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Canonical Correlation 典型相關

Canonical Correlation 典型相關. 基本概念. Analyze the relationships between two sets of variables Canonical correlation( r c ): Correlation between two composition of variables. R xy. IV1. DV1. IV2. DV2. r c. R xx. R yy. IV3. DV3. IV4. DV4. R yx. IV5. DV5.

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Canonical Correlation 典型相關

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  1. Canonical Correlation典型相關

  2. 基本概念 • Analyze the relationships between two sets of variables • Canonical correlation(rc): Correlation between two composition of variables Rxy IV1 DV1 IV2 DV2 rc Rxx Ryy IV3 DV3 IV4 DV4 Ryx IV5 DV5

  3. Procedures for Canonical correlation analysis • Stage 1: Objectives of canonical correlation analysis • Stage 2: Designing a canonical correlation analysis • Stage 3: Testing the assumptions • Stage 4: Deriving the canonical functions and assessing overall fit • Eigenvalues(特徵值) and eigenvectors(特徵向量) • Canonical correlation and test of significance • Stage 5: Interpreting the canonical variates • Canonical weights(典型權數) • Canonical loadings(典型負荷量) and Canonical cross-loadings(典型交叉負荷量) • Redundancy Index Analysis(重疊指數)

  4. Canonical correlation matrix Rxx Rxy Ryx Ryy R=R-1yyRyxR-1xxRxy

  5. Stage 4: Deriving the canonical functions and assessing overall fit : Eigenvalues

  6. Stage 4: Deriving the canonical functions and assessing overall fit: Test of significance

  7. Raw and standardized canonical coefficients

  8. Stage 5: Interpreting the canonical variatesCanonical loadings and Canonical cross-loadings

  9. Canonical Redundancy Analysis

  10. Redundancy Index Analysis • Redundancy (rd): • How much variance the canonical variates from the IVs extract from DVs • rd=(pv)(rc2) • For canonical correlation1 • rdY1=.48*.84=.40 • (rdX1=.58*.84=.48) • For canonical correlation2 • rdY2=.52*.58=.30 • (rdX2=.42*.58=.24)

  11. Path diagram for canonical analysis Proportion of variance extracted by X pv= (-.742+.792)/2=.58=58% by Y pv=(-.442+.882)/2=.48=48% 58%+42%=100% Proportion of variance extracted by X pv= (-.682+.622 )/2=.42=42% by Y pv= (-.902+.482 )/2=.52=52%

  12. Correlation analysis Example 2

  13. Canonical correlation Example 2

  14. Tests for significance Example 2

  15. Coefficients Example 2

  16. Canonical structure Canonical loadings and canonical cross-loadings Example 2

  17. Canonical Redundancy Analysis

  18. Final result loading rc=.506 loading Canonical variate Canonical variate pv=.4030 pv=.7848 rd=.201

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