# Direction Dependence Analysis

**News:**

- (December, 2020) New article on DDA in the latent variable domain: Pollaris, A. & Bontempi, G. (2020).
*Latent Causation: An algorithm for pairs of correlated latent variables in linear non-Gaussian structural equation modeling*. In L. Cao, W. Kosters and J. Lijffijt (eds.) BNAIC/BENELEARN 2020: Proceedings of the 32nd Benelux Conference on Artificial Intelligence (BNAIC 2020) and the 29th Belgian-Dutch Conference on Machine Learning (Benelearn 2020), pp. 209-223 (click here for the article).

- (December 3, 2020) New book: "
*Direction Dependence in Statistical Modeling: Methods of Analysis*" (Wiedermann, Kim, Sungur & von Eye, 2020) published by Wiley & Sons (click here for details)

- (August 7, 2020) New article: "
*Prosocial skills causally mediate the relation between classroom management and academic competence: An application of direction dependence analysis*" published in*Developmental Psychology*(click here for the article)

- (November 12, 2019) New article: "
*Conditional direction dependence analysis: Evaluating the causal direction of effects in linear models with interaction terms*" published in*Multivariate Behavioral Research*(click__here__for the article)

- (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:**

- College Park, Maryland, January 25, 2021: "
**Direction Dependence Analysis: A Statistical Framework to Test the Causal Direction of Effects in Observational Data**". Paper presented online at the Monday Symposium in Measurement and Statistics (MSMS) University of Maryland together with Ohio State University, University of North Carolina at Chapel Hill, and University of Notre Dame.

- Washinton, D.C., August 6-8, 2020 (Annual American Psychological Association (APA) Convention): "
**Predictor-Residual Independence Tests for Examining Causal Assumptions of Synchronous Effects Models".**Paper presented at the Symposium "Advanced Quantitative Methods for Addressing Complexities in Psychological Research".

- Arlington, Virginia, March 11-14, 2020 (Spring 2020 Conference of the Society for Research on Educational Effectiveness; SREE):
**"Examining the Causal Direction of Synchronous Effects In Structural Panel Models: Using Residual-Predictor Independence Tests to Identify Model Mis-specifications"**. Paper presented at the Symposium "Considerations and Choices in Modeling Complex Data".

- 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*:

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

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

##### III) 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

##### DDA component patterns can be used to uniquely distinguish between the three explanatory models. DDA patterns are summarized below (rectangles represent observed variables and circles represent unobserved variables). 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__

**Direction Dependence in Statistical Modeling**

Questions concerning the direction of dependence in statistical models are common in situations where causally competing theories exist to explain the relationship between variables. Such data situations are common in exploratory (hypothesis-generating) research settings but also occur in confirmatory research. The book *Direction Dependence in Statistical Modeling: Methods of Analysis* (Wiedermann, Kim, Sungur & von Eye, 2020, Wiley & Sons) gives an overview of the latest developments of methods for the analysis of hypotheses that are compatible with the causal direction of dependence of variable relations. The edited volume provides

- an introduction into principles of evaluating the presence of reverse causation (e.g., a causal model of the form
*y*→*x*instead of*x*→*y*) and confounding biases (e.g.,*x*←*u*→*y*instead of*x*→*y*) in continuous and categorical variables, - an introduction into copula-based directional dependence methods for continuous and categorical variables,
- an overview of state-of-the-art algorithms for causal learning,
- a discussion of statistical software, and various application examples using real-world data from developmental, epidemiological, and clinical research.

### 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., Kim, D., Sungur, E., & von Eye, A. (2020).
**Direction dependence in statistical modeling: Methods of analysis**. Hoboken, NJ: Wiley & Sons. - Wiedermann, W., Reinke, M. W., & Herman, K. C. (2020).
**Prosocial skills causally mediate the relation between classroom management and academic competence: An application of direction dependence analysis**.*Developmental Psychology, 56, 1723-1735*. - Li, X. & Wiedermann,
*.*(2020).**Conditional Direction Dependence Analysis: Evaluating the Causal Direction of Effects in Linear Models with Interaction Terms.***Multivariate Behavioral Research, 55, 786-810.* - Wiedermann, W., & Sebastian, J. (2020).
**Sensitivity analysis and extensions of testing the causal direction of dependence: A rejoinder to Thoemmes (2019)**.*Multivariate Behavioral Research*,*55*, 523-530. - Wiedermann, W., & Li, X. (2020).
**Confounder detection in linear mediation models: Performance of kernel-based tests of independence**.*Behavior Research Methods,**52*, 342-359. [__R Scripts__] - Wiedermann, W., & Sebastian, J. (2020). Direction dependence analysis in the presence of confounders: Applications to linear mediation models.
*Multivariate Behavioral Research, 55, 495-515*. [__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. (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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