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).

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This is one awesome answer! Thanks!