Is inference based on a full model appropriate, and if so, in which circumstances?
Suppose you are interested in the potential relationship between a response variable and several candidate predictor variables, and use some form of regression (e.g. generalized linear model) to answer that. One approach to inferring which predictors are "important" or have an apparently genuine relationship with the response would be information-theoretic criterion (say AIC) based model comparison. Even though variables that are not retained in the final model might have some relationship with the response, they essentially provide no additional substantial information, given other predictors retained in the model.
Is there a case where it would be more appropriate to simply fit a full (global) model (with all candidate predictors), stop there, and base inferences on individual predictors solely on the t-statistics (or other statistics) and p-values in this full model, without further model selection?
I have come across suggestions (e.g. Whittingham et al. "Why do we still use stepwise modelling in ecology and behaviour?" (2006) that this might be a sensible thing to do, albeit with potential drawbacks. The authors say that estimated parameters are unbiased, but other sources say that these estimates and p-values are not to be trusted, as other ("non-important") variables in the model may affect them.
If the aim is to understand potential biological relationships, which method would be more appropriate?