I have one response variable and a large number (>100) of explanatory variables.
METHOD 1: I have completed one approach where the explanatory variables have been reduced via a PCA (in accordance with existing literature looking at this common set of explanatory variables), before modelling the reduced set of independent variables by ranking the AIC scores of different models (the DREDGE function in the MuMIN package, R), after the necessary data exploration (e.g. colinearity checks).
However, I would also like to do a separate analysis that explores the significance of each explanatory variable individually. Following this, I would like to compare the most reliable models and influential variables against those included in the previous analysis (i.e. considering if the PCA approach stripped out some potentially influential independent variables).
METHOD 2: I thought of applying multiple GLMs and GAMs(with some models likely to be both linear and non-linear) accounting for the individual influence of each independent variable. All models would then be ranked by the AIC score.
Is method 2 a good way of achieving this? I am aware that with so many explanatory variables, type I error is a big concern, but the AIC score would be used informatively to rank which independent variables exert the most control over the response variable. I have seen debates about using AIC in nonnested setups, but some people seem to suggest it could be used as part of a model building procedure (e.g. see an answer here Non-nested model selection). The assumptions of the top X amount of models (X being consistent with METHOD 1) would then be validated, with all variables being tested for colinearity before then modelling the reduced set of variables as conducted in the METHOD 1.
Thank you in advance for any help and advice.