I used the
brms package to carry out a mixed-effects logistic regression analysis with random intercepts. I'm having trouble interpreting the coefficients, in particular the transformation of the coefficients from log odds to probabilities with the
plogis() function, which is equal to
exp() / 1 + exp().
Here are the results:
Family: bernoulli Links: mu = logit Formula: OUTCOME ~ PREDICTOR + (1 | WORD) Data: lang.data (Number of observations: 584) Samples: 6 chains, each with iter = 5000; warmup = 1000; thin = 1; total post-warmup samples = 24000 Group-Level Effects: ~WORD (Number of levels: 196) Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS sd(Intercept) 3.57 0.65 2.45 4.99 1.00 7968 13158 Population-Level Effects: Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS Intercept -5.49 0.79 -7.19 -4.09 1.00 13082 15203 PREDICTOR:LEVEL1 6.45 0.80 5.00 8.14 1.00 18012 16581 PREDICTOR:LEVEL2 0.80 0.74 -0.64 2.27 1.00 26702 20032 Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS and Tail_ESS are effective sample size measures, and Rhat is the potential scale reduction factor on split chains (at convergence, Rhat = 1).
PREDICTOR variable has three levels and the
OUTCOME is a dichotomous variable, with the values 0 for absence and 1 for presence.
Here are my questions:
- When I transform the estimate of the intercept with
plogis(), I get the following:
plogis(-5.49)  0.004110875
Does this mean that when
PREDICTOR is at the reference level, the probability of
OUTCOME being 1 is 0.41 percent?
- When I add the transformed intercept and the estimate of
PREDICTOR:LEVEL1, I get the following result:
plogis(-5.49 + 6.45)  0.7231218
I understand this to mean that the probability of
OUTCOME being 1 is about 72 percent when
PREDICTOR has the value of
When I add the transformed intercept and the estimate of
PREDICTOR:LEVEL2, I get the following result:
plogis(-5.49 + 0.80)  0.009103059
What I don't understand is why the three values above (
0.009103059) do not sum to 1. If these values exhaust the space of predictor-variable values, the outcome has to occur in one of these three conditions, so why then do they not sum to 1?
- How do interpret the value of
sd(Intercept)? I know that it refers to the standard deviation around the value of the intercepts, but what do I make of the value 3.57? Is it high? Is it low?