Comparing LOOIC when one covariate has missing data

Modeling
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1

Hello,

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.

Thanks~

2

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.
1 Like
3

Very helpful! Thanks Jacob :)