Collider Bias - when you condition on a collider, it creates statistical - but not necessarily causal associations among its causes. 
Relationship between trustworthiness, worthiness and selection

Collider Bias

Omitted Variable Bias - missing variables that could affect the experiment
Included Variable Bias - including variables that could affect the experiment
Post-treatment Bias - example of included variable bias, pg 171 example

Post-treatment bias

University of Michigan - Ann Arbor

Below are some of the potential issues when adding variables to a regression model without a clear idea of the causal model - 

- Multicollinearity
- Post-Treatment Bias
- Collider Bias
- How  to recognize and prevent these confounding issues

Perils of Multiple Regression

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)

Multicollinearity = Very  strong correlation between two or more predictor variables. 

- As a result the posterior distribution will appear to suggest that none of the variables are reliably  associated with the outcome - when in fact they might be strongly associated with the outcome.
- The model will still have accurate predictions, but interpreting it will lead to confusion.  You wont be able to determine the actual effect of the variables on the outcome. 

- See next node for an example 

Solutions:
- Identifying highly correlated variables, eliminating all but one
- Combining them into one variable
- However, it is best to take a causal approach -  to determine conditional associations, and not just correlations. 

Multicollinearity 

Bias in Multiple Regression

- Confounding is defined as any context where the association between an outcome and a predictor of interest is different from the association we would get if we had experimentally determined the values of the predictor. 
- Multiple regression and confounding develop a relationship where multiple regression can be used to deal with confounding, however, if you controlling for the wrong variables ruins the inference of a multiple regression; multiple regression causes the confounding. 

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