STAT Principal Components Analysis

00000 282843 1150000 264575 prin3 x3 sum 0 0 0

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Unformatted text preview: CORR DATA=pcstuff; VAR x1 x2 x3; WITH prin1 prin2 prin3; RUN; PROC FACTOR DATA=stuff SCREE; VAR x1 x2 x3; RUN; Note that the SAS default is to use the correlation matrix to perform this analysis! SAS output for Principal Components Analysis: The PRINCOMP Procedure Observations 4 Variables 3 Mean StD Correlation Matrix x1 Random Variable 1 1.0000 Random Variable 2 0.8333 Random Variable 3 0.3563 x1 x2 x3 x3 11.50000000 2.64575131 x2 0.8333 1.0000 0.6236 x3 0.3563 0.6236 1.0000 Eigenvalues of the Correlation Matrix Eigenvalue Difference Proportion Cumulative 2.22945702 1.56733894 0.7432 0.7432 0.66211808 0.55369318 0.2207 0.9639 0.10842490 0.0361 1.0000 1 2 3 x1 x2 x3 Simple Statistics x1 x2 3.000000000 10.00000000 1.414213562 2.82842712 Random Variable 1 Random Variable 2 Random Variable 3 Eigenvectors Prin1 0.581128 0.645363 0.495779 Prin2 -0.562643 -0.121542 0.817717 Prin3 0.587982 -0.754145 0.292477 SAS output for Correlation Matrix – Original Random Variables vs. Principal Components: The CORR Procedure 3 With Variables: 3 Variables: Variable Prin1 Prin2 Prin3 x1 x2 x3 N 4 4 4 4 4 4 Prin1 x1 Prin2 x2 Simple Statistics Mean Std Dev 0 1.49314 0 0.81371 0 0.32928 3.00000 1.41421 10.00000 2.82843 11.50000 2.64575 Prin3 x3 Sum 0 0 0 12.00000 40.00000 46.00000 Minimum -2.20299 -0.94739 -0.28331 1.00000 6.00000 9.00000 Pearson Correlation Coefficients, N = 4 Prob > |r| under H0: Rho=0 x1 x2 x3 Prin1 0.86770 0.1323 0.96362 0.0364 0.74027 0.2597 Prin2 -0.45783 0.5422 -0.09890 0.9011 0.66538 0.3346 Prin3 0.19361 0.8064 -0.24832 0.7517 0.09631 0.9037 Maximum 1.11219 0.99579 0.47104 4.00000 12.00000 15.00000 SAS output for Factor Analysis PRINCIPAL COMPONENTS ANALYSIS FOR QA 610 SPRING QUARTER 2001 Using PROC FACTOR to obtain a Scree Plot for Principal Components Analysis The FACTOR Procedure Initial Factor Method: Principal Components Prior Communality Estimates: ONE Eigenvalues of the Correlation Matrix: Total = 3 Average = 1 Eigenvalue 1 2 3 Difference Proportion Cumulative 2.22945702 0.66211808 0.10842490 1.56733894 0.55369318 0.7432 0.2207 0.0361 0.7432 0.9639 1.0000 1 factor will be retained by the MINEIGEN criterion. Note that this is consistent with the results from PCA SAS output for Factor Analysis The FACTOR Procedure Initial Factor Method: Principal Components Scree Plot of Eigenvalues ‚ ‚ ‚ ‚ ‚ ‚ 2.5 ˆ ‚ ‚ ‚ 1 ‚ ‚ 2.0 ˆ ‚ ‚ E ‚ i ‚ g ‚ e 1.5 ˆ n ‚ v ‚ a ‚ l ‚ u ‚ e 1.0 ˆ s ‚ ‚ ‚ ‚ 2 ‚ 0.5 ˆ ‚ ‚ ‚ ‚ ‚ 3 0.0 ˆ ‚ ‚ ‚ ‚ ‚ Šƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒ 0 1 2 3 Number SAS output for Factor Analysis The FACTOR Procedure Initial Factor Method: Principal Components Factor Pattern Factor1 x1 x2 x3 Random Variable 1 Random Variable 2 Random Variable 3 0.86770 0.96362 0.74027 Variance Explained by Each Factor Factor1 Pearson Correlation Coefficients for the first principal com...
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