Math 5364/66 Notes Principal Components and Factor Analysis in SAS Jesse Crawford Department of Mathematics Tarleton State University.

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Presentation transcript:

Math 5364/66 Notes Principal Components and Factor Analysis in SAS Jesse Crawford Department of Mathematics Tarleton State University

Setting for Principal Components

Typical Coordinate System

Principal Components

Relation to Eigenvectors

Implementation in R

Simulating the Data in SAS

Covariance Matrix in SAS

Principal Components in SAS

Inputting a Covariance Matrix Manually

PCA Using Original Data

Example: Math and Reading Exams

Example: Adelges (Winged Aphids) 19 variables 4 principal components needed to explain 90% of the total variation PCA can be used to reduce dimensionality

PCA Summary

Setting for Factor Analysis

Observed data (Random) Intercept Term (Constant) Factor loadings (Constant) Common factors (Random) Specific factors (Random)

Setting for Factor Analysis Observed data (Random, Observable) Intercept Term (Constant) Factor loadings (Constant) Common factors (Random) Specific factors (Random) Unobservable

Communality or Common variance Uniqueness or Specific variance

Principal Component Method for Factor Analysis

Estimating Factor Scores

Rotation of Factors