I tried figuring out the answer by reading the comments in this thread but I am still confused. Should I remove a covariate from analysis when it comes as significant but power simulations finds that it is underpowered?
Using lme4, I created a mixed-effects model with several fixed effects like so:
m1 <- lmer(outcome ~ x1 + x2 + x3 + x4 + (1 | participant), data = data)
Each of the fixed variables is a factor with two levels 'yes/no', indicating 'presence/absence'. I find that for all variables the estimated value is significant, thanks to lmertest.
Next with simr, I run 200 simulations using Kenward-Roger approximation to find if based on observed effect each of fixed variables is sufficiently powered (above 80%).
x3 come around ~95%, while
x4 is ~50%.
My understanding was that, if a variable is underpowered, it is more likely to find a false positive. However, after speaking to someone, they suggested that since I achieved significance, the power analysis does not matter. They cited the linked question as a source.
I'm unsure what conclusion to draw from my power analysis. Should I remove