  There has been recent interest in extending the ideas of False Discovery
Rates (FDR) to variable selection in regression settings. Traditionally the FDR
in these settings has been defined in terms of the coefficients of the full
regression model. Recent papers have struggled with controlling this quantity
when the predictors are correlated. This paper shows that this full model
definition of FDR suffers from unintuitive and potentially undesirable behavior
in the presence of correlated predictors. We propose a new false selection
error criterion, the False Variable Rate (FVR), that avoids these problems and
behaves in a more intuitive manner. We discuss the behavior of this criterion
and how it compares with the traditional FDR, as well as presenting guidelines
for determining which is appropriate in a particular setting. Finally, we
present a simple estimation procedure for FVR in stepwise variable selection.
We analyze the performance of this estimator and draw connections to recent
estimators in the literature.
