Predict change in dependent variable over three time points using independent variable at baseline

Question

I want to predict the change in my dependent variable (DV) over time using an independent variable (measured only at baseline). My DV was measured at three points in time. The easiest way would be to calculate a change score for my DV by subtracting DV_t3 - DV_t1. However, with this approach, I would be “throwing away” the information about my DV at t2. I wonder if there is a way to include this information in my analysis?

Here's a dummy dataset (just for visualization purposes):

Subject_id	IV_t1	DV_t1	DV_t2	DV_t3
Subject_1	0.17	0.3	0.01	0.95
Subject_2	0.86	0.62	0.39	0.4
Subject_3	0.39	0.23	0.3	0.51
Subject_4	0.93	0.86	0.76	0.03
Subject_5	0.17	0.87	0.77	0

Possibly related (but referring to ANOVA / categorical IV):

Best model for change in scores over three time points

Answer 1

Chapter 7 of Frank Harrell's Regression Modeling Strategies discusses longitudinal data like yours. It's often not a good idea to model change scores directly. Then you are also throwing out the information about DV_t1 values and are assuming that the change is independent of that value.

You can instead fit the model with the DV values in their original scale. It's often a good idea to use DV_t1 as a predictor along with IV_t1 as you model of DV_t2 andDV_t3. Instead of a single change (analogous to a paired t-test and throwing out DV_t2) to try to handle intra-individual correlations, you use all of the observations and handle those correlations with generalized least squares (as Harrell would probably recommend here), or with a mixed model. After you've built that model, you can always use the model results to show the changes over time.