Are multigroup analyzes via structural equation model an alternative to investigate the influence of background variables, considering the model of the Theory of Planned Behavior?
If so, would this also be a way to deal with confounding factors?
a multigroup analysis is typically used to test for differences in structural effects across categories of the grouping factor. Hence, such an approach would concur with the moderator or better: effect-modyfier perspective. If this is what you mean with the effect of background variables then yes; it would be an option. Background variables, however, can effect variables (and not effects of variables)--such a perspectives would rather specify the background variable in the model (as a cause of one or several of the variables)
Likewise if the grouping factor acts as a confounder--which affects two variables within the TPB than a multigroup approach will adjust for this (as any other kind of stratification).
Thank you very much for your response, Professor Holger Steinmetz.
I just thought about using the background variables as control variables. Excellent. So, it would be to think of multigroup analysis as a way to verify the moderating role of sociodemographic variables on the model's relationships. Another role that background variables can play, close to what you also considered, would be mediation - but, for now, that would not be the objective of my research.
I use multiple-group analysis to test the control variables in my study. It is convenient to test the different mediation effects in causal path of SEM. These tested variables may be Background variables.