1. MS 204
Principle Components Analysis
By Shannon Bros-Seemann

2. PCA - Purpose
Descriptive
Results from PCA used in another analysis

3. Describe habitat characteristics of sites with mosquitoes.
Example:
Describe habitat characteristics of sites with mosquitoes.

4. PCA - Purpose

5. PCA
Try to identify habitat characteristics for four species of mosquito

6. PCA
Sp. A
Sp. B
Sp. C
Sp. D

7. PCA Example Quantify Limpet Shell Shape Height Width Length
Limpet image from

8. PCA
Limpet image from

9. PCA
Determine shell shape associated with highest mortality from crab predation.

10. PCA
Survived
Eaten
Crab image from

11. How does it work?

12. Locate the axis that describes the greatest variation
Then locate the axis of variation that is at right angles to the first
Locate the axis that describes the greatest variation

13. Rotate the graph so that the axes of variation are the new axes

14. Factor 2
Factor 1

15. Factor 1
Factor 2
Factor 1
Factor 2 -2 -1 1 2 -3 3

16. There are as many factors as there are variables. WHY??

17. All of the possible factors explain all of the variance in the data.

18. Therefore, it is possible to express the relative contribution for each factor as:
Percentage of variance explained

19. In this example: Factor Percentage of variance explained 1 73.24% 2
26.76%
TOTAL
100.00%

20. The formula for determining the position on the Factor 1 axis is called the First Principle Component
Factor 1
Factor 2 -2 -1 1 2 -3 3

21. Standardized values (Z scores)
Coefficients

22. 9 8 7 6
Height (mm) 5 4 3 2 1 10 20 30
Width (mm)

24. 9 8 7 6
Height (mm) 5
1.241 4 3 2 1 10 20 30
Width (mm)

26. 9 8 7 6
Height (mm)
1.238 5
1.241 4 3 2 1 10 20 30
Width (mm)

28. How do you interpret the factors?

29. Correlate
R=0.856

30. Loading
Width

31. Correlate
R=0.856

32. Loading
Width
Height

33. Correlate Width and Height with Factor 2

34. Height Width Loading Width Height 0.30-0.49 0.50-0.69 0.70-0.89
Width
Height