Interaction effect with two-stage-approach

[BurghardtK]

Dear all,

when calculating an interaction effect with the two-stage-approach suggested by Henseler & Chin (2010), p. 87, SmartPLS will calculate the path coefficients equivalent to standardized (beta) weights in multiple regression.
But as Aiken & West (p. 44) point out, in this case the unstandardized weights should be taken:

"Friedrich (1982) suggested a straightforward procedure that solves this problem. One first calculates Zx and Zz and then forms their crossproduct ZxZz. These values are used as predictors in a regression analysis with Zy as the criterion. The unstandardized solution from that analysis is the appropriate "standardized" solution for use with multiplicative terms".

The values for b and beta are identical for the main effect predictors, but different for the interaction term.
Thus, shouldn't the path coefficient for the interaction term (a beta weight) be transformed into the unstandardized b weight using b = beta * Sy / Sx?


Best regards,

Karsten Burghardt


Henseler, J./Chin, W. W. (2010): A Comparison of Approaches for the Analysis of Interaction Effects Between Latent Variables Using Partial Least Squares Path Modeling, Structural Equation Modeling, 17, 82-109.

Aiken, L. S./West, S. G. (1991): Multiple regression: Testing and interpreting interactions. Newbury Park: Sage.