This box continues with the Low et al. example starting in Box 2.2

Preliminaries

Use rstanarm and BayesFactor packages; also needs bayestestR Add bayesplot for control over plot

Load graphics packages (if ggplot version of figures wanted)

Note that iso is reference group so diff between means is -ve

Uninformative priors

low <- read_csv("../data/lowco2.csv")
Rows: 23 Columns: 2── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): anesth
dbl (1): co2
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
low1 <- stan_glm(co2~anesth,family = gaussian(link = "identity"),data=low)

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posteriors1 <- describe_posterior(low1)
print_md(posteriors1, digits = 2)
Summary of Posterior Distribution
Parameter Median 95% CI pd ROPE % in ROPE Rhat ESS
(Intercept) 70.77 [ 60.98, 80.89] 100% [-1.91, 1.91] 0% 1.000 3659.00
anesthiso -20.68 [-34.88, -7.00] 99.80% [-1.91, 1.91] 0% 1.000 3267.00 
# plot posterior distribution for all three parameters (intercept, mean diff, sigma)
plot(low1,plotfun="mcmc_hist")

# get Bayes factor for mean diff
lowx <- as.data.frame(low)
lmBF(co2~anesth, data=lowx,posterior=FALSE)
Bayes factor analysis
--------------
[1] anesth : 8.039109 ±0%

Against denominator:
  Intercept only 
---
Bayes factor type: BFlinearModel, JZS

Informative priors

Run three options, mean difference with high and low precision, and a bigger mean difference with high precision

#for mean difference with high precision
low2 <- stan_glm(co2~anesth,family = gaussian(link = "identity"),prior=normal(-25,5),data=low)

SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
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posteriors2 <- describe_posterior(low2)
print_md(posteriors2, digits = 2)
Summary of Posterior Distribution
Parameter Median 95% CI pd ROPE % in ROPE Rhat ESS
(Intercept) 72.30 [ 63.82, 80.40] 100% [-1.91, 1.91] 0% 1.000 3049.00
anesthiso -23.68 [-31.37, -15.78] 100% [-1.91, 1.91] 0% 1.000 3407.00 
# informative prior for mean difference with low precision
low3 <- stan_glm(co2~anesth,family = gaussian(link = "identity"),prior=normal(-25,20),data=low)

SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
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posteriors3 <- describe_posterior(low3)
print_md(posteriors3, digits = 2)
Summary of Posterior Distribution
Parameter Median 95% CI pd ROPE % in ROPE Rhat ESS
(Intercept) 71.23 [ 61.36, 81.29] 100% [-1.91, 1.91] 0% 1.000 3412.00
anesthiso -21.67 [-34.70, -8.40] 99.85% [-1.91, 1.91] 0% 1.000 3497.00 
# informative prior for bigger mean difference with high precision
low4 <- stan_glm(co2~anesth,family = gaussian(link = "identity"),prior=normal(-50,5),data=low)

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posteriors4 <- describe_posterior(low4)
print_md(posteriors4, digits = 2)
Summary of Posterior Distribution
Parameter Median 95% CI pd ROPE % in ROPE Rhat ESS
(Intercept) 82.00 [ 72.44, 91.80] 100% [-1.91, 1.91] 0% 1.000 2229.00
anesthiso -41.93 [-51.43, -32.93] 100% [-1.91, 1.91] 0% 1.000 2596.00

Generate ggplot-compatible figure for mean difference posterior distribution

posterior<-as.array(low1)
color_scheme_set("gray")
p<-mcmc_hist(posterior, pars = c("anesthiso"))+
  xlab("Mean difference")
p

# ggsave ("QK F2_07.pdf", plot = p, height = ph, width = pw, units='cm')
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