The asym_laplace has three parameters of interest: location, scale, and quantile (point of interest/evaluation; asymmetry parameter). Apart from the obvious need to set the quantile value, location and scale are typically assumed to be 0 and 1, respectively. Would any other values for those two parameters be meaningful, in particular, if one wishes to define a conservative model? If so, how can this be achieved? Any example would be welcomed.
Thanks!
@striatum hello, in the parameterization used in brms, the location parameter mu for the asymmetric Laplace corresponds to the predicted value of the selected quantile. So the ‘standard’ asymmetric Laplace with location = 0 and quantile = 0.5 is symmetric with its median at 0, whereas with location = 1, it is symmetric but with its median at 1. The coefficients of a simple quantile regression model in brms therefore represent shifts in the location of the selected quantile. You could verify this using the dasym_laplace() function from brms. Priors for parameters influencing location should be fairly simple to set, including weak priors, because they are analogous to priors for the location in linear (Gaussian) models.
In quantile regression applications the scale has no direct interpretation, because generally the asymmetric Laplace is used as a working likelihood (the response is not being proposed to be conditionally asymmetric Laplace distributed); in some implementations the scale parameter is fixed, with some implications for interpreting the posteriors. Good information here (https://doi.org/10.1111/insr.12114).
This is one awesome answer! Thanks!