Canonical Correlation: Equations

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# Canonical Correlation: Equations - PowerPoint PPT Presentation

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

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
• 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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• 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