# Bayes Factors for brms model with one categorical predictor

**URL:** <https://discourse.mc-stan.org/t/bayes-factors-for-brms-model-with-one-categorical-predictor/33467>\
**Category:** brms\
**Created:** [November 29, 2023, 9:00am UTC](https://discourse.mc-stan.org/t/bayes-factors-for-brms-model-with-one-categorical-predictor/33467 "2023-11-29T09:00:53Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![SophieHerbst](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/sophieherbst/32/17448_2.png) [@SophieHerbst](https://discourse.mc-stan.org/u/SophieHerbst)\
**Post date:** [November 29, 2023, 9:00am UTC](https://discourse.mc-stan.org/t/bayes-factors-for-brms-model-with-one-categorical-predictor/33467/1 "2023-11-29T09:00:53Z")

</div>

I am trying to compute linear models and Bayes factors for a categorical predictor variable. Both, the frequentist lmer and brm model summary show significant effects of the predictor, however when computing the BF for the predictor versus a null model (intercept only), it indicates no effect (BF = 0.017).  
Puzzled by this non-convergence, I changed the same predictor to numeric and now the effects converge between the models and the BF (219.07). I would prefer to keep the categorical predictor though for theoretical reasons. Can you help me understand where it goes wrong?  
Many thanks in advance

```no-highlight
**With position as a categorical predictor:** 

res_RP_5 <- lmer(RP ~ position + (1|subj),
           data = SUMMDATA_AVG_5items)
print(anova(res_RP_5))

> Type III Analysis of Variance Table with Satterthwaite's method
> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)    
> position 0.0928016 0.0232004 4 72 7.12666 0.000068326 ***
> ---
> Signif. codes: 0 ‘ ***’ 0.001 ‘** ’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

pr = prior(normal(0, 1), class = 'b')

res_CV_B_5_position <- brm(CV ~ position + (1|subj),
             data = SUMMDATA_AVG_5items,
             prior = pr,
            cores = 3, save_pars = save_pars(all=TRUE))

print(summary(res_CV_B_5_position))
> Family: gaussian 
> Links: mu = identity; sigma = identity 
> Formula: CV ~ position + (1 | subj) 
> Data: SUMMDATA_AVG_5items (Number of observations: 95) 
> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
> total post-warmup draws = 4000
> 
> Group-Level Effects: 
> ~subj (Number of levels: 19) 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> sd(Intercept) 0.05 0.01 0.03 0.08 1.00 1080 1400
> 
> Population-Level Effects: 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> Intercept 0.31 0.02 0.28 0.35 1.00 1939 2294
> position2 0.03 0.02 -0.00 0.07 1.00 3387 2987
> position3 0.07 0.02 0.04 0.11 1.00 3182 2872
> position4 0.07 0.02 0.03 0.11 1.00 3444 3028
> position5 0.09 0.02 0.05 0.13 1.00 3669 3032
> 
> Family Specific Parameters: 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> sigma 0.06 0.01 0.05 0.07 1.00 2749 3091

res_CV_B_5_null = update(res_CV_B_5_position, formula = ~ .-position)
BF_5_position <- bayes_factor(res_CV_B_5_position, res_CV_B_5_null)
print(paste('Effect of position:', BF_5_position))

> [1] "Effect of position: 0.0166357493642797" "Effect of position: FALSE" 

**With position as a numerical predictor:** 

res_RP_5 <- lmer(RP ~ position + (1|subj),
           data = SUMMDATA_AVG_5items)
print(anova(res_RP_5))

> Type III Analysis of Variance Table with Satterthwaite's method
> Sum Sq Mean Sq NumDF DenDF F value Pr(>F)    
> position 0.0824642 0.0824642 1 75 25.2721 0.0000032914 ***
> ---
> Signif. codes: 0 ‘ ***’ 0.001 ‘** ’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

pr = prior(normal(0, 1), class = 'b')
res_CV_B_5_position <- brm(CV ~ position + (1|subj),
             data = SUMMDATA_AVG_5items,
             prior = pr,
            cores = 3, save_pars = save_pars(all=TRUE))

print(summary(res_CV_B_5_position))

> Family: gaussian 
> Links: mu = identity; sigma = identity 
> Formula: CV ~ position + (1 | subj) 
> Data: SUMMDATA_AVG_5items (Number of observations: 95) 
> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
> total post-warmup draws = 4000
> 
> Group-Level Effects: 
> ~subj (Number of levels: 19) 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> sd(Intercept) 0.05 0.01 0.03 0.08 1.00 1124 1665
> 
> Population-Level Effects: 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> Intercept 0.30 0.02 0.27 0.34 1.00 2212 2724
> position 0.02 0.00 0.01 0.03 1.00 6785 3076
> 
> Family Specific Parameters: 
> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
> sigma 0.06 0.01 0.05 0.07 1.00 3608 2748

res_CV_B_5_null = update(res_CV_B_5_position, formula = ~ .-position)
BF_5_position <- bayes_factor(res_CV_B_5_position, res_CV_B_5_null)
print(paste('Effect of position:', BF_5_position))

> [1] "Effect of position: 219.065334966854" "Effect of position: FALSE"

```