As for A), B), and c) this is a very complicated question and it does not have a straightforward answer. I agree with many other members of this Forum that there is little or no legitimate role for stepwise regression approaches. But there is no simple way to summarize how one goes about selecting variables for inclusion in a model. Certainly nothing simple enough to cover in a post here. I think the most important issues are:
It is best to have a theory behind what you are investigating and have the model reflect the relationships predicted or assumed by that theory as best you can.
It is important to include as many confounders as you can. Inferences based on models that omit confounders produce misleading results.
It is important to exclude colliders. Inferences based on models that include colliders also produce misleading results.
If you are using a linear model, but the real relationships are not truly linear, it may be important to transform variables or include higher power terms or interactions to achieve good model fit.
Those are the general principles. But applying them in real situations is quite complicated. A lot of thought and research into prior studies of related questions is required to do that.
As for D), this one is simple: interaction and effect modification are the same thing.
It is best to have a theory behind what you are investigating and have the model reflect the relationships predicted or assumed by that theory as best you can.
It is important to include as many confounders as you can. Inferences based on models that omit confounders produce misleading results.
It is important to exclude colliders. Inferences based on models that include colliders also produce misleading results.
If you are using a linear model, but the real relationships are not truly linear, it may be important to transform variables or include higher power terms or interactions to achieve good model fit.
Those are the general principles. But applying them in real situations is quite complicated. A lot of thought and research into prior studies of related questions is required to do that.
As for D), this one is simple: interaction and effect modification are the same thing.
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