I am using brms with family = bernoulli(). The coefficients, if I understand correctly, are in log odds. Here is a piece of the output of the population-level effects:
Population-Level Effects: Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS Intercept 1.27 0.45 0.41 2.16 1.00 584 1192 varB 0.33 0.62 -0.85 1.52 1.01 674 1362 varC -1.57 0.61 -2.85 -0.38 1.00 613 1000
For what I know, if I want to report the probabilities of getting the correct answer at variable A (the intercept), then use this formula:
That gives me 0.7807427, or 78% or probabilities of getting the response correct after one day.
If I want the probability of getting it correct at VarB:
Which is 83%. However, the CIs include 0, so there is no effect. If I want to report the CIs of VarB, if I use the same formula
exp(0.41 - 0.85) / (1 + exp(0.41 - 0.85)) #for lower CI exp(2.16 - 1.52) / (1 + exp(2.16 - 1.52)) #for upper CI
I get two positive numbers, which I should not because it looks like there is an effect when actually is not!
I think this is another way of doing it:
samples <- posterior_samples(model, pars = "Intercept") quantile(samples$b_varB, probs = c(0.025, 0.975))
But again, I get a number that I think it's in log odds.
So, the question is: can I leave the coefficient as a probability and the CIs as log odss?