Getting adjusted estimates from a Bayesian regression model

Modeling
1

Can you please confirm that my following understanding is correct about getting adjusted estimates from a Bayesian regression model?

Model
m = y ~ continuous_predictor + categorical_predictor

And I am interested in getting the effect of the continuous predictor on y while adjusting/fixing the value of the categorical predictor.

Frequentist vs Bayesian

  • In frequentist regression analysis, I can do predictions from the model while fixing only one level of the categorical predictor at a time? E.g. the continuous predictor’s effect on y are shown at the level A of the categorical predictor.
  • In contrast, in Bayesian approach, I can do predictions from the model while fixing all levels of the categorical predictor at a time (newdata argument is specified in a way that all categorical predictor’s levels are included). E.g. the continuous predictor’s effect on y are shown while adjusted to all levels of the categorical predictor simultaneously. Or in other words, the predicted posterior object includes all the categorical predictor values. And finally, Bayesian predictions can be also done similarly to the frequentist approach.
2

If I understand you correctly, your understanding what is possible in Bayesian analysis, and how that differs from frequentist analysis, is incorrect.

Since you do not have an interaction in your model, the effect of continuous_predictor on the linear predictor will be the same for any level of categorical_predictor in both the frequentist and the Bayesian analysis. If your model uses an identity link (for example if it’s a traditional linear model with Gaussian error), that also means that continuous_predictor's effect on y is the same for any level of categorical_predictor. If your model is a GLM with a link other than identity, then the effect of categorical_predictor on y will depend on categorical_predictor in both the frequentist and Bayesian analysis.