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Multivariate recap

Multivariate recap. PC1. PC 1. PC 1. PC 2. PC 1. PC 2. PC 1. PC 2. PC 1. Multivariate excercise. My apologies for computor-wrestling. Food preferences. Food preferences. Food preferences. Conclusions: Young people like Lasagne, older people like sallad.

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Multivariate recap

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  1. Multivariate recap

  2. PC1

  3. PC 1

  4. PC 1 PC 2

  5. PC 1 PC 2 PC 1

  6. PC 2 PC 1

  7. Multivariate excercise • My apologies for computor-wrestling.

  8. Food preferences

  9. Food preferences

  10. Food preferences • Conclusions: • Young people like Lasagne, older people like sallad. • Europeans are more often vegetarians (Falafel, Vegetariana, Thai Wok, Fresh sallad) • Africans like Pressbyrån. (why?) • Pizza is the same shit (except for Kebab pizza and Vegetariana). • Kebab is Kebab is Kebab. (Kebab wok?)

  11. Food preferences

  12. Food preferences • Conclusions: • Niklas, Malin and Karin are indeed vegetarians? • Nizar is NOT vegetarian, but likes kebab? • Nok likes Thai Wok (surprise?)

  13. Food preferences Scree plot Food pref 15 10 Inertia 5 0 PC1 PC3 PC5 PC7 PC9

  14. 1.0 Kebab Pizza 0.5 0.0 Vesuvio Calzone PC2 Capriciosa Hawaii Margharita -0.5 Quattro Stagione Marinara -1.0 -1.5 Vegetariana -2.0 -1.5 -1.0 -0.5 0.0 0.5 PC1

  15. Screeplot Pizza pref 10 8 6 Inertia 4 2 0 PC1 PC3 PC5 PC7 PC9

  16. Music taste

  17. Music taste

  18. Music taste

  19. Music taste • Conclusions • Africans prefer R&B. • Europeans like Heavy Metal • Britney Spears is ”black”…… and could use 50 cent for support!

  20. Music taste Screeplot Music taste 14 12 10 8 Inertia 6 4 2 0 PC1 PC3 PC5 PC7 PC9

  21. 3 Metallica IronMaiden ACDC Beyonce 2 FooFighters BritneySpears FiftyCent MichaelJackson BobMarley 1 JustinTimberlake Africa PC2 BruceSpringsteen RobbieWilliams KayneWest Esther Shayer Beatles Malin JeanCharles Peter U2 Didrik Asia Nok 0 Niklas DepecheMode Joana Madonna Europe Nizar Karin -1 -2 -3 -2 -1 0 1 2 3 PC1

  22. Music taste

  23. Music taste • Conclusions • Esther is the R&B queen? • Malin has an ”african” taste? • Peter and Didrik like Heavy Metal? • Young is a Madonna fan?

  24. A real example

  25. No. of plant species increased with increasing water exchange in the bay (p<0.01). • Note that water exchange (= Bay area / Bay opening) is on a logged scale.

  26. The biomass of animals increased with increasing No. of plant species (p < 0.01).[ left axis, triangels, middle line ] • Total number (□) and mean number (◊) of animal species increased with increasing No. of plant species (p < 0.01). [ right axis]

  27. Ordination plot (PCA). Animal biomasses are shown with thin arrows. (cf. our movies) • Mytilus edulis and Macoma baltica (both mussles) have high biomasses in the same bays! These bays are also deep.

  28. Ordination plot (PCA). Animal biomasses are shown with thin arrows. (cf. our food) • Water exchange, Salinity, Total & Mean plant species richness, and plant biomass are all high in the same bays. Northern bays are less saline. •  Common species (= high biomass) in these bays are Gammarus (”shrimp”) and Theodoxus (snail).

  29. Constrained ordination plot (RDA). Shows the flatted cloud, that exhibits most variation explained by the explanatory variables Mean no. of plant species and Water exchange. • The cloud shape changes a bit •  E.g., Leptoceridae and Anisoptera are found in bays that are similar because of their Water exchange and plant diversity characteristics.

