Understanding fitted function in binomial model about statistical_rethinking_with_brms_ggplot2_and_the_tidyverse HOT 5 CLOSED

For reference, Paul addressed the question here.

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If I follow, it seems like you’re asking about the distinction between predict() and fitted(). From the predict subsection of the brms reference manual:

Predict responses based on the fitted model. Can be performed for the data used to fit the model (posterior predictive checks) or for new data. By definition, these predictions have higher variance than predictions of the fitted values (i.e., the ’regression line’) performed by the fitted method. This is because the measurement error is incorporated. The estimated means of both methods should, however, be very similar.

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Thanks for your reply! I understand that, in the case of a linear regression model, the measurement error is incorporated via the sigma value, i.e. N(mu, sigma). In the case of the binomial model, do you know where this measurement error is coming from?

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It's been a bit since I've updated them, but you might also look at my vignettes on how to work with fitted() and predict(). I stick to the Gaussian, but the vignettes might still clarify the distinction, here.

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Ah. Okay. I see what you're saying. My math stats isn't strong enough to give you a satisfying answer. My sense is that in this situation you might think of it as simulation variance.

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