Explanation and the quest for ‘significant’ relationships. Part II

In Part I I argue that the search and discovery of statistically significant relationships does not amount to explanation and is often misplaced in the social sciences because the variables which are purported to have effects on the outcome cannot be manipulated.

Just to make sure that my message is not misinterpreted – I am not arguing for a fixation on maximizing R-squared and other measures of model fit in statistical work, instead of the current focus on the size and significance of individual coefficients. R-squared has been rightly criticized as a standard of how good a model is** (see for example here). But I am not aware of any other measure or standard that can convincingly compare the explanatory potential of different models in different contexts. Predictive success might be one way to go, but prediction is altogether something else than explanation.

I don’t expect much to change in the future with regard to the problem I outlined. In practice, all one could hope for is some clarity on the part of the researchers whether their objective is to explain (account for) or find significant effects. The standards for evaluating progress towards the former objective (model fit, predictive success, ‘coverage’ in the QCA sense) should be different than the standards for the latter (statistical & practical significance and the practical possibility to manipulate the exogenous variables).

Take the so-called garbage-can regressions, for example. These are models with tens of variables all of which are interpreted causally if they reach the magic 5% significance level. The futility of this approach is matched only by its popularity in political science and public administration research. If the research objective is to explore a causal relationship, one better focus on that variable and  include covariates only if it is suspected that they are correlated with the outcome and with the main independent variable of interest. Including everything else that happens to be within easy reach not only leads to inefficiency in the estimation. One should refrain from  interpreting causally the significance of these covariates altogether. On the other hand, if the objective is to comprehensively explain (account for) a certain phenomenon, then including as many variables as possible might be warranted but then the significance of individual variables is of little interest.

The goal of research is important when choosing the research design and the analytic approach. Different standards apply to explanation, the discovery of causal effects, and prediction.

**Just one small example from my current work – a model with one dependent and one exogenous time-series variables in levels with a lagged dependent variable included on the right-hand side of the equation produces an R-squared of 0.93. The same model in first differences has an R-squared of 0.03 while the regression coefficient of the exogenous variable remains significant in both models. So we can ‘explain’ 90% of the variation in the first case by reference to the past values of the outcome. Does this amount to an explanation in any meaningful sense? I guess that depends on the context. Does it provide any leverage to the researcher to manipulate the outcome? Not at all.

Explanation and the quest for ‘significant’ relationships. Part I

The ultimate goal of social science is causal explanation*. The actual goal of most academic research is to discover significant relationships between variables. The two goals are supposed to be strongly related – by discovering (the) significant effects of exogenous (independent) variables, one accounts for the outcome of interest. In fact, the working assumption of the empiricist paradigm of social science research is that the two goals are essentially the same – explanation is the sum of the significant effects that we have discovered. Just look at what all the academic articles with ‘explanation’, ‘determinants’, and ’causes’ in their titles do – they report significant effects, or associations, between variables.

The problem is that explanation and collecting significant associations are not the same. Of course they are not. The point is obvious to all uninitiated into the quantitative empiricist tradition of doing research, but seems to be lost to many of its practitioners. We could have discovered a significant determinant of X, and still be miles (or even light-years) away from a convincing explanation of why and when X occurs. This is not because of the difficulties of causal identification – we could have satisfied all conditions for causal inference from observational data, but the problem still stays. And it would not go away after we pay attention (as we should) to the fact that statistical significance is not the same as practical significance. Even the discovery of convincingly-identified causal effects, large enough to be of practical rather than only statistical significance, does not amount to explanation. A successful explanation needs to account for the variation in X, and causal associations need not to – they might be significant but not even make a visible dent in the unexplained variation in X. The difference I am talking about is partly akin to the difference between looking at the significance of individual regression coefficients and looking at the model fit as a whole (more on that will follow in Part II). The current standards of social science research tend to emphasize the former rather than the later which allows for significant relationships to be sold as explanations.

The objection can be made that the discovery of causal effects is all we should aim for, and all we could hope for. Even if a causal relationship doesn’t account for large amounts of variation in the outcome of interest, it still makes a difference.  After all, this is the approach taken in epidemiology, agricultural sciences and other fields (like beer production) where the statistical research paradigm has its origins. A pill might not treat all headaches but if it has a positive and statistically-significant effect, it will still help millions. But here is the trick – the quest for statistically significant relationships in epidemiology, agriculture, etc. is valuable because all these effects can be considered as interventions – the researchers have control over the formula of the pill, or the amount of pesticide, or the type of hops. In contrast, social science researchers too often seek and discover significant relationships between an outcome and variables that couldn’t even remotely be considered as interventions. So we end up with a pile of significant relationships which do not account for enough variation to count as a proper explanation and they have no value as interventions as their manipulation is beyond our reach. To sum up, observational social science has borrowed an approach to causality which makes sense for experimental research, and applied its standards (namely, statistical significance) to a context where the discovery of significant relationships is less valuable because the ‘treatments’ cannot be manipulated. Meanwhile, what should really count – explaining when, how and why a phenomenon happens, is relegated to the background in the false belief that somehow the quest for significant relationships is a substitute. It is like trying to discover the fundamental function of the lungs with epidemiological methods, and claiming success when you prove that cold air reduces significantly lung capacity. While the inference might still be valuable, it is no substitue for the original goal.

In Part II, I will discuss what needs to be changed, and what can be changed in the current practice of empirical social science research to address the problem outlined above.

*In my understanding, all explanation is causal. Hence, ‘causal explanation’ is tautology. Hence, I am gonna drop the ‘causal’ part for the rest of the text.