W11 - PCA - MULTIVARIATE

Question 1

What does PCA stand for and what is it used for

Answer 1

Principal Component Analysis
It describes the variation in multivariate data

Question 2

What are the benefits of using PCA’s

Answer 2

Allows for the descriptions of p >2 data clouds in fewer dimensions (reduces complexity)
Find biological interesting interactions between variables
Defines new variables free from multicollinearity

Question 3

In a PCA, what happens to the axis of the graph

Answer 3

They become vectors

Question 4

What is an eingenvector

Answer 4

The longest vector in space taken from a multivariate dataset
It accounts for the vector with the most variance in the dataset

Question 5

Are eigenvectors correlated to one another?

Answer 5

no

Question 6

How do we graph eigenvectors

Answer 6

Eigenvectors are unstructured data and we consider both variables as responses (plot variables on Y and X axis)
No biological reason to assume one variable causes change on the other

Question 7

Describe eigenvalue

Answer 7

Eigenvalue = length
variance in direction described by the corresponding eigenvector

Question 8

Describe eigenvector

Answer 8

Eigenvector = direction
Coefficients or loading of measured variables to describe the direction

Question 9

What are the assumptions of eigenanalysis

Answer 9

Best fitted for linear relationships between variables
Does not assume multivariate normality
Is influenced by outlier
Sensitive to sampling error

Question 10

What is a vector?

Answer 10

An axes

Question 11

What is a trace - how do we calculate it?

Answer 11

The addition of the diagonal values in a matrix
Eg. (1 0.74)
(0.74 1) Trace is 1+1 = 2
OR
(1.7 0)
(0 0.3) Trace is 1.7 + 0.3) = 2

The trace tells us the percentage variance in a single vector
Eg. 1.7 / 2 (trace) = 87% variance described

Question 12

Finish this sentence
Eigenvector =
&
First eigenvector =

Answer 12

principal component = PC
principal component 1 = major axis