When running a GLiM...how do you decide which estimation method to use?

When running a generalized linear model, how do you decide which estimation to use? For example, maximum likelihood, forward selection, lasso, elastic net, etc. Would I prefer to keep all of my predictors and choose a method that doesn't select (i.e., maximum likelihood or ridge) when I only have a few predictors that I think are all important? Would I choose a method that selects when I have a lot of predictors and I'm trying to build a predictive model? When should I use a method that provides shrinkage?


Not a robit
If you are model building instead of just testing a priori variables, then shrinkage should be used. Ridge shrinks coefficients, LASSO more likely to remove variables, while E-net is a blend of the two.

Forward selection is usually frowned upon, since it is not taking into account knowledge you may have. As you likely know, it comes down to what your purpose is, while most all of the approaches use a form of MLE unless you are using OLS related to continuous outcomes.
Currently, I'd say I'm trying to develop an explanatory model that (unfortunately) only has a few predictor variables. I've got a blocking term, a continuous predictor, the interaction between those two, and two additional covariates. With so few IV's, should I even be using selection techniques? Especially if I'm not trying to develop a predictive model?
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Not a robit
Thanks for the clarification. Correct, you likely need no special model development strategy. Just model what you have and document the process in write-up.

Our strategies sound cool and sophisticated, but would likely be inappropriate in this setting.