Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models

• Published in: Multivariate behavioral research Vol. 52; no. 2; pp. 222 - 241
• Main Authors: Wiedermann, Wolfgang, Artner, Richard, von Eye, Alexander
• Format: Journal Article
• Language: English
• Published: United States Routledge 04.03.2017; Taylor & Francis Ltd
• Subjects: Algorithms; Child; Child Development; Cognition; Computer Simulation; Data Interpretation, Statistical; Dependence; Direction dependence analysis; Economic models; Female; heteroscedasticity; Humans; Linear Models; linear regression model; Male; Mathematical Concepts; Monte Carlo Method; Multivariate Analysis; Nonlinear Dynamics; nonnormality; Normal Distribution; Observational Studies as Topic; Psychological Tests; Regression analysis; Software; heteroscedasticity; linear regression model; nonnormality; Direction dependence analysis
• ISSN: 0027-3171; 1532-7906
• DOI: 10.1080/00273171.2016.1275498

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.