Techniques for studying correlation and covariance structure

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# Techniques for studying correlation and covariance structure - PowerPoint PPT Presentation

Techniques for studying correlation and covariance structure. Principle Components Analysis (PCA) Factor Analysis. Principle Component Analysis. Let. Assume. Let. have a p -variate Normal distribution. with mean vector. Definition:. The linear combination.

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### Techniques for studying correlation and covariance structure

Principle Components Analysis (PCA)

Factor Analysis

### Principle Component Analysis

Let

Assume

Let

have a p-variate Normal distribution

with mean vector

Definition:

The linear combination

is called the first principle component if

is chosen to maximize

subject to

Consider maximizing

subject to

Using the Lagrange multiplier technique

Let

Now

and

Summary

is the first principle component if

is the eigenvector (length 1)of S associated with the largest eigenvalue l1 of S.