The algorithms used in version 3.0 of WarpPLS have been revised so as to pick up instances of what is known as “Simpson’s paradox”. As a result, there may be changes in some coefficients and P values, when compared with previous versions.

Often the P value of the ARS fit index will go up, if instances of Simpson’s paradox are present in the model.

Simpson’s paradox is characterized by the path coefficient and correlation for a pair of variables having different signs. In this situation, the contribution of a predictor variable to the explained variance of the criterion variable in a latent variable block is negative.

In other words, if the predictor latent variable were to be removed from the block, the R-squared for the criterion latent variable would go up. A similar effect would be observed if the direction of the causality was reversed.

One widely held interpretation is that Simpson’s paradox could be an indication that the direction of a hypothesized relationship is reversed, or that the hypothesized relationship is nonsensical/improbable.

In the context of WarpPLS analyses, this is more likely to occur when nonlinear algorithms are used and/or full collineary VIFs are high, but may also occur under other conditions.

## Friday, May 11, 2012

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