I’m reanalyzing a dataset of student outcome data that I have previously analyzed using frequentist methods. I’ve imputed missing values using MICE and run a bayesian regression of the data (code below). I’m looking at differences in group means on a test that is take before and after a course across demographic groups. In this model test is an indicator variable for pre or posttest.

```
FCI_model_alg <- brm_multiple(
score ~ 1 + test*(collab_pedagogy + gender_other_new + race_other_new + female*(black + hawaiian_or_other_pacific_islander + hispanic+ white + hispanic*white) + retake) + (1|course_id:student),
data = MIdata_alg,
seed=1,
chains = 4,
cores=8)
```

The model runs great, and the coefficients (below) look reasonably similar to what I get from my frequentist analysis.

```
Links: mu = identity; sigma = identity
Formula: score ~ 1 + test * (collab_pedagogy + gender_other_new + race_other_new + female * (black + hawaiian_or_other_pacific_islander + hispanic + white + hispanic * white) + retake) + (1 | course_id:student)
Data: MIdata_alg (Number of observations: 11214)
Samples: 40 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 40000
Group-Level Effects:
~course_id:student (Number of levels: 5607)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 11.66 0.24 11.19 12.12 1.04 672 2335
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 27.58 1.78 24.08 31.06 1.03 987 9042
test 11.66 2.08 7.60 15.79 1.06 376 1692
collab_pedagogy 5.58 1.02 3.60 7.58 1.01 3667 31943
gender_other_new -0.44 3.76 -7.82 6.91 1.11 221 726
race_other_new 1.67 1.78 -1.79 5.16 1.03 1020 10330
female -7.16 1.76 -10.59 -3.71 1.04 620 7502
black -7.61 2.37 -12.23 -2.93 1.04 612 2451
hawaiian_or_other_pacific_islander 3.14 3.86 -4.46 10.58 1.08 285 1105
hispanic -3.60 1.91 -7.39 0.12 1.02 1386 14867
white 6.79 1.59 3.69 9.89 1.04 629 3245
retake 3.18 0.84 1.52 4.84 1.04 528 3098
hispanic:white 0.85 2.16 -3.34 5.11 1.03 963 12150
female:black 2.40 2.87 -3.21 7.98 1.04 551 2236
female:hawaiian_or_other_pacific_islander -5.45 5.33 -16.08 4.73 1.09 278 759
female:hispanic 2.63 2.31 -1.89 7.18 1.02 1858 20145
female:white -5.22 1.89 -8.93 -1.52 1.04 674 4558
test:collab_pedagogy 2.98 1.27 0.48 5.47 1.12 202 810
test:gender_other_new 0.45 4.94 -9.51 9.58 1.28 105 320
test:race_other_new -1.36 2.02 -5.27 2.62 1.03 871 9918
test:female -0.06 2.06 -4.18 3.90 1.09 274 869
test:black -6.87 3.22 -13.26 -0.61 1.24 115 370
test:hawaiian_or_other_pacific_islander 2.88 4.67 -6.05 12.26 1.16 162 546
test:hispanic -1.43 2.41 -5.99 3.49 1.14 181 360
test:white 2.86 1.89 -0.86 6.55 1.11 233 769
test:retake 9.24 1.07 7.16 11.37 1.19 140 586
female:hispanic:white -1.86 2.71 -7.15 3.48 1.02 1276 16028
test:hispanic:white -0.18 2.65 -5.48 4.87 1.12 212 608
test:female:black 4.69 3.69 -2.69 11.74 1.18 146 418
test:female:hawaiian_or_other_pacific_islander -2.07 6.38 -14.50 10.53 1.15 170 871
test:female:hispanic 0.74 2.87 -4.91 6.31 1.13 202 981
test:female:white -0.29 2.29 -4.71 4.30 1.12 206 555
test:female:hispanic:white -1.14 3.32 -7.59 5.35 1.11 222 1063
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 15.42 0.18 15.06 15.76 1.22 127 409
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).
```

What I don’t know how to do now is create predicted outcomes for groups that require combining multiple variables. For example, to know how white men did on the posttest I need to combine the white and test:white variables. I know how to do it in a frequentist model, but not in a Bayesian model. Adding the point estimate together is trivial. Figuring out how to combine the uncertainty is what has me stumped. I’m sure this is easy, but any help that you can offer would be greatly appreciated. Thank you!