lognormal.md

Haha so this should have been obvious to me all along, but the results for log_gdpPercap with gaussian() are identical to original gdpPercap with lognormal()

library(tidyverse)
library(gapminder)
library(brms)
library(broom)
library(broom.mixed)
library(modelsummary)

gapminder <- gapminder %>% 
  mutate(log_gdpPercap = log(gdpPercap))

ggplot(gapminder, aes(x = gdpPercap)) + geom_density()

ggplot(gapminder, aes(x = log_gdpPercap)) + geom_density()

# This is all a **super bad** way to model panel data like this, but it's just an example
# Models with lm()
model_ols_original <- lm(gdpPercap ~ lifeExp, data = gapminder)
model_ols_logged <- lm(log_gdpPercap ~ lifeExp, data = gapminder)

# Models with brms
model_brms_original <- brm(bf(gdpPercap ~ lifeExp),
                           data = gapminder, seed = 1234,
                           family = gaussian(), chains = 2)
#> Compiling Stan program...

model_brms_lognormal <- brm(bf(gdpPercap ~ lifeExp),
                            data = gapminder, seed = 1234,
                            family = lognormal(), chains = 2)
#> Compiling Stan program...

# Compare results
modelsummary(list("lm, original outcome" = model_ols_original, 
                  "brms, original outcome" = model_brms_original, 
                  "lm, logged outcome" = model_ols_logged,
                  "brms, original outcome, lognormal family" = model_brms_lognormal),
             coef_omit = "^sd__", gof_omit = ".", output = "markdown")

	lm, original outcome	brms, original outcome	lm, logged outcome	brms, original outcome, lognormal family
(Intercept)	-19277.249	-19314.015	3.543	3.544
	(914.093)	(910.017)	(0.084)	(0.082)
lifeExp	445.445	445.880	0.078	0.078
	(15.020)	(14.987)	(0.001)	(0.001)

^{Created on 2021-02-28 by the reprex package (v0.3.0)}