signChangeCorrection: Sign change corrections for bootstrap

Description

These functions selectively reverse the signs of the weights in boostrap samples to be consistent with the weights calculated based on the original sample.

Usage

signChange.individual(Worig, W)
signChange.construct(Worig, W)

Arguments

Worig

The original weight matrix.

a Weight matrix of a bootstrap sample.

Value

A weight matrix with the same dimensions as W after applying the correction.

Functions

signChange.individual: individual sign change correction
signChange.construct: individual sign change correction

Details

Sign change corrections are a controversial and inconsistently implemented feature in PLS analysis. The two corrections described in the literature are the individual sign chance correction and the construct level sign chance corrections. The individual correction changes the signs of W to match Worig.

The construct level correction changes the signs of W on all rows where the sign of the sum of the row differs between Worig and W.

The sign chance corrections are described ambiquosly and sometimes implemented inconsistently between software. matrixpls implements the corrections by adjusting the weights before calculating parameter estimates in each bootstrap replication. Some software implement the correction post-hoc by adjusting the bootstrap estimates directly. Moreover, the literature present at least two different formulas for the construct level correction. matrixpls implements the version described by Tenenhaus et al. (2005).

The sign chance corrections should not be confused with sign indeterminacy corrections applied to individual analyses (See signAmbiquityCorrection).

References

Tenenhaus, M., Esposito Vinzi, V., Chatelin, Y.-M., & Lauro, C. (2005). PLS Path Modeling. Computational Statistics & Data Analysis, 48(1), 159–205. doi:10.1016/j.csda.2004.03.005

Rönkkö, M., McIntosh, C. N., & Antonakis, J. (2015). On the adoption of partial least squares in psychological research: Caveat emptor. Personality and Individual Differences, (87), 76–84. http://doi.org/10.1016/j.paid.2015.07.019{DOI:10.1016/j.paid.2015.07.019}