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.