Converting back to unstandardized metric

General
#1

Dear all,

I am very new to brms and Bayesian inference. My end goal is to develop a nominal categorical hierachical model. I am currently playing around with a simple model that has 3 categories. It is a model with an intercept and a single predictor:

\begin{aligned} &\phi_k = \text{softmax}(\{\lambda^{(k)} \})\text{ , k=1,2,3} \\ &\lambda^{(k)} = \beta_{0,k} + \beta_{1,k}x\\ &\lambda^{(1)} = 0 \\ &\lambda^{(2)} = \beta_{0,2} + \beta_{1,2}x \\ &\lambda^{(3)} = \beta_{0,3} + \beta_{1,3}x \\ &\beta_{0,2} \sim \mathcal{N}(0,10) \\ &\beta_{0,3} \sim \mathcal{N}(0,10) \\ &\beta_{1,2} \sim \mathcal{N}(0,10) \\ &\beta_{1,3} \sim \mathcal{N}(0,10) \\ \end{aligned}

The first category serves as the reference category. I have standardized my predictor (mean = 0, sd = 1) and would like to know how I can recover the brms estimates on the original, unstandardized metric scale (is there some sort of built-in function that can do this)? I understand that I can convert them manually by utilizing a relationship outlined in the “Doing Bayesian Data Analysis” textbook (2nd edition, page 624-625), also outlined in Solomon Kurz’s bookdown (Right before section 21.2), and looks something like this:

\begin{aligned} \text{logit}(\mu) = \zeta_0 - \underbrace{\sum_{j}\frac{\zeta_j}{s_{x_j}}\bar{x_j}}_{\beta_0} + \underbrace{\sum_{j}\frac{\zeta_j}{s_{x_j}}{x_j}}_{\beta_j} \end{aligned}

However, the above method might get a little tedious and complicated when considering a hierarchical structure to the model later on. Can anyone help me with this ? Your suggestions and guidance will be very much appreciated ! Please do let me know if I have been unclear in my description, I will try my best to clarify.

Clyde