Logistic regression with partially ordered parameters

Modeling
1

Hi there,

I’m currently trying to model a logistic regression where parts of the parameters are known to be ordered, while others are not, i.e. \theta_5 < \theta_6 < \theta_7, and \theta_8 < \theta_9, while for the other parameters, there is no ordering. How can I model this with Stan?

Thanks in advance, Tim

2

Sorry this took so long to answer. It’s hard to answer in general, but I can show you how to code the specific instance you asked about:

data {
  int<lower=9> N;
}
parameters {
  ordered[3] theta567;
  ordered[2] theta89;
  vector[N - 5] theta_other;
}
transformed parameters {
  vector[N] theta;
  theta[1:4] = theta_other[1:4]
  theta[5:7] = theta567;
  theta[8:9] = theta89;
  theta[9:] = theta_other[5:];
}

It may be easier to consider with scalars as it’s easier to add upper bounds as well as lower bounds.

parameters {
  real theta5;
  real<lower=theta5> theta6;
  real<lower=theta6> theta7;
  real theta8;
  real<lower=theta8> theta9
  vector[N - 5] theta_other;
}

There’s only so far you can go in describing partial orders this way, though.

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