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I have data from a 3-wave panel study which I don't know how to analyze. I am interested in how an independent variable (IV) affects a dependent variable (DV). Therefore, I am not interested in the change of the single variables but how the change in one variable affects the change in the other. If I had only two timepoints, I would simply regress the change score of the DV on the change score of the IV. However, I am not sure how to deal with the 3rd time point.

Here are some things I have been looking into:

  • Hierarchical Regression with time-varying covariate: Implementing a hierarchical regression of DV ~ time + IV with random intercepts and slopes for the time parameter. The IV would then be a time varying covariate and I would interpret it's relationship with the DV. At the same time, I would account for individual time trends via the random parameters. This was my favorite way to go. However, it led to a lot of convergence issues which I could not resolve
  • Autoregressive SEM: Simply look at the relationship between IV and DV at all time points seperately and add autoregressive paths to the model. However, this is not considering the change in the variables / I could only interpret the relationship between DV and IV as cross-sectional, therefore not benefitting from the longitudinal character of the data. I also would like to calculate only one relationship between IV and DV as this relationship should not differ between the time points.
  • Lagged dependent model: I'd perform a linear regression like this: DV ~ DV_lagged + IV, with DV_lagged being the DV one timepoint prior than DV. However, I am not sure how exactly one would then interpret the coefficient of the IV (in which I am interested).

As you might see, I don't have any prior experience with analyzing longitudinal data. I would really appreciate if you could explain what analysis you would recommend? (of course it does not need to be one of the above!)

Also: Is it possible to simply calculate two change scores (T3 - T2 and T2 - T1) and put them into one variable?

Thank you!

mkt
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lt0519f
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  • Was your IV an experimental intervention, and did it happen in between any of the time points? – mkt Sep 20 '22 at 14:51
  • No, it is a purely correlational design but we assessed both the IV and DV at all 3 timepoints. – lt0519f Sep 20 '22 at 14:53

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Change scores are a bad idea. And 3 is too few groups to use a random effect; I've heard estimates ranging from a minimum of 6-30 groups, though 6 is a number you'll see more often. Basically, the problem is that the modelling approaches you are interested in require more information in the time dimension than you have available to you in your data, especially since there was no experimental intervention.

I think the most straightforward way to analyse your data would be DV ~ time + IV, with time treated as categorical in the absence of further information about the problem. You could consider an interaction term as well. If you are interested in specific comparisons, you could do post-hoc tests, though I'm generally not a fan of them.

mkt
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  • Thank you for your answer! I would then interpret the coefficient of the IV as the relationship with the DV that cannot be explained by the general time effect, right? This then is not too different from the lagged dependent model, but I would not only control for one prior timepoint but for the general influence of the time point? – lt0519f Sep 20 '22 at 15:11
  • @lt0519f (i) About coefficient interpretation, you are correct - assuming you have no interaction in the model. My standard recommendation is to plot your model output - it always helps with interpretation. – mkt Sep 20 '22 at 15:14
  • @lt0519f (ii) About the comparison with the lagged model, it's fairly different to this. I've not put in any lagged values here, just time point (with time intended to be categorical - I should have specified that). Lagging can often be a good idea but yours is a curious in-between level of temporal structure and I'm inclined to just treat the time points as categories. But a lagged approach sounds defensible to me. – mkt Sep 20 '22 at 15:22
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    Okay, I see. Thank you again for your help! – lt0519f Sep 20 '22 at 16:56