# Bayes factor favours reduced model without the predictor of interest: how do to explain?

Hello,

I have compared two models with the same priors using the Bayes factor function in brms.

Model 1 is:

``````ACC1_post.bmodel = brm(correctResponse  ~  conditionStimuli * sequenceTrials + (conditionStimuli * sequenceTrials | Num_part)
, data = data_nogo
, family = bernoulli(link = "logit")
, warmup = 500
, iter = 3000
, chains = 2
, inits = "0"
, cores = 2
, seed =123
, save_pars = save_pars(all = TRUE)
, control = list(adapt_delta = 0.99)
, prior = prior1_ACC
)
``````

while the other model is reduced removing the predictor conditionStimuli which is the predictor of interest for the experiment.

``````ACC1_noStim.bmodel = brm(correctResponse  ~ sequenceTrials + (conditionStimuli * sequenceTrials | Num_part)
, data = data_nogo
, family = bernoulli(link = "logit")
, warmup = 500
, iter = 3000
, chains = 2
, inits = "0"
, cores = 2
, seed =123
, save_pars = save_pars(all = TRUE) #later will be usefu for bayes factor
, control = list(adapt_delta = 0.99)
, prior = prior1_ACC
)

``````

the prior for both models is the same:

``````prior1_ACC = set_prior("normal(0,10)", class = "b")+
set_prior("normal(0, 10)", class = "sd")
``````

Following (Schad et al., 2021), comparing these two models using the BF should test the existence of the effect of the predictor. The BF is 50000 in favour of the reduced model.

How do I interpret and report this in Bayesian terms?

I tried: " The Bayes factor showed that the data were more likely under the model containing only sequenceTrials as a predictor, suggesting that conditionStimuli is not affecting the parameters of the reaction times distribution"

The equivalent frequentist generalised linear mixed model showed a significant effect of conditionStimuli (even though p = 0.048), I guess this is a case of Lindleyâ€™s paradox.

Thank you,

previous discussion on this topic here: Proper interpretation of Bayes factor (from rstanarm + bridgesampling). hope this helps