I understand that a longitudinal study assesses change in same variable among same respondents over time. For example, changes in cognitive development over time. A time-lagged design involves study of different cohorts over different period(s) of time.

My question is, If i have three variables, IV, Mediator, DV, (not attempting to assess change in the same variable over time ) and i intend to see how IV-->Mediator and how Mediator--> DV, that would require the same sample of respondents and different time periods, vis., T1, T2, T3.

For my study, does it constitute a longitudinal or time lagged design?

Is there a specific time period for IV-->Mediator--> DV effect to take place, hence is there any specific time difference required for data collection?

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