  30. Constrained ordination plot (RDA). Shows the flatted cloud, that exhibits most variation explained by the explanatory variables Mean no. of plant species and Water exchange. • Many animal species are associated with the bays’ mean plant diversity.

  31. Ordination plot (PCA). Functional group biomasses are shown with thin arrows. (cf. our movies) • Filterers are common in bays with high Water exchange. • Scrapers are common in bays with high plant biomass (= productive bays? = much algal mats?)

  32. Constrained ordination plot (RDA). Shows the flatted cloud of functional group biomasses, that exhibits most variation explained by the explanatory variables Mean no. of plant species and Water exchange. • Scrapers and Filterers are found in bays with high Water exchange and high plant diversity.

  33. More examples of multivariate statistics • How does plant communities differ? • Which old growth forests are most similar, which are unique? • Does the morphology differ betwen european and american magpies? • Is it two different species? • But do we need multivariate staistics?

  34. Methods (for stat literacy) • ”Actual” distances in the multi-dimensional cloud: • PCA = Principal Component Analysis • RDA = Redundancy Analysis (with explanatory variables) • Deviations in the table from the null hypothesis : • CA = Correspondence Analysis • CCA = Canonical Correspondence Analysis(with explanatory variables) • The most similar ranks • NMDS = Non-Metric multi-Dimensional Scaling 

  35. More on multivariate statistics • Zuur, Ieno & Smith • Analysing Ecological Data • Oksanen, Jari • Manual for the vegan packagehttp://cc.oulu.fi/~jarioksa/opetus/metodi/vegantutor.pdf • ?rda • Multivariate courses at SLU • For PhD Studentswww.ma.slu.se/MVA

  36. Break?

  37. Nested and paired sampling • When you have sampled one thing many times. • Why? • To handle pseudoreplication. • or • To reduce noise.

  38. Simple nested anovas • Are rose hips larger on Rosa canina than on Rosa dumalis? • 10 R. canina shrubs, 10 R. dumalis shrubs • 10 rose hips on each.

  39. Simple nested anovas • Are rose hips larger on Rosa canina than on Rosa dumalis? • 10 R. canina shrubs, 10 R. dumalis shrubs • 10 rose hips on each. • Calculate means per shrub. • Specify Error term in aov() • aov(hipsize~species + Error(shrub))

  40. Simple nested anovas • Are lichens larger on larger trees? • 30 trees. • 5 lichens on each.

  41. Simple nested anovas • Are lichens larger on larger trees? • 30 trees. • 5 lichens on each. • Calculate means per tree.  Regression type • Specify Error term in aov() • aov(lichsize~treesize + Error(tree)) • You can not specify error term in lm()

  42. Not a nested anova • Are rose hips larger on larger shrubs? • 10 R. canina shrubs, 10 R. dumalis shrubs • 5 large and 5 small of each species • 1 rose hip on each shrub. • aov(hipsize~species + shrubsize)

  43. But a nested anova • Are rose hips larger in R. canina? • 10 R. canina shrubs, 10 R. dumalis shrubs • 10 fields with either R. canina or R. dumalis • 2 shrubs in each field • 1 rose hip on each shrub. • aov(hipsize~species + Error(field))

  44. Also a nested anova • Are rose hips larger in R. canina? • 10 R. canina shrubs, 10 R. dumalis shrubs • 10 fields with either R. canina or R. dumalis • 2 shrubs in each field • 10 rose hips on each shrub. • aov(hipsize~species + Error(field/shrub))

  45. Fixed factors • Random factors

  46. Simple nested anovas • Why measure many things on the same thing? • No more data points. • No higher degrees of freedom.

  47. Simple nested anovas • Why measure many things on the same thing? • No more data points. • No higher degrees of freedom. • BUT: • Higher accuracy of your data point. • MORE or BETTER data points? • Which is easiest to get?

  48. Variance Components Analysis • MORE or BETTER data points? • Which is easiest to get? • How much variation does each hierarchical level contribute? In %. Which is important to get? Relatively...

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