Comparison of Canonical Correlation and Partial Least Squares analyses of simulated and empirical data

Abstract BackgroundWith the availability of large datasets containing multiple measures, there has been a renewed interest in applying multivariate statistical analysis. Two methods, Canonical Correlation Analysis (CCA) and Partial Least Squares (PLS) have been used most frequently given their historical links to classic statistical modelling of the dimensions that relate to two data blocks. Though similar in the decomposition of the cross-block structure, there are important differences in specific steps. In this paper, we apply the most general form of CCA and PLS to three simulated and two empirical datasets, all having large sample sizes on the order of n=10,000. We take successively smaller subsamples of these data to evaluate sensitivity, reliability, and reproducibility. ResultsIn null data having no correlation within or between blocks, both methods showed equivalent false positive rates regardless of sample size. Both methods also showed equivalent detection in data with weak but reliable effects until sample sizes drop below n=50. In the case of strong effects, both methods showed similar performance unless the correlations of items within one data block were high. In these instances, the reproducibility in CCA declined. This was ameliorated if a principal components analysis (PCA) was performed on a data block and the component scores used to calculate the cross-block matrix. For PLS, the results were reproducible across sample sizes for strong and moderate cross-block effects, regardless of the within-block correlations, but show lower detectability at small sample sizes (n=20). ConclusionsThe general outcome of our examination gives three messages. First, for data with low within and high between block structure, CCA and PLS give comparable results, with equivalent sensitivity and false positive rate. Second, if there are high correlations within either block, this can compromise the reliability of CCA results. This can be remedied with PCA before cross-block calculation. However, this assumes that the PCA structure is stable for a given sample. Third, statistical significance by null hypothesis testing does not guarantee that the results are reproducible, even with large sample sizes. This final outcome suggests that researchers should routinely assess both statistical significance and reproducibility for their data.

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