# Significance of the control predictors in a non-significant full-null model comparison (mixed model)

The situation:

A, B, C, and D are fixed effects, and RandomEffect is a random effect, all of which are being use to predict the variable Response.

My prediction was that A and B would show a detectable effect on Response, but my analyses showed no such pattern. I assumed C and D to have some effect, but this was based on scientific reasoning (the topic is understudied). As C and D were "control" predictors, they were included in both the full and null model.

I am interested in understanding how to obtain appropriate p-values and confidence intervals for variables which were not part of my prediction (C and D), and how to present my results.

My analysis:

I used a model with all possible random slopes and correlations between random slopes and intercepts (see this paper for more information).

Full model R formula: (A, B, C, and D impact Response)

full = Response ~ A + B + C + D + (1 + A + B + C + D | RandomEffect)


Null model R formula: (only C, and D impact Response)

null = Response ~ C + D + (1 + A + B + C + D | RandomEffect)


Results:

The full-reduced model comparison - anova(null, full, test="Chisq") - was not significant, i.e. no evidence A and B impact Response. However, C and D do have a detectable effect. Since there is not much known about C and D’s effect on Response, it would be interesting to discuss it in my paper.

My questions are...

1. Even though my full-null model comparison was not significant, is it still acceptable to report the coefficients / p-values / confidence intervals / etc. for C and D?

2. If yes, would I use values derived from...

• a. The full model
• b. The null model
• c. A simpler model excluding all aspects of the main effects, like:
• Response ~ C + D + (1 + C + D | RandomEffect)
3. If the answer to 2 is b. or c., then would I further test the null/simplified model against another, further simplified, model which excludes C and D? Would I then need to make a correction for multiple testing?

• You state at the beginning that your goal is to test the effects of A and B, but your questions are all based on analyses that say that A & B have no detectable effect. Could you clarify what you are trying to achieve?
– mkt
Jul 4, 2017 at 10:40
• My prediction was that A and B have an effect on Response. My data show that they do not. My assumption was that C and D have an effect on Response, and the data show they do. My questions are about how to report the significance/effect of C and D on Reponse, even though they are not part of my original prediction. Does that clarify the question? Is there something else that needs more explanation? Please let me know and I will try to clarify more. Thanks! Jul 4, 2017 at 11:27
• Thanks, that helps (and I have submitted edits to clarify your question).
– mkt
Jul 4, 2017 at 11:41