732A37 Multivariate Statistical Methods, Autumn Semester 2015
Computer lab 4: Canonical correlation analysis
Sometimes we are interested to study the associations between two sets of variables. This
can be performed by studying the correlations between each pair of variables, one from
set 1 and the other from set 2. However, this can be an overwhelming task even with a
rather moderate number of variables. Instead we look at the correlation between a linear
combination of the variables in set 1 and the corresponding in set 2. In canonical
correlation analysis we successively choose uncorrelated linear combinations from each
set which have the largest correlations between the sets. Hopefully, some few pairs of
combinations will give the essential associations between the two sets.
Learning objectives
After reading the recommended text and completing the computer lab the student shall be
able to:
formulate the association concept between two variable sets and the simplification behind
the concept canonical correlations
use suitable software for canonical correlation analysis (e.g. CANCORR in SAS)
use the output to interpret the canonical correlations and the canonical variates
validate the results from the output.
Recommended reading
Chapter 10 in Johnson-Wichern
Assignment: Canonical correlation analysis by utilizing suitable software
Look at the data described in exercise 10.16. The data for 46 patients are summarized in a
covariance matrix, which will be analyzed by e.g. the SAS procedure CANCORR.
a) Test at level 5 % if there is any association between primary and secondary
variables.
b) How many pairs of canonical variates are “significant”?
c) Interpret the “significant” squared canonical correlations.
d) Interpret the canonical variates by using the coefficients and suitable correlations.
e) Are the “significant” canonical variates good summary measures of respective
data sets?
f) Give your opinion of the success of this canonical correlation analysis
To hand in
Solutions to all parts of the assignment
No later than Wednesday December 9