A post about how, for some causal models, causal relationships can be inferred without doing experiments that control one of the random variables.
If correlation doesn’t imply causation, then what does?
To help address problems like the two example problems just discussed, Pearl introduced a causal calculus. In the remainder of this post, I will explain the rules of the causal calculus, and use them to analyse the smoking-cancer connection. We’ll see that even without doing a randomized controlled experiment it’s possible (with the aid of some reasonable assumptions) to infer what the outcome of a randomized controlled experiment would have been, using only relatively easily accessible experimental data, data that doesn’t require experimental intervention to force people to smoke or not, but which can be obtained from purely observational studies.
The correlation/causation conundrum is a particularly frustrating one in the social sciences due to the complex interaction of variables related to human experience.
I've found looking at time-order and thinking of variables-as-events is a helpful way to simplify experimental design seeking to get at causal mechanisms in my behavioral research.
Take the smoking example:
I would consider measuring changes in strength of correlation at various points in an ongoing experiment.
Once a baseline measurement is obtained from those already smoking subjects/participants, we measure the correlation between avg. number of cigarettes smoked per weak and lung capacity. This way one doesn't have to randomize or control, unethically asking people to smoke if they don't already. We already have a hypothesis based on the prior that volume of cigarettes smoked has a strong positive correlation with lung damage, and so reducing the number of cigarettes smoked would improve lung functioning in smokers.
But here we assume that the lifestyles of the smokers studied are relatively stable across the span of the experiment.
The researcher must take into account mediating factors that could impact lung functioning outside of smoking - i.e Intermittent exercise and lifestyle improvements.
In any case, following the same group of people over time is a lot easier than matching comparison groups by race/age/gender/education, or any of the other million human variables.
It was not clear from this descriptio... (read more)