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Tag: causal inference

Correlation does not imply causation. Then what does it imply?

‘Correlation does not imply causation’ is an adage students from all social sciences are made to recite from a very early age. What is less often systematically discussed is what could be actually going on so that two phenomena are correlated but not causally related. Let’s try to make a list: 1) The correlation might be due to chance. T-tests and p-values are generally used to guard against this possibility. 1a) The correlation might be due to coincidence. This is essentially a variant of the previous point but with focus on time series. It is especially easy to mistake pure noise (randomness) for patterns (relationships) when one looks at two variables over time. If you look at the numerous ‘correlation is not causation’ jokes and cartoons on the internet, you will note that most concern the spurious correlation between two variables over time (e.g. number of pirates and global warming): it is just easier to find such examples in time series than in cross-sectional data. 1b) Another reason to distrust correlations is the so-called ‘ecological inference‘ problem. The problem arises when data is available at several levels of observation (e.g. people nested in municipalities nested in states). Correlation of two variables aggregated at a higher level (e.g. states) cannot be used to imply correlation of these variables at the lower (e.g. people). Hence, the higher-level correlation is a statistical artifact, although not necessarily due to mistaking ‘noise’ for ‘signal’. 2) The correlation might be due to a third variable being causally related to the two correlated variables we observe. This is the well-known omitted…

Is unit homogeneity a sufficient assumption for causal inference?

Is unit homogeneity a sufficient condition (assumption) for causal inference from observational data? Re-reading King, Keohane and Verba’s bible on research design [lovingly known to all exposed as KKV] I think they regard unit homogeneity and conditional independence as alternative assumptions for causal inference. For example: “we provide an overview here of what is required in terms of the two possible assumptions that enable us to get around the fundamental problem [of causal inference]” (p.91, emphasis mine). However, I don’t see how unit homogeneity on its own can rule out endogeneity (establish the direction of causality). In my understanding, endogeneity is automatically ruled out with conditional independence, but not with unit homogeneity (“Two units are homogeneous when the expected values of the dependent variables from each unit are the same when our explanatory variables takes on a particular value” [p.91]). Going back to Holland’s seminal article which provides the basis of KKV’s approach, we can confirm that unit homogeneity is listed as a sufficient condition for inference (p.948). But Holland divides variables into pre-exposure and post-exposure before he even gets to discuss any of the additional assumptions, so reverse causality is ruled out altogether. Hence, in Holland’s context unit homogeneity can indeed be regarded as sufficient, but in my opinion in KKV’s context unit homogeneity needs to be coupled with some condition (temporal precedence for example) to ascertain the causal direction when making inferences from data. The point is minor but can create confusion when presenting unit homogeneity and conditional independence side by side as alternative assumptions for inference.

Inspiring scientific concepts

EDGE asks 159 selected intellectuals What scientific concept would improve everybody’s cognitive toolkit? You are welcome to read the individual contributions which range from a paragraph to a short essay here. Many of the entries are truly inspiring but I see little synergy of bringing 159 of them together. Like in a group photo of beauty pageant contenders, the total appeal of the group photo is less than sum of the individual attractiveness of its subjects. But to my point: It is remarkable that so many of the answers (on my count, in excess of 30) deal, more or less directly, with causal inference. What is even more remarkable is that most of the concepts and ideas about causal inference mentioned by the worlds’ intellectual jet-set (no offense to those left out) are anything but new. Many of the ideas can be traced back to Popper’s The Logic of Scientific Discovery (1934) and Ronald Fisher’s The Design of Experiments (1935). So what is most remarkable of all is how long it takes for these ideas to sink-in and diffuse in society. Several posts focus on the Popperian requirement for falsifiability (Howard Gardner, Tania Lombrozo) and skeptical empiricism more generally (Gerald Holton). The scientific method is further evoked by Richard Dawkins on the double-blind control experiment (see also Roger Schank), Brian Knutson on replicability, and Kevin Kelly the virtues of negative results. Mark Henderson advocates the use of the scientific method outside science (e.g. policy) – a plea that strikes a chord with this…