Various relationships are shown hold between monotonic effects and weak monotonic effects and the monotonicity of certain conditional expectations. This relationship is considered for both binary and non-binary variables. Counterexamples are provide to show that the results do not hold under less restrictive conditions. The ideas of monotonic effects are furthermore used to relate signed edges on a directed acyclic graph to qualitative effect modification.
Statistical Methodology | Statistical Theory
VanderWeele, Tyler J. and Robins, James M., "Properties of Monotonic Effects" (November 2006). COBRA Preprint Series. Working Paper 15.