1 / 18

Understanding Canonical Correlation Analysis: Concepts, Methodology, and Interpretation

Learn the basics of canonical correlation analysis, including relationships between variables, stages of analysis, eigenvalues and eigenvectors, redundancy index, and interpretation of canonical variates. Discover how to assess the overall fit and significance tests.

candrews
Télécharger la présentation

Understanding Canonical Correlation Analysis: Concepts, Methodology, and Interpretation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related