== Canonical Correlation ==

Canonical correlation is a multivariate correlation between two sets of variables e.g. two sets of questionnaire items. There is qualified support for using binary variables with one replier[[https://www.researchgate.net/post/Can_decrete_categorical_variables_example_sex_be_used_in_Canonical_correlation_regression_analysis | here]] saying he has seen binary variables used in Canonical Correlation quite often. 

This cannot be implemented using the SPSS menu system but a macro is available in a file called Canonical correlation.sps located in a folder of form C:\Program Files(x86)\IBM\SPSS\Statistics\19\Samples\English which can be run from a SPSS syntax window. A worked example running this SPSS macro is given [[http://www.unt.edu/rss/class/Jon/SPSS_SC/Module9/CanCorr/SPSS_M9_CC.htm | here]]. 

The output from the SPSS macro includes the percentage of variance explained in the variables in Set 2 by each canonical variate in Set 1 (and vice-versa) and is equal to the sum of the squares of each outputted column of cross-loadings for Set 1 divided by the number of variables in Set 1 (equal to 3 in the example). So, for instance in the example data, the percentage of variance in Set 2 due to the first canonical variate in Set 1 = [ (-0.233)^2 ^ + (-0.291)^2 ^ + (-0.257)^2 ^ ] / 3 = 0.068 since the first column of 'Cross Loadings for Set-1' equals -0.233, -0.291, -0.257.

Canonical Correlation can also be run using [[ http://www.ats.ucla.edu/stat/spss/output/SPSS_CCA.htm | SPSS syntax]] with the MANOVA command (note: MANOVA cannot be run using the SPSS menu). Tabachnick and Fidell (2007, pages 567-606) in a chapter on Canonical Correlation mention both approaches together with SAS CANCORR but recommend the SPSS macro as its output is easier to understand than that produced by MANOVA.

The [[http://www.ats.ucla.edu/stat/r/dae/canonical.htm | CCA package]] may also be used to fit canonical variates using R. This link also includes a suggestion on how to report the results from a canonical variate analysis.

__References__

Clark, M. J. (2006). Canonical correlation with SPSS. Benchmarks Online: RSS Matters, 01/2006.  (Available [[http://www.unt.edu/benchmarks/archives/2006/january06/rss.htm | here]])

Tabachnick BG and Fidell LS (2007) Using multivariate statistics. Fifth Edition. Pearson International:Boston.