When to what when building a linear model?

Question

There a many tools to building linear models, such as adding non-linearity, adding splines, adding interactions, variable selection.

It can feel overwhelming when considering all of the options… For example, should you try interactions first or try polynomials?

Coefficients and P-values slide around with changes, so it is apparent that depending on your early decisions in building a model…you can end in very different places with your model (including different variable selection).

So, what should be done when?

Answer 1

It all depends on your scenario and/or the question you try to answer.

When data provides reason to use non-linearity instead of linearity, you should consider doing that. It could also be that e.g. physical knowledge or behavior require to use a nonlinear model. Note, in statistics linear and non-linearity differs from average understanding. If you want to figure out which parameters dominate/influence your object/subject, you have to check e.g. p-values and effect sizes or run tests (t-test, Anova and so on). When you want to consider interactions (like how is temperature combined with humidity affecting your medium), you have to consider this in a model. When you want to compare students across universities you have to consider a mixed model and so on. It all depends.