strong evidence for H1 with Bayes factor but very weak with Bayesian regression estimation

Question

I performed a Bayesian hierarchal regression with the brm package. Looking at the parameter estimation and confidence interval, I found no support for one of the parameters. However, when I computed Bayes Factor (using different packages), I found strong evidence (BF=11).

I am assuming I am doing some kind of a syntax mistake. How could this be?

I attach the code and output below. Any idea would be appreciated. Thank you

#this summary shows the effect of condition is very weak (CI includes 0)

summary(brm_reward_noint)

#this BF analysis shows strong evidence in favor of the hypothesis that condition_num_c has an effect

bayesfactor_models(brm_reward_nocondition, brm_reward_noint)

Answer 1

The bayes factor that you calculated is the evidence that your model with condition is better than your model without it. Even if you effect of condition overlap 0 (not that much in reality, and consider that 95% interval is as arbitrary as a p value of 0.05, some recommend 89% https://joss.theoj.org/papers/10.21105/joss.01541.pdf as it is more stable even if still arbitrary), it does not mean that taking into account the condition do not help your model (and your bayes factor seem to say that it does).

Now investigating if condition have a robust effect coud lead to the conclusion that even if the model is improved adding this variable, the effect of condition could be close to 0. Imagine that your effect of condition have a positive effect on 4/10 of your participant, a negative effect on 4/10 and a neutral effect of 2/10 of the rest. You will end with an effect of condition appearing not existent as overlapping 0 on both side but it could still improve your model as knowing the condition could predict that 8/10 of the time the effect is not close to 0 (either positive or negative).

Cheers.