Sign change corrections for bootstrap
These functions selectively reverse the signs of the weights in boostrap samples to be consistent with the weights calculated based on the original sample.
1 2 3
signChange.individual(Worig, W) signChange.construct(Worig, W)
The original weight matrix.
a Weight matrix of a bootstrap sample.
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
The construct level correction changes the signs of
W on all rows where the sign of the
sum of the row differs between
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
A weight matrix with the same dimensions as
W after applying the correction.
signChange.individual: individual sign change correction
signChange.construct: individual sign change correction
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. DOI:10.1016/j.paid.2015.07.019
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