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A Non-parametric Test for Partial Monotonicity in Multiple Regression

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  • Misha Beek
  • Hennie Daniels

Abstract

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Misha Beek & Hennie Daniels, 2014. "A Non-parametric Test for Partial Monotonicity in Multiple Regression," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 87-100, June.
    • Handle: RePEc:kap:compec:v:44:y:2014:i:1:p:87-100
    DOI: 10.1007/s10614-013-9386-7
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    References listed on IDEAS

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    1. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
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    3. Daniëls, H.A.M. & Feelders, A.J., 2001. "Integrating Economic Knowledge in Data Mining Algorithms," Discussion Paper 2001-63, Tilburg University, Center for Economic Research.
    4. Neumeyer, N. & Van Keilegom, I., 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," LIDAM Reprints ISBA 2010006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    6. Daniëls, H.A.M. & Feelders, A.J., 2001. "Integrating Economic Knowledge in Data Mining Algorithms," Other publications TiSEM 039b0321-bd0b-487b-a542-b, Tilburg University, School of Economics and Management.
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