gives Pillai's trace for the matrices m1 and m2.
- PillaiTrace[m1,m2] gives Pillai's trace between m1 and m2.
- Pillai's trace is a measure of linear dependence based on partitions of the pooled covariance matrix.
- Pillai's trace is computed as where is the covariance matrix of the pooled sample, which can be partitioned into where and correspond to the covariance matrices of the individual datasets.
- The arguments m1 and m2 can be any real‐valued matrices or vectors of equal length.
Examplesopen allclose all
Basic Examples (3)
Properties & Relations (4)
HoeffdingD can be used to detect some nonlinear dependence structures:
Pillai's trace is asymptotically equivalent to WilksW:
Statistical significance can be tested using PillaiTraceTest:
Alternatively, use IndependenceTest to automatically choose a test:
Wolfram Research (2012), PillaiTrace, Wolfram Language function, https://reference.wolfram.com/language/ref/PillaiTrace.html.
Wolfram Language. 2012. "PillaiTrace." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PillaiTrace.html.
Wolfram Language. (2012). PillaiTrace. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PillaiTrace.html