mild updates and a new plot

Author: Solomon Kurz

13.Rmd

@@ -684,7 +684,7 @@ Just like in the text, our `male` slopes are much less dispersed than our interc
 Figure 13.6.a depicts the correlation between the full UCB model's varying intercepts and slopes.
 
 ```{r, fig.width = 3, fig.height = 3, warning = F, message = F}
-lost <- posterior_samples(b13.3)
+post <- posterior_samples(b13.3)
 
 post %>% 
   ggplot(aes(x = cor_dept_id__Intercept__male, y = 0)) +
@@ -1073,9 +1073,9 @@ posterior_summary(b13.7) %>%
   round(digits = 2)
 ```
 
-Our Gaussian process parameters are different than McElreath's. From the `gp` section of the [brms reference manual](https://cran.r-project.org/package=brms/brms.pdf), here's the brms parameterization:
+Our Gaussian process parameters are different than McElreath's. From the `gp` section of the [brms reference manual](https://cran.r-project.org/package=brms/brms.pdf), we learn the brms parameterization follows the form
 
-$$k(x_{i},x_{j}) = sdgp^2 \exp \big (-||x_i - x_j||^2 / (2 lscale^2) \big )$$
+$$k(x_{i},x_{j}) = sdgp^2 \exp \big (-||x_i - x_j||^2 / (2 lscale^2) \big ).$$
 
 What McElreath called $\eta$, Bürkner called $sdgp$. While McElreath estimated $\eta^2$, brms simply estimated $sdgp$. So we'll have to square our `sdgp_gplatlon2` before it's on the same scale as `etasq` in the text. Here it is.
 
@@ -1535,13 +1535,27 @@ tidy(b13.10) %>%
   mutate_if(is.numeric, round, digits = 2)
 ```
 
-And if you wanted a one-sided Bayesian $p$-value for the `male` dummy for the full model, you might execute this.
+And if you wanted a one-sided Bayesian $p$-value for the `male` dummy for the full model, you execute something like this.
 
 ```{r}
 posterior_samples(b13.10) %>%
   summarise(one_sided_Bayesian_p_value = mean(b_male <= 0))
 ```
 
+Here's a fuller look at the posterior.
+
+```{r, fig.height = 2.5, fig.width = 6}
+posterior_samples(b13.10) %>% 
+  ggplot(aes(x = b_male, y = 0)) +
+  geom_vline(xintercept = 0, color = "#E8DCCF", alpha = 1/2) +
+  stat_halfeyeh(.width = c(.5, .95),
+                color = "#80A0C7", fill = "#394165") +
+  scale_y_continuous(NULL, breaks = NULL) +
+  xlab("b_male (i.e., the population estimate for gender bias)") +
+  coord_cartesian(xlim = c(-1.5, 1.5)) +
+  theme_pearl_earring()
+```
+
 So, the estimate of the gender bias is small and consistent with the null hypothesis. Which is good! We want gender equality for things like funding success.
 
 ## Reference {-}