A non-parametric test for partial monotonicity in multiple regression

Partial positive (negative) monotonicity in a dataset is the property that an increase in an independent variable, ceteris paribus, generates an increase (decrease) in the dependent variable. A test for partial monotonicity in datasets could (1) increase model performance if monotonicity may be assumed, (2) validate the practical relevance of policy and legal requirements, and (3) guard against falsely assuming monotonicity both in theory and applications. To our knowledge, there is no test for this phenomenon available yet. In this article, we propose a novel non-parametric test, which does not require resampling or simulation. It is formally proven that the test is asymptotically conservative, and that its power converges to one. A brief simulation study shows the characteristics of the test. Finally, in order to show its practical applicability, we apply the test to a dataset and interpret its results.