# Direction Dependence Analysis

**News:**

- (September 23, 2019) New article: "Sensitivity analysis and extensions of testing the causal direction of dependence: A rejoinder to Thoemmes (2019)" published in
*Multivariate Behavioral Research*(click__here__for the article; click__here__for Thoemmes' (2019) original commentary)

- (April 15, 2019) New article: "
*Direction dependence analysis in the presence of confounders: Applications to linear mediation models using observational data*" published in*Multivariate Behavioral Research*(click__here__for the article)

- (March 19, 2019) New article: "
*Confounder detection in linear mediation models: Performance of kernel-based tests of independence*" published in*Behavior Research Methods*(click__here__for the article)

- (December 7, 2018) R functions for standard DDA (v. 0.1) and introductory material have been released (click
__here__to download)

- (May 2, 2018) SPSS GUI Component package for standard DDA (v. 2.0) has been released (click
__here__to download).

- (April 19, 2018) SPSS Macros and Auxiliary GUI Component for conditional DDA (CDDA; beta version) has been released (click
__here__to download)

**Workshops/Presentations:**

- Lausanne, Switzerland, September 10-12, 2019 (31st Conference of the Austo-Swiss Region (ROeS) of the International Biometric Society):
**"Using higher moments to test requirements for causal inference"**.

- Basel, Switzerland, July 9-12, 2019 (Conference of the International School Psychology Association):
**"Prosocial Skills Causally Mediate the Relation Between Effective Classroom Management and Academic Competence: An Application of Direction Dependence Analysis"**. Paper presented at the Symposium "Specifying Mediators of Classroom Social-Behavioral Interventions".

- Chicago, IL, May, 26, 2019 (45th Annual Convention of the Association for Behavior Analysis International): "
**Direction Dependence Analysis: Testing the direction of causation in non-experimental person-oriented research**". Paper presented at the B. F. Skinner Lecture Series.

- Vancouver, BC, August 1, 2018 (Joint Statistical Meeting): "
**Direction Dependence Modeling: A Diagnostic Framework to test the Causal Direction of Effects in Linear Models**". Paper presented at the Symposion "Recent Development in the Assessment and Modeling of Asymmetric Dependence".

- San Francisco, CA, May 24-27, 2018 (30th APS Annual Convention): "
**Conditional Direction Dependence Analysis: A Framework to Examine the Direction of Effect in Moderation with Implementation in SPSS**".

**What is Direction Dependence Analysis?**

##### A common problem with observational research is that it is often difficult to prove that a specific action causes an effect. Further, in many cases, alternative causal theories exist which may serve as an explanation for observed variable associations. In non-experimental studies, at least three possible explanations exist for the association of two variables *x* and *y*:

*x* is the cause of *y *(*i.e., x *→* y*)

*y* is the cause of *x *(*i.e., y *→* x*)

##### an unmeasured confounder *u* is present (*i.e.*, *x* ← *u* → *y*).

**Direction Dependence Analysis **(DDA) can be used to uniquely identify each explanatory model. DDA assumes that variables are non-normally distributed and makes use of higher moments (i.e., skewness and kurtosis) to gain deeper insight into the data-generating mechanism. DDA consists of three core components:

- Distributional properties of observed variables
- Distributional properties of error terms of competing models
- Independence properties of predictors and error terms of competing models

##### Statistical inference methods for model selection, SPSS macros, and R scripts to implement DDA are provided here. Please go to the __RESOURCES__ section to download source codes, manuals, posters, slides, and further information.

