A positive residual indicates that the observed rate is higher than what the model expected. A negative residual indicates that the observed rate is lower than what the model expected. 

University of Virginia, Charlottesville

Three good interpretative plot models:
1) Predictor residual plots. These plots show the outcome against residual predictor values. They are useful for understanding the statistical model, but not much else.
2) Posterior prediction plots. These show model-based predictions against raw data, or otherwise display the error in prediction. They are tools for checking fit and assessing predictions. They are not causal tools. 
3) Counterfactual plots. These show the implied predictions for imaginary experiments. These plots allow you to explore the causal implications of manipulating one or more variables.


Plotting multivariate posteriors.

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd ed.). Chapman and Hall/CRC.

Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

Positive and Negative Residual

1. Pick a variable to manipulate (the intervention variable)
2. Define the range of values to set the intervention variable to.
3. For each value of the intervention variable, and for each sample in posterior, use
the causal model to simulate the values of other variables, including the outcome.

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