12.7 Interpretation

equality %>%
  add_fitted_draws(equality_model, n = 50) %>%
  ggplot(aes(x = percent_urban, y = laws, color = historical)) +
  geom_line(aes(y = .value, group = paste(historical, .draw)), 
              alpha = .1) +
  geom_point(data = equality) +
  labs(title = "Anti-Discrimination Laws",
       subtitle = "Human Rights Campaign State Equality Index",
       caption = "R4DS Bayes Rules book club") +
  scale_color_manual(values = c("blue", "red", "purple")) +
  theme_minimal()

tidy(equality_model, conf.int = TRUE, conf.level = 0.80)
## # A tibble: 4 × 5
##   term            estimate std.error conf.low conf.high
##   <chr>              <dbl>     <dbl>    <dbl>     <dbl>
## 1 (Intercept)       1.71     0.303     1.31      2.09  
## 2 percent_urban     0.0164   0.00353   0.0119    0.0210
## 3 historicalgop    -1.52     0.134    -1.69     -1.34  
## 4 historicalswing  -0.610    0.103    -0.745    -0.477

log(λi)=1.71+0.0164Xi1−1.52Xi2−0.61Xi3 or λi=e1.71+0.0161Xi1−1.52Xi2−0.61Xi3

  • β0=1.71: the “typical state” has e1.71≈5.53 anti-discrimination laws
  • β1=0.0164: when controlling for historical voting trends, if the urban population in one state is 1 percentage point greater than another state, we’d expect it to have 1.0165 times the number of, or 1.65% more, anti-discrimination laws e0.0164≈1.0165
  • β2=−1.52: when controlling for historicalgop voting trends, if the urban population in one state is 1 percentage point greater than another state, we’d expect it to have about 88 percent fewer anti-discrimination laws e−1.52≈0.2187
  • β3=0.61: when controlling for historicalswing voting trends, if the urban population in one state is 1 percentage point greater than another state, we’d expect it to have about 46 percent fewer anti-discrimination laws e−1.52≈0.5434