I am reflecting on the discussion around this question and particularly Frank Harrell's comment that the estimate for variance in a reduced model (ie one from which a number of explanatory variables have been tested and rejected) should use Ye's Generalized Degrees of Freedom. Professor Harrell points out this will be much closer to the residual degrees of freedom of the original "full" model (with all the variables in) than that from a final model (from which a number of variables have been rejected).
Question 1. If I want to use an appropriate approach to all the standard summaries and statistics from a reduced model (but short of a full implementation of Generalized Degrees of Freedom), would a reasonable approach be to just use the residual degrees of freedom from the full model in my estimates of residual variance, etc?
Question 2. If the above is true and I want to do it in
R, might it be as simple as setting
finalModel$df.residual <- fullModel$df.residual
at some point in the model fitting exercise, where finalModel and fullModel were created with lm() or a similar function. After which functions such as summary() and confint() seem to work with the desired df.residual, albeit returning an error message that someone has clearly mucked around with the finalModel object.