STAT242: Principal Component Analysis

Outliers in PCA?

- No significant outliers - these produce a disproportionate influence on the results - Outliers are component scores more than 3 standard deviations away from the mean

Bartletts test of sphericity

- P value smaller than 0.05 = multivariate normality

What are eigenvalues in PCA

- They are the variance of that principal component

How many principal components can you have?

- Can have as many principal components as the number of original variables

Principal component with reversed sign...?

- Component still measuring the same aspect of the data but in the opposite direction

If the original variables are highly variable should you use a correlation or covariance matrix?

- Covariance matrix used - Leads to a more sensible analysis

What kind of variables are used in PCA?

- Mostly continuous but also ordinal variables can be used

What is the aim of principal component analysis?

-Data reduction technique -Produces a small number of derived variables to be used in place of larger number of original variables -They are linear combinations of the original variables and are UNCORRELATED (measure different dimensions in the data)

Sampling Adequacy needed

-Generally 5/10 cases per variable

Can you complete a principal component analysis if the original variables are uncorrelated?

-No. Nothing is achieved by PCA if the original variables are not correlated

What is the sum of the eigenvalues in PCA equal to ?

-Sum of principal component variances are equal to the sum of the variances of the original variables

Scree plot

-Tells how many principal components to use

KMO statistic what does it tell you?

-Tests for sampling adequacy -Must be bigger than 0.5 for overall -For individual, 0.9 is excellent, 0.8, good, 0.5 poor. Variable with lowest MSA removed, analysis repeated