# Multiple regression with repeatedly measured independent variables?

Design and hypothesis: we measured wellbeing at Time-1 and Time-2, we want to see whether factor A (measured at Time-1 and supposed to be a stable factor over time) is a significant predictor of factor B (measured at Time-2). We also expect wellbeing, current or past, will contribute to B.

Question: is it appropriate to do multiple regression with wellbeing measured at both time points (using the same instrument) as simultaneous predictor? - significant correlations amongst predictors are present, but multicollinearity diagnostics seemed fine... is there a better way to test the hypothesis that'd make good use of the longitudinal design?

Many thanks!

• I'm not used to seeing designs called longitudinal when the dependent variable is measured at only one point in time. I would probably treat this as a cross-sectional problem, but you might look into path analysis or structural equation modeling to take advantage of what seems to be a chain of potential causes and effects. – rolando2 Feb 1 '13 at 1:23
• Thanks @rolando2. The question we'd like to answer is whether A is a predictor of B, over and above the contribution of wellbeing measured at either time point. Multiple regression seems to be able to answer that, but not sure whether it's the best approach... – Sootica Feb 1 '13 at 1:48
• Multiple regression wouldn't make much use of the longitudinal aspect; it would (if set up properly) simply treat each wellbeing variable as a covariate to adjust for. The other methods I mentioned would go farther, though, to disentagle the sequence of causal relationships. – rolando2 Feb 1 '13 at 21:51

If we were interested in the unique contribution of A to B, over and above current and past wellbeing, we could run hierarchical regression. There will be plenty of overlapping variance explained by current and past wellbeing, but entering them in separate steps can help us understand the unique contribution of either to B. In our case, we first entered wellbeing at Time-1, followed by wellbeing at Time-2. Even though Time-1 wellbeing explained a great deal of the variance in B, it was no longer a significant predictor when we entered Time-2 wellbeing. This suggests that current, rather than past wellbeing is a more important contributing factor. We entered A in the final step, and it made significant improvement to the model with Time-1 and Time-2 wellbeing in it, and this supports our initial hypothesis.
If we were interested in how the change in wellbeing from Time-1 to Time-2 predicts B, we could compute the difference scores, or use more elaborate latent change score models to account for the repeatedly measured nature of wellbeing. A couple of useful resources for this approach: McArdle's 2009 review paper, Cambridge Powerpoint slides with examples and Mplus syntax