Comparing LOOIC when one covariate has missing data


I am wondering if LOOIC can be used to compare models when one model has a covariate with some missing data, and the other doesn’t.


LOO requires that you be able to compute the posterior predictive density over all of the points under comparison. To compare your models, you have (at least) three options:

  1. Fit the model with missingness using some form of parametric model-based missing data imputation, and use the full model (including the imputation model) to predict at those data points (but beware that PSIS-LOO is likely to fail for those observations and may require re-fits).
  2. Use some sort of non-parametric imputation scheme to fit the model with missingness, and then compare only over the points for which you are able to make model-based predictions (i.e. the ones without missingness).
  3. Use only the points without missingness in both model fitting and model comparison.
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Very helpful! Thanks Jacob :)