Advertisement

Prevention Science

, Volume 20, Issue 3, pp 442–451 | Cite as

Granger Causality Testing with Intensive Longitudinal Data

  • Peter C. M. MolenaarEmail author
Article

Abstract

The availability of intensive longitudinal data obtained by means of ambulatory assessment opens up new prospects for prevention research in that it allows the derivation of subject-specific dynamic networks of interacting variables by means of vector autoregressive (VAR) modeling. The dynamic networks thus obtained can be subjected to Granger causality testing in order to identify causal relations among the observed time-dependent variables. VARs have two equivalent representations: standard and structural. Results obtained with Granger causality testing depend upon which representation is chosen, yet no criteria exist on which this important choice can be based. A new equivalent representation is introduced called hybrid VARs with which the best representation can be chosen in a data-driven way. Partial directed coherence, a frequency-domain statistic for Granger causality testing, is shown to perform optimally when based on hybrid VARs. An application to real data is provided.

Keywords

Granger causality Standard VAR Structural VAR Hybrid VAR Partial directed coherence 

Notes

Funding

Funding of the research presented in this paper was partially provided by NSF 1157220 (PI PCM Molenaar).

Compliance with Ethical Standards

Conflict of Interest

The author declares that there is no conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by the author.

Informed Consent

Informed consent was not required for this study.

References

  1. Barnett, L., & Seth, A.K. (2014). The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inferemve. Journal of Neuroscience Methods, 223, 50–68.Google Scholar
  2. Borsboom, D. (2017). A network theory of mental disorders. World Psychiatry, 16, 5–13.  https://doi.org/10.1002/wps.20375.CrossRefGoogle Scholar
  3. Brillinger, D. R. (1975). Time series: Data analysis and theory. New York: Holt, Rinehart & Winston.Google Scholar
  4. Faes, L., & Nollo, G. (2010). Extended causal modeling to assess partial directed coherence in multiple time series with significant instantaneous interactions. Biological Cybernetics, 103, 387–400.  https://doi.org/10.1007/s00422-010-0406-6.CrossRefGoogle Scholar
  5. Gates, K. M., & Molenaar, P. C. M. (2012). Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples. NeuroImage, 63, 310–319.  https://doi.org/10.1016/j.neuroimage.2012.06.026.CrossRefGoogle Scholar
  6. Gates, K.M., Molenaar, P.C.M., Hillary, F.G., & Slobounov, S. (2011). Extended unified SEM approach for modeling event-related fMRI data. NeuroImage, 54, 1151–1158.Google Scholar
  7. Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association, 77, 304–313.  https://doi.org/10.1080/01621459.1982.10477803.CrossRefGoogle Scholar
  8. Gibbons C.J. (2016) Turning the page on pen-and-paper questionnaires: Combining ecological momentary assessment and computer adaptive tests to transform psychological assessment in the 21st century. Frontiers in Psychology, 7 DOI:  https://doi.org/10.3389/fpsyg.2016.01933.
  9. Goebel, R., Roebroeck, A., Kim, D. S., & Formisano, E. (2003). Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magnetic Resonance Imaging, 21, 1251–1261.  https://doi.org/10.1016/j.mri.2003.08.026.CrossRefGoogle Scholar
  10. Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37, 424–438.  https://doi.org/10.1017/ccol052179207x.002.CrossRefGoogle Scholar
  11. Lane, S., Gates, K.M., & Molenaar, P. C. M. (2014). Gimme: Group iterative multiple model estimation. R package version 0.1–2. http://CRAN.R-project.org/package=gimme.
  12. Liu, S., & Molenaar, P. C. M. (2016). Testing for Granger causality in the frequency domain: A phase resampling method. Multivariate Behavioral Research, 51, 53–66.  https://doi.org/10.1080/00273171.2015.1100528.CrossRefGoogle Scholar
  13. Lütkepohl, H. (2007). New introduction to multiple time series analysis. Berlin: Springer-Verlag.Google Scholar
  14. Molenaar, P. C. M. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181–202.  https://doi.org/10.1007/BF02294246.CrossRefGoogle Scholar
  15. Molenaar, P. C. M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement: Interdisciplinary Research and Perspectives, 2, 201–218.  https://doi.org/10.1207/s15366359mea0204_1.Google Scholar
  16. Molenaar, P. C. M., & Campbell, C. G. (2009). The new person-specific paradigm in psychology. Current Directions in Psychology, 18, 112–117.  https://doi.org/10.1111/j.1467-8721.2009.01619.x.CrossRefGoogle Scholar
  17. Molenaar, P. C. M., & Lo, L. L. (2016). Alternative forms of Granger causality, heterogeneity and nonstationarity. In W. Wiedermann & A. von Eye (Eds.), Statistics and causality: Methods for applied empirical research (pp. 205–229). Hoboken: Wiley.Google Scholar
  18. Pearl, J. (2000). Causality: Models, reasoning and inference. Cambridge: Cambridge University Press.Google Scholar
  19. Schlögl, A., & Supp, G. (2006). Analyzing event-related EEG data with multivariate autoregressive parameters. In C. Neuper & W. Klimesch (Eds.), Event-related dynamics of brain oscillations. Progress in brain research 159 (pp. 135–147). Amsterdam: Elsevier.CrossRefGoogle Scholar
  20. Spaniel, F., Vohlidka, P., Hrdlicka, J., Kozeny, J., Novak, T., Motlova, L., Cermak, J., Bednarik, J., Novak, D., & Höschl, C. (2008). ITAREPS: Information technology aided relapse prevention programme in schizophrenia. Schizophrenia Research, 98, 312–317.  https://doi.org/10.1016/j.schres.2007.09.005.CrossRefGoogle Scholar
  21. Trull, T. J., & Ebner-Priemer, U. (2013). Ambulatory assessment. Annual Review of Clinical Psychology, 9, 151–176.  https://doi.org/10.1146/annurev-clinpsy-050212-185510.CrossRefGoogle Scholar
  22. Wen, X., Rangarajan, G., & Ding, M. (2013). Multivariate Granger causality: An estimation framework based on factorization of the spectral density matrix. Philosophical Transactions of the Royal Society A, 371, 20110610.  https://doi.org/10.1098/rsta.2011.0610.CrossRefGoogle Scholar
  23. White, H., Chalak, K., & Lu, X. (2013). Linking Granger causality and the Pearl causal model with settable systems. In F. Popescu & I. Guyon (Eds.), Causality in time series. Challenges in machine learning 5 (pp. 107–137). Brookline: Microtome Publishing.Google Scholar

Copyright information

© Society for Prevention Research 2018

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations