I'm trying to fit a two-level normal response model. I include an interaction term between
two level-1 variables ('year' and 'x'). I want to test whether the association between the
interaction term and the outcome, y, is consistent across my level-2 units — i.e. whether
the model is improved by including a random coefficient for the interaction term. However,
I'm stuck on a few points:
- Should I also include random coefficients for the main effects involved in the interaction?
I.e. for the interaction between year and x, I could include random coefficients for year, x and year*x.
- How should I test the significance of the level-2 variation? (i.e. should I test the variance of
the interaction only, or the variance of all main effects and the interaction, or the variances and
covariances of all of the above?
- How should I plot the random coefficients?