bayes_factor: Bayes Factor
In manschmi/blmr: Bayesian Linear Regression

Description Usage Arguments Details Examples

Computes the Bayes factor for comparison of 2 blm objects.

1	bayes_factor(model1, model2)

`model1`	first `blm` object
`model2`	second `blm` object

Returns the ratio of the probability of model1 divided by the probability of model2. A value of K > 1 means that M1 is more strongly supported by the data under consideration than M2 (https://en.wikipedia.org/wiki/Bayes_factor). Wikipedia mentions additional scales for interpretation, ie by Harold Jeffreys:

K < 1: supports model2
K > 10: strong support for model1
K > 100: decisive support for model1

. An alternative table, widely cited, is provided by Kass and Raftery.

K 1-3: not worth more than a bare mention
K 3-20: positive support for model1
K 20-150: strong support for model1
K >150: very strong support for model1

set.seed(1) 
x <- seq(-10,10,.1) 
b <- 0.3

w0 <- 0.2 ; w1 <- 3 ; w2 <- 10

y <- rnorm(201, mean = w0 + w1 * x + w2 *sin(x), sd = sqrt(1/b)) 
mod1 <- blm(y ~ x + sin(x))

pblm(mod1) ## -886.4801 this is the log-probability (log=TRUE by default)

#another model removing the sinus term 
mod2 <- blm(y ~ x)

pblm(mod2) ## -891.0581 
bayes_factor(mod1, mod2) #97.31074 #strong support for mod1 over mod2

mod3 <- blm(y ~ x + 0)
pblm(mod3) ## -891.842
bayes_factor(mod1, mod3) #213.128 #very strong support for mod1 over mod3