A Model Must Be Wrong to be Useful: The Role of Linear Modeling and False Assumptions in Theoretical Explanation

It is true that many times relationships in the real world do not fall into a linear pattern. Nevertheless, even if the true causal structure of the phenomenon under study is not linear, it does not mean that the causal relationship cannot be detected using linear modeling. With the advanced use of non-linear modeling, especially in the field of business data mining, researchers feel the tension of choosing between linear and nonlinear models. It is the conviction of the author that the appropriateness of non-linear modeling and linear modeling depends on specific research purposes (prediction vs. explanation). While nonlinear models are suitable to illustrate a physical or mechanical process under a natural interpretation, researchers occasionally have to go beyond the natural interpretation to look for theoretical explanations of the relationships between attributes. Judging the efficacy of statistical modeling, which is essentially a scientific method, should be based upon the criteria developed throughout the history of science, rather than through observations from the business market and political events within one or two decades. Examples from the history of science, including Dalton’s atomic model, Galileo’s law of uniform acceleration, and the Titius-Bode Law, will be cited to illustrate the usefulness of linear models in terms of providing explanation with theoretical depth. It is not the case that explanatory models are still useful in spite of the fact that they are wrong to some degree. On the contrary, they are useful because they are wrong.