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Update PLS-Regression.md
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tim-b90 authored Dec 19, 2023
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Expand Up @@ -97,11 +97,11 @@ Selectivity fraction (**SF**) is calculated by dividing the explained variance b

- **SF<sub>*i*</sub>** = sign variance<sub>explained, *i*</sub> / variance<sub>total</sub> , *i* = 1, 2, 3, ..., n )

The multivariate correlation coefficient, or short MCorrC, is calculated by using SF and the explained variance in y (R<sup>2</sup>Y). Thus, in contrast to SR and SF, this coefficient related to the actual outcome, not the predicted outcome. MCorrC is equivalent to a bivariate correlation coefficient but is derived from the multivariate space. It is favorable for comparing association patterns between groups since coefficients can be compared directly towards the actual outcome.
The multivariate correlation coefficient, or short MCorrC, is calculated by using SF and the explained variance in y (R<sup>2</sup>Y). MCorrC is related to a bivariate correlation coefficient, but is derived from the multivariate space.

- **MCorrC** = sign \|**SF** R<sup>2</sup>Y\|<sup>1/2</sup>

The multivariate covariance coefficient (MCovC) is derived from the MCorrC by dividing MCorrC with the standard deviation (SD) of the **X**. Note that associations using MCovC will be fully dependent on how variables from an intensity spectrum is created or binned. Thus, this coefficient should be used carefully and interpreted appropriately.
The multivariate covariance coefficient (MCovC) is derived from the MCorrC by dividing MCorrC with the standard deviation (SD) of **X**. Note that associations using MCovC will be fully dependent on how variables from an intensity spectrum were created or binned. Thus, this coefficient should be used carefully and interpreted appropriately.

- **MCovC** = **MCorrC** / SD<sub>**X**</sub>

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