.852 -0.143 0.116Bill -0.500 -0.381 -0.742 -0.232H.and.B -0.505 -0.107 0.589 -0.622

  11. Bi-Plot

  12. Male or Female?

  13. Linear Discriminant > gulls.lda <- lda(Sex ~ Wing + Weight + H.and.B + Bill, gulls) lda(Sex ~ Wing + Weight + H.and.B + Bill, data = gulls) Prior probabilities of groups: 0 1 0.5801105 0.4198895 Group means: Wing Weight H.and.B Bill0 410.0381 871.7619 115.1143 17.625241 430.6118 1054.3092 125.9474 19.50789 Coefficients of linear discriminants: LD1Wing 0.045512619Weight 0.001887236H.and.B 0.138127194Bill 0.444847743

  14. Discriminating

  15. Relationship between PCA and LDA

  16. CVA

  17. CVA

  18. b) Use Distance or Dissimilarity(Multi-Dimensional Scaling)

  19. A Distance Matrix

  20. Uses of Distances Distance/Dissimilarity can be used to:- • Explore dimensionality in data(using PCO) • As a basis for clustering/classification

  21. UK Wet Deposition Network

  22. Fitting Environmental Variables

  23. A Map based on Measured Variables

  24. Fitting Environmental Variables

  25. c) Summarise by Weighted Averages

  26. Species and Sites as Weighted Averages of each other SITES 1 1 1111 1 2111 SPP. 23466185750198304927 Bel per 3.2....2..2..22..... Jun buf .3..........4..…42.. Jun art ...3..4..3..4..4.... Air pra ........2........3.. Ele pal ...8..4..5.....44... Rum ace ....6..5....2..…23.. Vic lat ..........12.1...... Bra rut ..246.22.4242624.342 Ran fla .2.2..2..2.....42... Hyp rad ........2..2.....5.. Leo aut 522.3.33223525222623 Pot pal .........2......2... Poa pra 424.34421.44435.…4.. Cal cus ...3...........34... Tri pra ....5..2........…2.. Tri rep 521.5.22.163322.6232 Ant odo ....3..44.4......4.2 Sal rep .............3.5.3.. Ach mil 3...21.22.4.....…2.. Poa tri 79524246..4.5.6…45.. Ely rep 4.4..4.4....6.4..... Sag pro .25...2....22....34. Pla lan ....5..52.33.3..…5.. Agr sto .587..4..4..3.454.4. Lol per 5.5.6742..67226.…6.. Alo gen 2524..5.....3.7...8. Bro hor 4.3....2..4.....…2..

  27. Species and Sites as Weighted Averages of each other

  28. Site A B C D E F SpeciesPrunus serotina 6 3 4 6 5 1 Tilia americana2 0 7 0 6 6Acer saccharum0 0 8 0 4 9 Quercus velutina0 8 0 8 0 0 Juglans nigra3 2 3 0 6 0 Reciprocal Averaging - unimodal

  29. Site A B C D E F Species ScoreSpecies Iteration 1Prunus serotina 6 3 4 6 5 1 1.00Tilia americana2 0 7 0 6 60.63Acer saccharum0 0 8 0 4 9 0.63Quercus velutina0 8 0 8 0 0 0.18Juglans nigra3 2 3 0 6 00.00 Iteration11.00 0.00 0.86 0.60 0.62 0.99SiteScore Reciprocal Averaging - unimodal

  30. Site A B C D E F Species ScoreSpecies Iteration 12Prunus serotina 6 3 4 6 5 1 1.00 0.68Tilia americana2 0 7 0 6 6 0.63 0.84Acer saccharum0 0 8 0 4 9 0.63 0.87Quercus velutina0 8 0 8 0 0 0.18 0.30Juglans nigra3 2 3 0 6 0 0.00 0.67 Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99Site20.65 0.00 0.88 0.05 0.78 1.00Score Reciprocal Averaging - unimodal

  31. Site A B C D E F Species ScoreSpecies Iteration 1 23Prunus serotina 6 3 4 6 5 1 1.00 0.68 0.50Tilia americana2 0 7 0 6 6 0.63 0.84 0.86Acer saccharum0 0 8 0 4 9 0.63 0.87 0.91Quercus velutina0 8 0 8 0 0 0.18 0.30 0.02Juglans nigra3 2 3 0 6 0 0.00 0.67 0.66 Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99Site 2 0.65 0.00 0.88 0.05 0.78 1.00Score30.60 0.01 0.87 0.00 0.78 1.00 Reciprocal Averaging - unimodal

  32. Site A B C D E F Species ScoreSpecies Iteration 1 2 3 9Prunus serotina 6 3 4 6 5 1 1.00 0.68 0.50 0.48Tilia americana2 0 7 0 6 6 0.63 0.84 0.86 0.85Acer saccharum0 0 8 0 4 9 0.63 0.87 0.91 0.91Quercus velutina0 8 0 8 0 0 0.18 0.30 0.02 0.00Juglans nigra3 2 3 0 6 0 0.00 0.67 0.66 0.65 Iteration 1 1.00 0.00 0.86 0.60 0.62 0.99Site 2 0.65 0.00 0.88 0.05 0.78 1.00Score 3 0.60 0.01 0.87 0.00 0.78 1.0090.59 0.01 0.87 0.00 0.78 1.00 Reciprocal Averaging - unimodal

  33. Site A C E B D F Species Species ScoreQuercus velutina8 8 0 0 0 0 0.004Prunus serotina6 3 6 5 4 10.477Juglans nigra0 2 3 6 3 0 0.647Tilia americana0 0 2 6 7 6 0.845Acer saccharum0 0 0 4 8 9 0.909 Site Score0.000 0.008 0.589 0.778 0.872 1.000 Reordered Sites and Species

  34. Managing Dimensionality (but not acronyms)PCA, CA, RDA, CCA, MDS, NMDS, DCA, DCCA, pRDA, pCCA

  35. Type of Data Matrix species attributes desert macroph inverts uses species sites attributes attributes watervar rain gulls individuals sites

  36. Ordination Techniques

  37. Models of Species Response There are (at least) two models:- • Linear - species increase or decrease along the environmental gradient • Unimodal - species rise to a peak somewhere along the environmental gradient and then fall again

  38. A Theoretical Model

  39. Linear

  40. Unimodal

  41. Alpha and Beta Diversity • alpha diversity is the diversity of a community (either measured in terms of a diversity index or species richness) • beta diversity (also known as ‘species turnover’ or ‘differentiation diversity’) is the rate of change in species composition from one community to another along gradients; gamma diversity is the diversity of a region or a landscape.

  42. A Short Coenocline

  43. A Long Coenocline

  44. Inferring Gradients from Species (or Attribute) Data

  45. Indirect Gradient Analysis • Environmental gradients are inferred from species data alone • Three methods: • Principal Component Analysis - linear model • Correspondence Analysis - unimodal model • Detrended CA - modified unimodal model

  46. Terschelling Dune Data

  47. PCA gradient - site plot

  48. PCA gradient - site/species biplot standard biodynamic& hobby nature

  49. Arches - Artifact or Feature?

  50. The Arch Effect • What is it? • Why does it happen? • What should we do about it?

More Related