Canonical Correlation: Getting Started with R or SPSS

Canonical correlation is a method of modelling the relationship between two sets of variables. This post provides: (a) Examples of when canonical correlation can be useful; (b) Links to good online resources where you can learn about the technique; (c) Links to examples of running the analysis in R or SPSS; and (d) Examples of articles showing how to report a canonical correlation analysis.

General Thoughts

You might want to consider a canonical correlation analysis in situations where you have:

• a set of predictors of task/job performance (e.g., ability, personality, demographics) and a set of performance measures (e.g., speed, accuracy, etc.)
• two tests each with multiple scales that are meant to measure similar things (e.g., two measures of the Big 5 personality factors). This can be useful if you are trying to validate a newer measure against a pre-existing measure.
• a set of self-report measures and a set of behavioural measures (e.g., performance on a task)
• a set of set of brain scan measures and a set of behavioural measures

In essence, canonical correlation tends to be interesting when you have two classes of variables and you are interested in what, if any, relationship might exist between the sets. It is a parsimonious way of dealing with the challenges of multivariate data. However, it can sometimes be more exploratory than you might want.

General References

The following references provide an overview of the technique.

• Sherry and Henson (2005) provide an excellent gentle primer on canonical correlation. This is probably the best place to start. It also provides many useful references. PDF is available here
• G. David Garson provides an explanation of key terms and concepts
• Tabachnick and Fidell (1996) have a chapter written for researchers in psychology
• Magnus Borga presents a mathematical overview of canonical correlation. If you understand calculus and linear algebra, it is worth reading.

R

If you want to implement your analyses in R, the following may provide a useful starting point.

• UCLA have a tutorial on canonical correlation in R.
• see the cancor function in base R; canocor in the calibrate package; and the CCA package.

SPSS

If you want to use SPSS to run a canonical correlation, these tutorials may be useful.

• G. David Garson provides an example of SPSS canonical correlation Output with interpretation.
• UCLA provide annotated SPSS Output for canonical correlation.

Note that the location script required to run CANCORR changes between versions and installations of SPSS. David Garson sets out the following code template:

INCLUDE 'c:\Program Files\SPSS\Canonical correlation.sps'.
CANCORR SET1=varlist/
SET2=varlist/.

In contrast on my installation, the script line needs to be:

INCLUDE 'C:\Program Files\SPSSInc\PASWStatistics18\Samples\English\Canonical correlation.sps'.

To find the script on your installation, go to your SPSS installation and search for "canonical".

Journal Articles reporting Canonical Correlation Analysis

The following references provide examples of how to justify, present, and interpret the results of a canonical correlation analysis.

• Rossier, Meyer and Berthoud (2004) [get pdf here] explore the commonalities between the NEO and 16PF personality inventories.
• Satterfield, Buelow, Lyddon, and Johnson (1995) look at the relationship between client expectations and attitude to change in a clinical psychology setting.
• Luthans, Welsh, and Taylor (1988) [get pdf here] present a canonical correlation relating a set of managerial effectiveness measures to a set of managerial activities.

References

• Luthans, F.; Welsh, D. & Taylor III, L. A descriptive model of managerial effectiveness Group & Organization Management, East Acad Manage, 1988, 13, 148
• Satterfield, W.; Buelow, S.; Lyddon, W. & Johnson, J. Client stages of change and expectations about counseling. Journal of Counseling Psychology, 1995, 42, 476-478
• Sherry, A. & Henson, R. Conducting and interpreting canonical correlation analysis in personality research: A user-friendly primer Journal of Personality Assessment, Routledge, 2005, 84, 37-48.
• Tabachnick, B. G. and L. S. Fidell. 1996. Using Multivariate Statistics. 3rdEdition. HarperCollins College Publishers.