I’m just working with my first Stan model and I have a question I have not been able to find an answer to. I want to know which of my datapoints have had the most influence/leverage on the posterior. Whenever I find some discussion that touches on the topic of identifying points with high leverage, the focus always seems to be on comparative module evaluation. But I am not interested in evaluating the out-of-sample predictive performance of my model, as I am not using it for making predictions. I just want to introspect the model to understand it.

I guess a naive strategy would to use full-blown LOO-CV to see which datapoints when omitted cause the mean of the posterior to change the most. But I was hoping for a less computationally expensive approach. I have tried using the loo function from Arviz, but the results are not what I hoped for. All of the points have a very low k value (< 0.05), and the ones that the highest values are unstable and change from Stan run to run. I’m not necessarily looking for true outliers that would make this an unreliable model, I just want to know what parts of the data have most leverage on the posterior.

My current tactic is to compute which of the observed datapoints are most improbable according to the full posterior. That is, I take the absolute value of subtracting the observed value for each datapoint from its mean predicted value. This procedure seems to produce sensible results, but I have no idea if it is mathematically justified. My intuitive reason for it is that the most improbable datapoints are the ones that the model will have tried the hardest to accommodate, even while inevitably failing to fit them well. Does that make sense?

Before I go ahead and use LOO-CV to re-fit my model 1,000 times, can anyone suggest a more efficient and mathematically justified procedure?

Thanks!

Peter