Estimation of scale parameter of standardized outcome in linear regression

Hi all,

I’m a big fan of pymc3 for parameter estimation in different kinds of regression models. In a situation in which:

  • a normally-distributed outcome variable has been z standardized (mean=0, sd=1), and
  • a linear model with dummy-coded categorical predictors describes the mean of the outcome distribution,
    is there any reason why one should or should not estimate the sd of the outcome distribution? We’re interested in pymc3’s take on the relative influence of each category on the mean, so we estimate that even though we know the grand value already? But why estimate the sd value that we already know?

I’ve seen the sd estimation done a few times in others’ models, clearly I’m missing something! See for one pymc3 example.