# Can a random slope in a linear mixed model mask the effect of my intervention?

I want to assess the impact of my intervention in a repeated-measures design. I have subject as a random intercept in order to account for the dependence of measurements within subjects:
Outcome ~ Condition*Time + (1|Subject), where Condition is treatment or placebo. I expected the effect of my intervention to increase over time, and I indeed see a significant Condition*Time interaction, which supports my hypothesis.

However, in reality, I guess that subjects will have variable effects of Time on Outcome. Indeed a model comparison confirms that the model Outcome ~ Condition*Time + (1+Time|Subject) fits the data significantly better, but my Condition*Time interaction is no longer significant in the presence of this random slope.

Now, I am wondering if the random slope may have masked the effect of my intervention, by falsely attributing the variation in the effect of Time to Subject, rather than to Condition. Is this possible?

• I guess a different way of phrasing the question would be: Assume I had a very large effect of my treatment in reality. Could the random slope (1+Time|Subject)  mask this effect? Jul 30 '18 at 12:45
• @galliwuzz If you are using R, try the user guide for lmer. Otherwise, look at any source of mixed effects models. The exact fitting algorithm will depend on the implementation and the distribution family (linear mixed model vs generalized mixed model). But in general, the "decision" will be based on a greedy optimization of the (posterior) likelihood Aug 24 '18 at 4:01