D are fixed effects, and
RandomEffect is a random effect, all of which are being use to predict the variable
My prediction was that
B would show a detectable effect on
Response, but my analyses showed no such pattern. I assumed
D to have some effect, but this was based on scientific reasoning (the topic is understudied). As
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 (
D), and how to present my results.
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: (
full = Response ~ A + B + C + D + (1 + A + B + C + D | RandomEffect)
Null model R formula: (only
null = Response ~ C + D + (1 + A + B + C + D | RandomEffect)
The full-reduced model comparison -
anova(null, full, test="Chisq") - was not significant, i.e. no evidence
D do have a detectable effect. Since there is not much known about
D’s effect on
Response, it would be interesting to discuss it in my paper.
My questions are...
Even though my full-null model comparison was not significant, is it still acceptable to report the coefficients / p-values / confidence intervals / etc. for
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
Response ~ C + D + (1 + C + D | RandomEffect)
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
D? Would I then need to make a correction for multiple testing?