expanded estimates (standardized) for categorical variables in quantile regression (a work around like in OLS?)

[#1]

I'm looking for a way to produce expanded estimates (standardized betas) for two categorical variables in a quantile regression. In OLS, standardizing all continuous predictors and the outcome first, then using the "expanded estimates" dropdown works great, and produces almost the exact same results as right-clicking on the original "parameter estimates" for "Std Beta" after simply switching out the reference level for the categorical variables, one-by-one. 

However, using this work around (switching out the reference level) in quantile regression gives me very different results for the categorical variables. And there is no "expanded estimates" option in quantile regression platform that I can find. Not being able to get that expanded estimate is a drag for constructing quantile process plots to compare with the OLS plots, as the former is missing two entire levels of the categorical variables. I'm suspecting that it can't be done b/c of the effects coding of categorical variables that jmp uses? Or, simply due to the type of regression differences (OLS vs quantile)? I'm new to quantile regression (yes, I have to use it here). But if expanded estimates for categorical variables are not impossible to produce here, does anyone know how? A work around?

[#2 · Accepted solution]

The reason that expanded estimates are available in Fit Least Squares but not in Generalized Regression has to do with the different way that the same linear predictor is parameterized by each platform. Each level of a categorical factor is represented by a parameter in the model. JMP automatically creates these parameters when a categorical factor is entered as a term in the model.

Fit Least Squares uses effect coding, in which the sum of the estimates must equal zero. So the estimate of the parameter of the last level k must equal the negative of the sum of the first k-1 estimates. JMP traditionally does not show this level because it is constrained, not estimated.

GenReg uses a different parameterization. in which the last level is the reference and set to zero. This parameterization is advantageous for model selection techniques.

[#3]

Excellent. Thanks for the explanation