"Don't select of the dependent variable" is a
stock phrase of social science, whether one is talking about quantitative or
qualitative analysis. In this paper (talk) we show how Pearl's theory of DAG's
(directed acyclic graphs), particularly his notion of a collider
variable, provides a very simple and general approach to understanding when
selection or conditioning a variable fatally biases an analysis. We start
by presenting the basics of Pearl's
theory. We contrast endogenous selection to
confounding. With endogenous selection, problems are created by conditioning on
a variable. With confounding, problems are created by failure to condition on a
variable. We demonstrate that some
situations, unfortunately, are "damned if you do, damned if you
don't". We then analyze a number of classic
examples with DAG's: traditional selection on the
dependent variable, Heckman's endogeneity bias,
ascertainment bias (Hernan), dependent censoring,
instrumental variables, and the healthy worker effect.