N(0, 10) is reasonable for alpha
. Cutpoints are assumed known so there’s no prior on c
.
The exact position of cutpoints is irrelevant as long as the prior on alpha
is vague.
The spacing between cutpoints (let’s call it s
) does two things
- the interpretation of
beta
is thatbeta/s
is the expected difference in y betweentheta=0
andtheta=1
individuals. - The probability assigned to a predicted y value is at most
(exp(s)-1)/(exp(s)+1)
The first effect could (and probably should) be removed by using alpha+s*beta*theta
instead of alpha+beta*theta
as the predictor.
If you think s=1
is too strong an assumption you can make s
a parameter
...
parameters {
real<lower=0> s[j];
...
}
transformed parameters {
vector[k-1] c1 = s[1] * c;
vector[k-1] c2 = s[2] * c;
...
}
s
needs an informative prior, maybe lognormal(0, 0.5)
.