"From the above discussion a general principle emerges. Whenever the response variable is informally or formally linked, in an unmasked fashion, to particular parameters that may be deleted from the model, special adjustments must be made in P-values, standard errors, test statistics, and confidence limits, in order for these statistics to have the correct interpretation. Examples of strategies that are improper without special adjustments (e.g., using the bootstrap) include examining a frequency table or scatterplot to decide that an association is too weak for the predictor to be included in the model at all or to decide that the relationship appears so linear that all nonlinear terms should be omitted. It is also valuable to consider the reverse situation; that is, one posits a simple model and then additional analysis or outside subject matter information makes the analyst want to generalize the model."

I think this means if you specify a model and then remove parts of it, including non-linear terms, the p values and CI are no longer valid. I am not sure if they can be made valid again.

Does this effect the effect sizes as well?