What is the best way to test a multilevel (serial) multiple mediator model (see my model attached which is 2-2-2-1)? Is there a way to do that in SPSS?
Yes, you could do this in SPSS by doing lots of regression models (TFL->PS, TFL->TL, PS,TL->IWB etc etc) but this would be a very poor way to proceed. The PROCESS macro for SPSS could do something very similar, but may not be able to have the direct effect between the mediators. The best way to proceed is to do a path analysis model in AMOS, LISREL, Mplus, or some other latent variable software. The model would be pretty straightforward to specify. You may want to consider adding some other variables in a way that the model is not just-identified, in this way you get a chance to test the plausibility of your model using a range of fit statistics that are available.
This video looks to cover most aspects of testing a model similar to yours-
Thanks a lot Mark. I'll check the video. But how to deal with the multilevel aspect (team level data is aggregated from individual measures)? I thought process can't handle this.