__RESOURCES__

### RESOURCES

##### PosterS AND SLIDES

##### SPSS mACROS

##### R SCRIPTS

##### uSER gUIDE & more

### team

Network for Educator Effectiveness

University of Missouri

Department of Psychology

Michigan State University

### REFERENCES

- Wiedermann, W., & Sebastian, J. (2019).
**Sensitivity analysis and extensions of testing the causal direction of dependence: A rejoinder to Thoemmes (2019)**.*Multivariate Behavioral Research*, (*in press*). - Wiedermann, W., & Li, X. (2019).
**Confounder detection in linear mediation models: Performance of kernel-based tests of independence**.*Behavior Research Methods,*(in press). [__R Scripts__] - Wiedermann, W., Li, X., & von Eye A. (2019).
**Testing the causal direction of mediation effects in randomized intervention studies**.*Prevention Science, 20, 419-430*. - Wiedermann, W., & Sebastian, J. (2019).
**Direction dependence analysis in the presence of confounders: Applications to linear mediation models**.*Multivariate Behavioral Research, (in press)*. [__R Scripts__] - Wiedermann, W. (2018).
**A note on fourth-moment based direction dependence measures when regression errors are non-normal**.*Communications in Statistics: Theory and Methods*, 47, 5255-5264. - Wiedermann, W., & Li, X. (2018).
**Direction dependence analysis: Testing the direction of effects in linear models with implementation in SPSS**.*Behavior Research Methods*, 50 (4), 1581-1601*.* - Wiedermann, W., & von Eye, A. (2018).
**Log-linear models to evaluate direction of effect in binary variables**.*Statistical Papers*, (in press). - von Eye, A. & Wiedermann, W. (2018).
**Locating event-based causal effects: A configural perspective**.*Integrative Psychological and Behavioral Science*, 52, 307-330. - Wiedermann, W., Merkle, E.C., & von Eye, A. (2018).
**Direction of dependence in measurement error models.***British Journal of Mathematical and Statistical Psychology, 71, 117-145*. [__R Script__] [__Supplement__] - Wiedermann, W., Artner, R., & von Eye, A. (2017).
**Heteroscedasticity as a basis for direction dependence in reversible linear regression models.***Multivariate Behavioral Research, 52, 222-241.* - Wiedermann, W., & von Eye, A. (2016).
**Directional dependence in the analysis of single subjects.***Journal of Person-Oriented Research, 2*, 20-33. [__pdf__] - Wiedermann, W., & von Eye, A. (2016).
**Testing directionality of effects in causal mediation analysis**. In W. Wiedermann & A. von Eye (eds), Statistics and Causality: Methods for applied empirical research, pp. 63-106. Hoboken, NJ: Wiley & Sons. - von Eye, A., & Wiedermann, W. (2016).
**Direction of effects in categorical variables: A structural perspective**. In W. Wiedermann and A. von Eye (eds), Statistics and Causality: Methods for applied empirical research, pp. 107-130. Hoboken, NJ: Wiley & Sons. - Wiedermann, W., & Hagmann, M. (2016).
**Asymmetric properties of the Pearson correlation coefficient: Correlation as the negative association between linear regression residuals.***Communications in Statistics: Theory and Methods, 45,*6263-6283. - Wiedermann, W. (2015).
**Decisions concerning the direction of effects in linear regression models using fourth central moments**. In M. Stemmler, W. Wiedermann, & A. von Eye (eds), Dependent data in social sciences research: Forms, issues, and methods of analysis, pp.149-169. Cham, CH: Springer. - Wiedermann, W., & von Eye, A. (2015).
**Direction dependence analysis: A confirmatory approach for testing directional theories****.***International Journal of Behavioral Development, 39, 570-580.* - Wiedermann, W., & von Eye, A. (2015).
**Direction of effects in mediation analysis.***Psychological Methods, 20,*221-244*.* - Wiedermann, W., & von Eye, A. (2015).
**Direction of effects in multiple linear regression models**.*Multivariate Behavioral Research, 50*, 23-40. - Wiedermann, W., Hagmann, M., & von Eye, A. (2015).
**Significance tests to determine the direction of effects in linear regression models.***British Journal of Mathematical and Statistical Psychology*, 116-141.**,**68 - von Eye, A., & Wiedermann, W. (2014).
**On direction of dependence in latent variable contexts.***Educational and Psychological Measurement,**74*, 5-30. - von Eye, A., & DeShon, R.P. (2012).
**Directional dependence in developmental resea****rch.***International Journal of Behavioral Development, 36*, 303-312.

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