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I apologize if this question has been asked previously.

I conduct mixed-effects model analyses in R and MATLAB, so this question is more conceptual than technical. MATLAB and R both produce p-values for each coefficient for GLMERS/fitglme.

In some cases, I may have a model in which there is a 3-way interaction in my fixed-effects structure with just a random intercept term. Here, most of my fixed effects are significant (p < .05).

However, when I add random slopes to the random effects structure, the significance of the fixed effects diminish. I'm assuming this has to do with the random effects accounting for individual variation, but I was curious if there was a fuller answer.

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    $\begingroup$ It's going to be helpful if you actually state the model and which variables are interacted with which other ones, which are random, etc. Otherwise it's a bit hard to say anything concrete. $\endgroup$ – conjugateprior Dec 6 '16 at 22:58
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Adding random effects to a model leads to shrinkage in fixed effects differences because the random effect variance component is included in the interval of the test. The authors of R mixed procedures do not believe in calculating standard errors and t-statistics for fixed effects as provided in SAS. Instead they use estimates of z statistics to obtain a confidence interval.

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