First, sorry, I didn’t realize
hypothesis actually does almost exactly the same thing I proposed for one-sided hypotheses. The only additional step is that
hypothesis converts the probability to evidence ratio (you may note that
0.884 / (1 - 0.884) = 7.62).
If you believe your model is correct, it tells you that you should also believe that there is 88% probability that the
eeg1_standard_age coefficient is smaller. Nothing more, nothing less.
Overall, I don’t think dichotomous thinking of changes/doesn’t change is very useful. Why wouldn’t the influence change at least a little bit after a correction? For any non-trivial correction I would expect the “influence” to change at least a little 100% of the time. You may be able to evaluate the probability (or evidence ratio, if you prefer) for something like
abs(eeg1_standard_age - eeg1_corrected_age) > some_value_you_consider_important, i.e. that the coefficient changes by a noticeable amount.
But I can’t help but wonder, whether the way you ask the question is sensible - what exactly is the correction? If your correction was that
eeg1_corrected = 0.1 * eeg1_standard, you would get
eeg1_standard_age * 0.1 = eeg1_corrected_age so the coefficients would change (with high probability / evidence ratio), but I don’t think it would be sensible to say that the “influence” of age changes.
It might be more sensible to fit separate models for
corrected and compare them with
loo or perform posterior predictive checks to see which is better “explained” by age (for some meaning of “explain”).
Does that make sense?