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Natural Experiments and Instrumental Variables Estimation
Now we consider the problem of measuring the strength of causal effects in the presence of confounding variables. As an example, let X be whether a person is a veteran and Y be their income.
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Common Effects and Selection Bias
In the last post we looked at causal effects based on intermediate causes and common causes, both of which introduce a correlation that goes away when the “middle” variable is conditioned on.
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Intermediate and Common Causes
We’ll continue with our example of the relationship between IQ (X) and income (Y). We’ll set aside models B (income causes IQ) and C (no relationship) and compare our model A (IQ causes income) with two new models D and E that include a third variable of years in school (Z).
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Causal Networks
As we discussed in the last post, Bayesian networks can often be written in multiple equivalent ways by reversing some of the arrows. Generally the most natural choice has arrows matching the causal direction of the effects.
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Bayesian Networks
I’ve found the concept of causal models as described in e.g. Pearl’s Causality 2009 to be a very useful tool for statistical thinking. This is the beginning of a series of posts introducing the concept and its applicability.
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