Subtraction of two latent variables

[sumasing]

How can I add or subtract two latent variables to create a new latent variable? For example, let L1 represent perceived benefit and L1 represent actual benefit. L3=L1-L2 represents the disconfirmation effect. Is it possible to do that in smart pls? Any suggestions?

[jmbecker]

You can use the latent variable scores from the PLS algorithm estimation to calculate your difference score.

However, there is quite some body of literature showing that difference scores are suboptimal and quite constrained and that you can actually better model the variables separately. This has nothing to do with PLS, but is a general observation for difference scores.

Edwards, J. R., & Parry, M. E. (1993). On the use of polynomial regression equations as an alternative to difference scores in organizational research. Academy of Management Journal, 36(6), 1577-1613.
Edwards, J. R. (1995). Alternatives to difference scores as dependent variables in the study of congruence in organizational research. Organizational Behavior and Human Decision Processes, 64(3), 307-324.
Edwards, J. R. (2001). Ten difference score myths. Organizational Research Methods, 4(3), 265-287.
Edwards, J. R. (2002). Alternatives to difference scores: Polynomial regression and response surface methodology. Advances in Measurement and Data Analysis, 350-400.