Causal inference I - Regularity and time perspectives by Darko Medin

In this article, Regularity theories for causal associations are discussed. Many such theories are established by different authors such as May, M & Gra?hoff, G (2001) or Mackie, J. L (1980).

Discussing this from a Statistical and Data Science perspective is very important as regularity perspective may help interpretation in today's Science, especially in Research and Development.

So here are my perspectives:

Starting with the notion that causes and effects (lets call them A and B) are associated in a specific nature where every time there is a a cause present, there should be an effect present is the main dogma in most of these theories. This does makes sense to me in the following way:

This means that mostly the cause is preceding the effect, and there where we all agree. However, i believe that the cause and effect can happen at the same time or nearly same time. Time scale is obviously from 0 to infinity, but there is no reason to drop 0 for me.

For an example lets say the delta t between cause and effect is >0 and the causal strength is 100%.

Here is a representation showing how regularity would be seen from a time series visual perspective:

There is actual a fantastic work and angle on this called Granger causality test [3], where a hypothesis test is proposed to actually testf the causality is there. obviously in any such approach its logical to look for the time aspect and the similarity of the patterns between the potential cause and effect time series variables.

However its difficult to really for this to hold in all situations. And there are also event which are regularly co-occurring, so, differentiating them from the direct causal association is another problematic aspect of this approach.

If the co-occurrence present, then there is third causative variable C in theory can cause both A and B and also cause them to be 100% correlated and have 100% regularity eventough these is not direct causal relation between them.

So this situation is problematic from a standpoint of identifying causality via regularity and tells us that the regularity alone in any of those theories is not enough to imply causality.

This is where the counter factual design comes into play. Counterfactual theories of Causality will be the theme of the next article on Causality in the series. Thank you for reading!

References :

1. May, Michael & Gra?hoff, Gerd (2001). Causal regularities. In Wolfgang Spohn, Marion Ledwig & Michael Esfeld (eds.), Current Issues in Causation. Mentis. pp. 85.

2. Mackie, J. L., 'Causal Regularities', The Cement of the Universe: A Study of Causation, Clarendon Library of Logic and Philosophy (Oxford, 1980; online edn, Oxford Academic, 1 Nov. 2003), https://doi.org/10.1093/0198246420.003.0004

3. ?Granger, C. W. J. (1969). "Investigating Causal Relations by Econometric Models and Cross-spectral Methods". Econometrica. 37 (3): 424–438. doi:10.2307/1912791. JSTOR 1912791.