Linearity being a major assumption in traditional empirical modeling...
Indeed, we should give up this assumption when we start an in depth analysis of operations. From the mathematical point of view a linear function is a good approximation in a more or less narrow neighborhood around an observed point or situation. If we assume that a real problem may be modeled sufficiently in some way this should allow us to argue on this base. The problem is that we should be careful when we extend / generalize our results. In empirical research the question could be: Why should we use (linear) equation modeling or usually linear regressions. Typical other reasons for non linear functions are stochastic variables that are transformed in deterministic functions. Other reasons come up form technical problems. Without any proof many times I find more than one influence factors behind the non linear function. Using them could be a refinement entailing a better approximation of the real structure. Problematic could be the question whether we are able to measure them. In this case a non linear approximation of the aggregated phenomenon is some times helpful like the development of series of exponential, logarithmic or trigonometric functions.
I am interested in the future discussion!
Apart from theory-driven investigation, there's also some room for empirical exploration. I think it might be useful to look at (or conduct) some meta-analyses that demonstrate conflicting significant linear trends. Where conflicts exist, we my actually be observing two sides of a non-monotonic relationship (rather than simply blaming differences on contextual moderation). I have a feeling some of the claims made regarding contextual effects are in fact nothing more that non-monotonicity at play.
As a beginner of BOM, I think the traditional linear model is helpful in answering the question "which variables influence the system's output? " It is convenient and straightforward to answer the question with p-value. As for the non-linear model, it seems to be used to answer "how do these variables influence the system?" The research question becomes more specific. In my research process, I usually take steps to try different models to analyze data, from linear to non-linear model. I do not know whether it is right or whether there is a better method. I would appreciate it very much if I can get any suggestion from you professors.
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