Linear mixed-effects regression on longitudinal data: Multicollinearity

Question

Panel data: subjects' value are repeatedly measured over time points. Suppose the first half was the pretest (grp=0) and the second half received the intervention (grp=1).

Take this post as an example:

  ID | time | grp | value |
  s_1| 1    |  0  | Q_11  |
  s_1| 2    |  0  | Q_12  |
  s_1| 3    |  0  | Q_13  |
  s_1| 4    |  1  | Q_14  |
  s_1| 5    |  1  | Q_15  |
  s_1| 6    |  1  | Q_16  |

Now, run a linear mixed-effecs regression value ~ time * factor(grp) + (time | ID). Each subject ID will have its own intercept and slope over time.

However, my concern is that grp can be derived from time, i.e., grp = ifelse(time <=3, 0, 1). This may be collinearity (I wonder if that's the exact word to use because one variable is categorical).

How do I fix the issue or even conduct another model? Thanks.

Answer 1

You don't need to be concerned. Multicolinearity occurs when one column of the design matrix (the matrix of values of predictor variables) can be derived as a linear combination of the other columns. Your variable grp does not fall into that category.

As another example, consider the case of a polynomial regression model with the continuous predictors $x$ and $x^2$. The latter can be derived from the former -- and the two are correlated -- but multicolinearity isn't usually a problem (e.g., parameter estimates and their SEs are usually stable).