weird bias in intercept estimation in JASP

Comments

• vandenman

  October 28

  Hi Nitzan,

  
  

  The Bayesian model uses a centered design matrix. So rather than y ~ intercept + b*x it does y ~ intercept * b * (x - mean(x)). This does not affect statistical significance but it does change the interpretation of the parameters. Specifically, the intercept models the overall mean of y instead of that of the reference category. If I center group_dummy with the R code `group_dummy - mean(group_dummy)` I get very similar results:

  

  Hope that helps!

  Don
• patc3

  October 28

  the difference between -29.402 and -24.435 is still very large no?
• vandenman

  October 29

  That's expected shrinkage due to both the parameter prior and the model prior. If you pick the priors "just right" then you can make the two approaches produce more or less identical results:

  

  Note, however, that this is a terrible thing to do. The shrinkage in the Bayesian parameter estimates reflects the uncertainty in the models and the possibility that the effect is absent. With the original more sensible prior setting we roughly get 0.908 * 29.402 + 0.1 * 0.0 = 26.697. The remaining shrinkage is due to the prior on the parameter.