When considering the relationships between two sets of variates, the number of nonzero population canonical correlations may be called the dimensionality. In the literature, several tests for dimensionality in the canonical correlation analysis are known. A comparison of seven sequential test procedures is presented, using results from some simulation study. The tests are compared with regard to the relative frequencies of underestimation, correct estimation, and overestimation of the true dimensionality. Some conclusions from the simulation results are drawn.
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Caliński et al. (2006) studied this question.
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