Centering covariates before estimating varying coefficients

For most of my Stan models, I typically center and scale the covariates (dividing by two SDs) before fitting the model. More recently, I have taken to centering and scaling the covariates within Stan, which makes it easy to extract the posterior of the coefficients on both the standardized and unstandardized scales (using generated quantities).

I’m relatively new to specifying varying-coefficient models in Stan. My question: is there any advantage to centering and scaling the covariates if I am going to allow them to have (correlated) varying coefficients, where the prior is specified using lkj_corr_chelesky (following section 1.13 of the Stan user’s guide)?

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Parameter scales are distinct from correlation (a correlation matrix is a covariance matrix with the scales divided out – I’d expect that if scaling helped with your previous model it would also help here.