- Hierarchical, random effects, varying effects, or mixed effects model 
- Models with lots of levels of uncertainty 
- Help with overfitting through partial pooling 
- Should be the primary regression model used

University of Michigan - Ann Arbor

- Bayesian data analysis
- Model comparison and prediction
- Multilevel models
- Graphical causal models

Tools for Golem Engineering


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)

- Use probability distributions to logically process information 
- Involves the frequentist approach – imaginary resampling of data means that if we were to take the same measurements several times, we would observe a pattern
- Note: only measurements have probability distributions (parameters and models do not)

Bayesian data analysis

Multilevel models

- Wind and branches example: it’s logical to conclude that the branches are swaying because of the wind, but that is not necessarily the causal relationship 
- Need to dig further to find causation because correlation does not imply causation 
- Models that are not accurate causally could still be better predictions than models that are casually correct because making correct predictions does not necessarily rely on having identified the specific cause 
- Directed acyclic graph (DAG) for making causal inferences; an example of a graphical causal model that can be used for causal hypotheses

Graphical causal models

- Compare models through cross validation and information criteria to determine the predictive accuracy and tendency for overfitting, in addition to highlighting any observations that are exerting significant influence to the model 
- Overfitting: simple models may lead to more accurate predictions than more complicated models

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