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In my dataset time is nested within person. I have done a multilevel analysis with time on the first level and subject on the second level. There is a significant fixed effect of time on the dependent variable. I interpret this as that there is a significant increase in Y over time. There is also a fixed effect of a second level variable (which is continuous and I will call the variable V at the moment). So, the higher people are in V, the higher the dependent variable.

In the random slope model, the fixed effect of time and of variable V are both still significant but there is also a significant cross-level interaction with time and variable V (the same second level variable that is continuous). The estimate of the cross-level interaction is negative. I interpreted this as people high in V have less growth in Y over time than people low in V.

Often you should not interpret the main effects when the interaction is significant. Though my question is, should I interpret both the interaction and the main effects? I think the main effect of V says something about the mean variance in Y, while the cross-level interaction says something about the variance of the slope between time and Y. So, the main effect is about the mean level of Y during the whole experiment while the interaction is about the growth of Y during the experiment.

I have read a lot about this and searched for it but I could not find the answer. Any help is much appreciated.

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I think you already have a very good understanding of your models and the interpretation. Just to ensure I understood you right, you found:

  1. A positive fixed effect of time (level 1) on your outcome Y
  2. A positive fixed effect of V (level 2) on Y
  3. A negative cross-level interaction of V*time

I f that is correct I see no reason why you should not interpret all effects. That means:

  1. The general mean effect of time across all participants is positive indicating a possitive association between time and your outcome.
  2. People scoring high on V also have higher mean values of Y
  3. For People scoring high on V the association between time and Y is less positive. That means, they deviate from the overall fixed effect of time from 1.

Before you enter the interaction term you could check a random slope model for time. There should be a significant random effect of time indicating that individuals deviate from the overall trend. Your interaction term then seems to be capable of explaining this individual deviations.

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