Linear regression models of various stripes are generally the models for most social sciences and medicine. A break in this trend is the use of ANOVA for treatment experiments, and the popularity of game theory in economics and political science. These also have their limits. ANOVA is only suited for testing certain types of hypotheses, and game theory models are often set up for optimizations, rather than exploring the array of outcomes that meet satisfaction behaviors (something we see commonly in economics). The other issue with game theory is that models often assume a fixed landscape in which optimization can occur, despite most of the areas under study featuring moving landscapes.

In grad school, we had tons of coursework on regressions. We read tons of papers on regressions. In almost every case, these were linear models foisted on to what we knew were non-linear dynamical systems, systems full of tipping points, periods of back bending curves, phase state transition-like behaviors, etc. I learned some non-linear regression techniques on my own for some questions, but they fit the non-linear regression to a line, using multiple dimensions for multiple variables.

The linear models bleed into public policy discourse. When we talk of education, we talk of funding per sped student, hours of tutoring per Y increase in scores. The public discourse on the nature of systemic racism is framed in terms of regression studies and mean differences. So to, the duration of wars, likelihood of conflicts, etc. gets framed in terms of: "more of X = more or less of Y. The linear relationship shows up everywhere, despite being a known fiction. This problem has been corrected in the physical sciences to a large extent, not so the social sciences.

For publications, I've worked with non-linear variables, stuff like multinomial logits, but only in intelligence work did I ever see attempts to model non-linearity. These weren't even always with ideal models for non-linearity, but we had Monte Carlo type models that had feedback that could flip the effects of a variable based on results in other state-variables, although this was still a case where the state had to be recursively defined by other state variables.

I only found out about kernel smoothers and kernal regression later. I would chalk this up to a deficit in my education except I don't see them that often in papers. Worse, graphics of all data points across variables also isn't very common to find, and even cross tabs of the data are often missing. This makes sense for print publications with a premium on space, but not for online publications. Splines represent another (for me more intuitive) option and are easy to use in Python.

So, my argument would be that social sciences need a major shake up in methodology. Smoothing shouldn't be an advanced topic, it should be an undergrad level necessity.

The argument that non-linearity is too hard to visualize only holds for multiple dimensions, it's not a good reason not to use local smoothing.

However, I realize asking a whole field to change its methods, especially when academia has a system of entrenched tenured staff at the top, isn't totally viable.

So my other idea was, why don't people start publishing their papers as Tableau, Power BI, etc. reports. Then you have robustness testing built in. People can unselect and deselect variables at will. They can visualize the raw data with filters for every IV. They can cross tab data across a matrix. They can use parameters to visualize the model with changes to the data.

What's more, papers wouldn't be dead static things you post once and forget about any more. They could live on because you could routinely refresh your data if it is from a set that keeps getting added to (Correlates of War, START GTD, state education data, etc.). GIS plug-ins mean mapping could also become more common, another neglected modeling technique.

Unfortunately, one reason this won't be adopted is the publish or perish environment. Including a built in robustness tester is going to mean way more null findings. This is good for science, catching publication bias, but bad for people who start doing interactive reports.

Still, it's an idea I think whose time has come. If you can learn Stata or R, you can learn DAX and M easy enough to make interactive reports, especially if journals give you a template.