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Estimated "true" repertoire as a predictor

Thanks for yet another instructive case study, Richard.

I was thinking whether there's a way to extend the example such that the estimated "true" repertoire size is used as a predictor in another model.

For instance, we might imagine a dataset composed of species (instead of individuals). Say we're interested in repertoire size and brain size at the level of species. However, the observed behavioral repertoire of any given species is always an imperfect measure; ideally, we'd want to estimate the "true" repertoire size (perhaps as a function of other variables, e.g. observed repertoire size, research effort, phylogeny, habitat, etc.) and plug that estimate (and uncertainty) in our outcome model predicting brain size.

It seems conceptually linked to the measurement error and missing data models that are so neatly explained in Statistical Rethinking, although repertoire size is an integer and therefore would require a different computational approach from Gaussian variables.

Best wishes

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