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Causal Inference and Direct Effects

Pearl’s Graph Surgery and Jouffe’s Likelihood Matching Illustrated with Simpson’s Paradox and a Marketing Mix Model

To this day, randomized experiments remain the gold standard for generating models that permit causal inference. In many fields, such as drug trials, they are, in fact, the conditio sine qua non. Without first having established and quantified the treatment effect (and any associated side effects), no new drug could possibly win approval. This means that a drug must be proven in terms of its causal effect and hence the underlying study must facilitate causal inference.

However, in many other domains, such controlled experiments are not feasible, be it for ethical, economical or practical reasons. For instance, it is obvious that the federal government could not create two different tax regimes in order to evaluate their respective impact on economic growth. For lack of such experiments, economists have been traditionally be constrained to studying strictly observational data and, although much-desired, causal inference is much more difficult to carry out on that basis. Causal inference from observational studies typically requires an extensive range of assumptions, which may or may not be justifiable depending on one’s viewpoint. Being subject to such individual judgement, it should not surprise us that there is widespread disagreement among economic experts and government leaders regarding the effect of economic policies.

While economists and social scientists have been using observational data for over a century for policy development, the business world has only recently been discovering the emerging potential of “big data” and “competing on analytics.” As these terms are becoming buzzwords, and are rightfully expected to hold great promise, the strictly observational nature of most “big data” sources is often overlooked. The wide availability of new, easy-to-use analytics tools may turn out to be counterproductive, as observational versus causal inference are not explicitly differentiated. While the mantra of “correlation does not imply causation” remains frequently quoted as a general warning, many business analysts would not know under what specific conditions it can be acceptable to derive a causal interpretation from correlation in observational data. Consequently, causal assumptions are often made rather informally and implicitly and thus they typically remain undocumented. The line between association and causation often becomes further blurred in the eyes of the end users of such research. Given that the concept of causality remains ill-understood in many practical applications, we seriously question today’s real-world business capabilities for deriving rational policies from the newly-found “big data.”

With these presumed shortcomings in business practice, it is our objective to provide a framework that facilitates a much more disciplined approach regarding causal inference while remaining accessible to (non-statistician) business analysts and transparent to executive decision makers. We believe that Bayesian networks are an appropriate paradigm for this purpose and that the BayesiaLab software package offers a robust toolset for distinguishing observational and causal inference.

 

Overview

The format of this document is essentially “two papers in one,” with the first chapter focusing on mostly theoretical considerations (although illustrated with an example), while the second chapter provides a practical, real-world example presented in the form of a tutorial.

Methods of Causal Inference

We will first introduce the reader to the idea of formal causal inference using the well-known example of Simpson’s Paradox. Secondly, we will provide a brief summary of the Neyman-Rubin model, which represents a traditional statistical approach in this context. Once this method is established as a reference point, we will introduce two methods within the Bayesian network paradigm, Pearl’s Do-Operator, which is based on “Graph Surgery”, and a method based on Jouffe’s “Likelihood Matching” algorithm (LM). LM allows fixing probability distributions and can be considered as a probabilistic extension of statistical matching.

Practical Applications of Direct Effects and Causal Inference

While our treatment of Neyman-Rubin is limited to the first chapter, the two Bayesian network-based methods will be further illustrated as practical applications in the second chapter. Special weight will be given to Likelihood Matching (LM), as it has not yet been documented in literature. We will explain the practical benefits of LM with a real-world business application and discuss observational and causal inference in the context of a marketing mix model. Using the marketing mix model as the principal example, we will go into greater detail regarding the analysis workflow, so the reader can use this example as a step-by-step guide to implementing such a model with BayesiaLab.

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