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I guess we will need special submodel fitters for this (or at least adapt the currently available ones), so that the observation-specific dispersion parameter values are taken into account when performing the projection.
This is a feature request to allow the dispersion parameter to be observation-specific, as, for example, in models like the following:
This came up in https://discourse.mc-stan.org/t/accounting-for-measurement-error-during-variable-selection-with-projpred-possibly-with-rstanarm-or-brms/11789.
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