Is there a way to use
projpred while accounting for measurement uncertainty in the dependent variable (e.g., target variable)?
I have a pretty simple linear model I’m looking to do some variable selection on. One issue, though, is my dependent expresses measurement error that is heteroskedastic with some other variable. That is, my "observed " dependent is conditionally distributed based on the “true” dependent value and some variable “w”, such that:
y_true ~ normal(y_obs, b0 + b1 / w).
My initial desire was to take advantage of the built-in compatibility between
rstanarm or possibly
brms. However, I do not see an obvious way of accounting for measurement error in any of those packages. But perhaps I’m missing some set of functionality, or don’t know what key words to use to properly search the documentation.
I was then looking into the custom reference model functionality provided by
projpred::init_refmodel. This looked promising at first, but upon closer inspection it appears that the argument
y is static (i.e., the target variable is assumed to be perfectly measured or known). Am I interpreting this argument correctly?
Anyone know of a way of addressing measurement uncertainty in the context of