Sign ambiguity corrections adjust the signs of the weights to satisfy a criterion.
weightSign.Wold1985(W, S)weightSign.dominantIndicator(W, S)
Weight matrix, where the indicators are on colums and composites are on the rows.
Covariance matrix of the data.
W after sign correction.
weightSign.Wold1985: Adjust the signs of W so that the majority of the indicators are positively
correlated with the composite as proposed by Wold (1985).
weightSign.dominantIndicator: Adjust the signs of W so that the first indicator of each composite has positive
weight.
Instead of fixing a weight to a particular value, composite variables are typically provided a
scale by standardization. This leads to sign indeterminacy because standardized weights W
and -W both satisfy the scaling constraint. The sing ambiguity corrections add additional
constraints that make
The sign indeterminacy
corrections should not be confused with sign chance corrections applied to boostrap samples
(See signChange).
Wold, H. (1985). Partial Least Squares. In S. Kotz & N. L. Johnson (Eds.), Encyclopedia of statistical sciences (Vol. 6, pp. 581<U+2013>591). New York: Wiley.