9.5 Comparing conditional effects

9.5.1 Comparing conditional effects in the additive multiple moderation model.

9.5.2 Comparing conditional effects in the moderated moderation model.

9.5.3 Implementation in PROCESS brms.

Since we don’t have the contrast feature automated like in PROCESS, we’ll have to carefully follow the equations at the bottom of page 344 to specify the values properly in R.

post %>% 
  transmute(`30-year-old men`   = b_negemot + `b_negemot:sex`*1 + `b_negemot:age`*30 + `b_negemot:sex:age`*1*30, 
            `50-year-old women` = b_negemot + `b_negemot:sex`*0 + `b_negemot:age`*50 + `b_negemot:sex:age`*0*30) %>%
  mutate(contrast = `30-year-old men` - `50-year-old women`) %>% 
  gather() %>%
  group_by(key) %>%
  summarize(mean = mean(value),
            sd = sd(value),
            ll = quantile(value, probs = .025),
            ul = quantile(value, probs = .975)) %>% 
  mutate_if(is.double, round, digits = 3)

## # A tibble: 3 x 5
##   key                mean    sd     ll    ul
##   <chr>             <dbl> <dbl>  <dbl> <dbl>
## 1 30-year-old men   0.371 0.062  0.252 0.495
## 2 50-year-old women 0.319 0.037  0.247 0.391
## 3 contrast          0.052 0.07  -0.084 0.191

Notice how our posterior \(SD\) corresponded nicely to the standard error in Hayes’s contrast test. And we didn’t even have to worry about using the frightening formula 9.21 on page 345. That information was contained in the posterior distribution all along. All we had to do was combine the parameter iterations with a little algebra and then summarize().