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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.
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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
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)
Canonical correlation matrix Rxx Rxy Ryx Ryy R=R-1yyRyxR-1xxRxy
Stage 4: Deriving the canonical functions and assessing overall fit : Eigenvalues
Stage 4: Deriving the canonical functions and assessing overall fit: Test of significance
Stage 5: Interpreting the canonical variatesCanonical loadings and Canonical cross-loadings
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)
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%
Correlation analysis Example 2
Canonical correlation Example 2
Tests for significance Example 2
Coefficients Example 2
Canonical structure Canonical loadings and canonical cross-loadings Example 2
Final result loading rc=.506 loading Canonical variate Canonical variate pv=.4030 pv=.7848 rd=.201