I have discovered that the regularity I described in my question has in fact been written about by several authors in the literature on Design of Experiments (DoE). It has been called the "hierarchical ordering principle" and also sometimes the "sparsity-of-effects principle."
In the chapter on fractional factorial designs in Montgomery (2013, p. 290), he writes:
The successful use of fractional factorial designs is based on three key ideas:
- The sparsity of effects principle. When there are several variables, the system or process is likely to be driven primarily by some of the main effects and low-order interactions.
...
Wu & Hamada (2000, p. 143) instead call this the "hierarchical ordering principle", and use the phrase "sparsity of effects" to refer to a related but distinct observation:
Three fundamental principles for factorial effects:
Hierarchical ordering principle: (i) Lower order effects are more likely to be important than higher order effects, (ii) effects of the same order are likely to be equally important .
Effect sparsity principle: The number of relatively important effects in a factorial experiment is small.
...
Li, Sudarsanam, & Frey (2006, p. 34) give two possible explanations for why hierarchical ordering should tend to occur. First they suggest that it is "partly due to the range over which experimenters typically explore factors":
In the limit that experimenters explore small changes in factors and to the degree that systems exhibit continuity of responses and their derivatives, linear effects of factors tend to dominate. Therefore, to the extent that hierarchical ordering is common in experimentation, it is due to the fact that many experiments are conducted for the purpose of minor refinement rather than broad-scale exploration
They next suggest that it is "partly determined by the ability of experimenters to transform the inputs and outputs of the system to obtain a parsimonious description of system behavior":
For example, it is well known to aeronautical engineers that the lift and drag of wings is more simply described as a function of wing area and aspect ratio than by wing span and chord. Therefore, when conducting experiments to guide wing design, engineers are likely to use the product of span and chord (wing area) and the ratio of span and chord (the aspect ratio) as the independent variables
References
- Li, X., Sudarsanam, N., & Frey, D. D. (2006). Regularities in data from factorial experiments. Complexity, 11(5), 32-45.
- Montgomery, D. C. (2013). Design and analysis of experiments (Vol. 8). New York: Wiley.
- Wu, C. J., & Hamada, M. S. (2000). Experiments: planning, analysis, and optimization (Vol. 552). John Wiley & Sons.