In longitudinal study (two wave), normally we will choose time 2 mediator and time 2 outcomes in the model. My question is: do we really need to control them by using time 1 mediator and time 1 outcomes respectively? Thanks a lot.
There a few different ways you can test mediation using a two-wave design. One approach is provided by Cole and Maxwell, where mediation is tested by assuming stationarity.
Another approach is provided by Nielsen and Munir, where they test mediation by comparing nested models against the baseline (full mediation) model. I am providing citations for both articles below. In both approaches, you will control for mediator and outcome at Time 1.
Citations:
Cole, D. A., & Maxwell, S. E. (2003). Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling. Journal of abnormal psychology, 112(4), 558.
Nielsen, K., & Munir, F. (2009). How do transformational leaders influence followers' affective well-being? Exploring the mediating role of self-efficacy. Work & Stress, 23(4), 313-329.
1) Do you want to test the relationships among IV, mediator, and DV using a time-lagged design (e.g., a two-wave design survey, which is different from a longitudinal study)? Then, you don't need to control time 1 mediator and time 1 outcomes.
2) Do you want to test how IV affects changes in mediator and outcomes? then you need to control time 1 mediator and time 1 outcomes.