How does rstanarm handles ordered predictors?

Developers
,
1

I’m confused about the behavior of rstanarm when you specify a formula where a predictor is of class "ordered" "factor". Here’s an example :

# Simulate data
n <- 100
y <- rnorm(n)
x_cont <- sample(1:5, n, replace = TRUE)
x_fac <- factor(sample(1:5, n, replace = TRUE))
x_ord <- ordered(sample(1:5, n, replace = TRUE))

data <- data.frame(y = y, x_cont = x_cont, x_fac = x_fac, x_ord = x_ord)

# Model
fit <- stan_lm(y ~ x_cont + x_fac + x_ord, data, prior = R2(0.5, "mode"))
print(fit, digits = 2)
stan_lm
 family:       gaussian [identity]
 formula:      y ~ x_cont + x_fac + x_ord
 observations: 100
 predictors:   10
------
            Median MAD_SD
(Intercept)  0.20   0.30 
x_cont      -0.02   0.06 
x_fac2      -0.28   0.31 
x_fac3       0.18   0.31 
x_fac4      -0.14   0.33 
x_fac5      -0.53   0.30 
x_ord.L      0.03   0.25 
x_ord.Q     -0.25   0.22 
x_ord.C      0.09   0.20 
x_ord^4      0.38   0.20 

Auxiliary parameter(s):
              Median MAD_SD
R2            0.14   0.05  
log-fit_ratio 0.03   0.07  
sigma         0.96   0.07  

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Looking at the posterior_vs_prior(fit, pars = "beta") plot, it looks like the effect parameters of the unordered parametrization are given wider prior distributions and I can’t figure out why.