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Behavior Research Methods

, Volume 50, Issue 4, pp 1581–1601 | Cite as

Direction dependence analysis: A framework to test the direction of effects in linear models with an implementation in SPSS

  • Wolfgang Wiedermann
  • Xintong Li
Article

Abstract

In nonexperimental data, at least three possible explanations exist for the association of two variables x and y: (1) x is the cause of y, (2) y is the cause of x, or (3) an unmeasured confounder is present. Statistical tests that identify which of the three explanatory models fits best would be a useful adjunct to the use of theory alone. The present article introduces one such statistical method, direction dependence analysis (DDA), which assesses the relative plausibility of the three explanatory models on the basis of higher-moment information about the variables (i.e., skewness and kurtosis). DDA involves the evaluation of three properties of the data: (1) the observed distributions of the variables, (2) the residual distributions of the competing models, and (3) the independence properties of the predictors and residuals of the competing models. When the observed variables are nonnormally distributed, we show that DDA components can be used to uniquely identify each explanatory model. Statistical inference methods for model selection are presented, and macros to implement DDA in SPSS are provided. An empirical example is given to illustrate the approach. Conceptual and empirical considerations are discussed for best-practice applications in psychological data, and sample size recommendations based on previous simulation studies are provided.

Keywords

Linear regression model Direction of effects Direction dependence Observational data Nonnormality 

Supplementary material

13428_2018_1031_MOESM1_ESM.pdf (84 kb)
ESM 1 (PDF 84 kb)
13428_2018_1031_MOESM2_ESM.pdf (94 kb)
ESM 2 (PDF 93 kb)
13428_2018_1031_MOESM3_ESM.doc (130 kb)
ESM 3 (DOC 130 kb)

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Copyright information

© Psychonomic Society, Inc. 2018

Authors and Affiliations

  1. 1.Statistics, Measurement, and Evaluation in Education, Department of Educational, School, and Counseling Psychology, College of EducationUniversity of MissouriColumbiaUSA

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