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Canonical Correlation: Equations. Psy 524 Andrew Ainsworth. Data for Canonical Correlations. CanCorr actually takes raw data and computes a correlation matrix and uses this as input data. You can actually put in the correlation matrix as data (e.g. to check someone else’s results). Data.

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canonical correlation equations

Canonical Correlation: Equations

Psy 524

Andrew Ainsworth

data for canonical correlations
Data for Canonical Correlations
  • CanCorr actually takes raw data and computes a correlation matrix and uses this as input data.
  • You can actually put in the correlation matrix as data (e.g. to check someone else’s results)
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Data
  • The input correlation set up is:
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  • To find the canonical correlations:
    • First create a canonical input matrix. To get this the following equation is applied:
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  • To get the canonical correlations, you get the eigenvalues of R and take the square root
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  • In this context the eigenvalues represent percent of overlapping variance accounted for in all of the variables by the two canonical variates
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  • Testing Canonical Correlations
    • Since there will be as many CanCorrs as there are variables in the smaller set not all will be meaningful.
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  • Wilk’s Chi Square test – tests whether a CanCorr is significantly different than zero.
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  • From the text example - For the first canonical correlation:
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  • The second CanCorr is tested as
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  • Canonical Coefficients
    • Two sets of Canonical Coefficients are required
      • One set to combine the Xs
      • One to combine the Ys
      • Similar to regression coefficients
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  • Canonical Variate Scores
    • Like factor scores (we’ll get there later)
    • What a subject would score if you could measure them directly on the canonical variate
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  • Matrices of Correlations between variables and canonical variates; also called loadings or loading matrices
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  • Redundancy
    • Within - Percent of variance explained by the canonical correlate on its own side of the equation
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  • Redundancy
    • Across - variance in Xs explained by the Ys and vice versa