Using WAIC to compare models

gistfile1.txt

# The example below shows why WAIC could be useful when studies are underpowered. 
# Here we simulate data with a weak polynomial relationship between x an y, with 
# only a small sample. Although the effect of the polynomial term does not reach 
# conventional standards for statistical significance, comparing WAIC (an estimate 
# of how effective each model will be at predicting new, out-of-sample data) indicates 
# we should assign a higher probability that `m2` is 'correct', when compared with `m1` 
# (more than twice as likely).


library(rethinking)
library(ggplot2)
library(dplyr)


set.seed(123)
multix <- data_frame(
  x=rnorm(50),
  y = rnorm(50) + x + .15*x^2
)

ggplot(multix, aes(y=y,x=x))+geom_point()+geom_smooth()

mx.1 <- lm(y~x, data=multix)
mx.2 <- lm(y~x+I(x^2), data=multix)

anova(mx.2)
compare(mx.1, mx.2)

plot(compare(mx.1, mx.2))