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Canonical Correlation in Dissertation & Thesis Research
One of the multivariate techniques used to in many dissertations and theses is canonical correlation. This statistic allows you to assess the relationship between two sets of variables -- the predictor set and the criterion variable set.
When to Use Canonical Correlation
A canonical correlation is used when there are multiple continuous dependent and independent variables and the goal of your dissertation or thesis is to assess the relationship between these two sets of variables. Let's suppose your dissertation is concerned with a set of variables measuring attractiveness (physical beauty, warmth, kindness, and sex appeal) and a set of demographic characteristics (religious affiliation, charitable contributions, socioeconomic status, and income). Your analysis includes a canonical correlation and it reveals two sets of variable relationships. That is, there are two reliable ways these two sets of variables are related.
The first way your variables relate is between socioeconomic status and income on the demographic variable side, and physical beauty and sex appeal on the "attractiveness" side. Taken together, these results indicate that there is a relationship between the physical attractiveness and financial status variable sets.
The second way your variables relate is religious affiliation and charitable contributions on the demographic variable side, and warmth and kindness on the attractiveness side. Together, these results suggest some type of relationship between variables that may be called spirituality and "goodness".
In canonical correlation, sets of variables are on each side of the regression equation and combined to produce a predicted value for each side of the equation. This predicted value has the highest correlation with the predicted value on the other side. Another way to think of it, the combination of variables on each side of the equation can be thought of in terms of a dimension that associates the variables on one side of the equation to the variables on the other side.
One complication of canonical correlations is that there are several variables on both sides of the equation. Thus, there are probably many ways to combine the variables on both sides of the equation and to relate them to each other. A good rule of thumb is that only the first two or three combinations are probably reliable and interpretable in your analyses.
Limited Acceptability of Canonical Correlation
Canonical correlation is not widely used in dissertation research for many reasons. The first could be the associated jargon. First, you have variables, then canonical variates, and canonical variate pairs. Variables are your measured dissertation variables (e.g. socioeconomic status, physical beauty, religious affiliation). Canonical variates are linear combinations of your variables, with one combination on the independent variable side (socioeconomic status and income), and one combination on the dependent side (physical beauty and sex appeal). These two combinations make up a pair of canonical variates. Of course, there may be more than one reliable pair of canonical variates.
The paucity of canonical correlation in the dissertation literature is also partly due to its theoretical limitations. The biggest of these limitations is interpretability. Although mathematically elegant, canonical solutions are often uninterpretable. Furthermore, the rotation of canonical variates to improve interpretability isn't a common practice in research, even though it is commonplace to do this for factor analysis and principle components analysis. Additionally, many statistical software programs don't even offer rotation as an option.
Another problem using canonical correlation for research is that the algorithm used emphasizes the linear relationship between two sets of variables. If the relationship between variables is not linear, then using a canonical correlation for the analysis may miss some or most of the relationship between variables.
As with other dissertation problems that are complex and unclear, make sure that you consult with a dissertation statistical advisor before undertaking a canonical correlation in your research. Look for those rare articles that describe the procedure and results using a canonical correlation. After consulting with your advisor, you may find that there are clearer and more concise ways of analyzing and interpreting your data.
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