Has anyone settled on a fast/simple approach to comparing models from lm to models from rstanarm? I am interested specifically in justifying selecting a model with shrunken coefficients over the seemingly incredible estimates offered by lm in this case. So far I have just specified a model in rstanarm with vague enough priors that the estimates are similar to OLS and then compared using loo and predictive checks but I wondered if there is something more simple/justifiable?
loo is the simplest justifiable thing we know of
And I’m not missing some super obvious way to use the output of lm in loo? I.e. it makes sense to you to compare against a rstanarm model that gives approximately the same coefficients?
loo requires MCMC output. You can obtain a posterior distribution (conditional on y) that is the same as the sampling distribution of the OLS estimator (integrated over y) with something like
Then use those draws of beta and sigma to create a matrix of log-likelihoods to pass to loo.
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Thanks. I feel like you should invoice me after today.