# Causal Speculation: A Meditation on Theory

In a post late last year on correlation and causality I touched on the role theory plays in making causal inferences. Specifically, I indicated that a causal inference cannot be made from the analysis of data from an observational study without a theoretical model. If conclusions of causality rely on theory, where does the theory come from? Fundamentally, how do we know when something causes another?

Before addressing those questions, let’s clarify the issues with a hypothetical example. Suppose physicians begin to notice that males who eat a particular exotic beetle of Zimbabwe also have no hair loss, independent of age. There are precisely four possibilities:

1. the observations are coincidental,
2. consumption of such beetles (causally) prevents hair loss,
3. lack of hair loss (causally) leads to consumption of the beetles,
4. beetle consumption and lack of hair loss are both jointly caused by something else.

Each of these possibilities is essentially a theory about the world, and each implies something about the causal relationship (or lack thereof) between beetle consumption and hair loss. Theories 1-3 are relatively simple since the causality implied only runs at most one way. Theory 4 is the source of many problems. Even when there is strong evidence in support of theories 2 or 3, one can never fully rule out theory 4. “Something else” could be anything.

That’s essentially why causal inferences cannot be made from correlations (or statistical analysis) alone. One needs to put a fence around the problem and assert that only the factors one has considered, measured, and included in the analysis are relevant, that there is no “something else” left out. With that assertion one can make causal inferences from statistical models and correlations (assuming the correct application of appropriate technique).

Where does this assertion that all relevant factors have been considered come from? Its origin is outside the data, outside the analysis. It is extra-empirical. Put simply, it is theory, a hypothesis about the nature of causality in the world that can be rejected, but never fully confirmed by the data. Without it no causal inference can be made no matter the quality of the data or what is done with it.

Where do causal theories–the fences around problems–come from? Why do we believe that x causes y and not vice versa or that some other factor z causes both? These questions are puzzling because all our experience is empirical yet theory stands outside the data.

Perhaps theory comes from extrapolation from the subset of our experience that is exactly like or darn near a randomized trial (either explicitly so or due to a natural experiment that makes it close enough)? If the “cause” seems random we’re comfortable inferring that it is responsible for much of what seems to “result.” No doubt this is hard-wired into our brains, a consequence of evolution. For example, “See lion eat chief. See lion again, run!”

But such causal inferences are formed quickly and easily can be wrong. Moreover, we frequently hold mutually exclusive causal ideas in our brains at the same time. The role of  theory is to force us to organize our causal ideas, to be explicit, and to iron out logical inconsistencies. Then we go to the data to test the theory.

It is tempting to believe that the world can be understood from data alone, that if x causes y we should not need theory to tell us so. Evidently that is not the case, at least insofar as observational studies are concerned. Observational methods comprise a great deal of science and, in far less rigorous form, most of our experience. This leads to a version of the anthropic principle: we can’t exist without theory (nor, I assert, could many animals). A world in which humans don’t rely on theory would be one in which humans, as we know them, do not exist.