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Network Model Trees

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  • Jones, Payton J.
  • Mair, Patrick
  • Simon, Thorsten
  • Zeileis, Achim

Abstract

In many areas of psychology, correlation-based network approaches (i.e., psychometric networks) have become a popular tool. In this paper we define a statistical model for correlation-based networks and propose an approach that recursively splits the sample based on covariates in order to detect significant differences in the network structure. We adapt model-based recursive partitioning and conditional inference tree approaches for finding covariate splits in a recursive manner. This approach is implemented in the networktree R package. The empirical power of these approaches is studied in several simulation conditions. Examples are given using real-life data from personality and clinical research.

Suggested Citation

  • Jones, Payton J. & Mair, Patrick & Simon, Thorsten & Zeileis, Achim, 2019. "Network Model Trees," OSF Preprints ha4cw, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:ha4cw
    DOI: 10.31219/osf.io/ha4cw
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    References listed on IDEAS

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    1. Epskamp, Sacha & Cramer, Angélique O.J. & Waldorp, Lourens J. & Schmittmann, Verena D. & Borsboom, Denny, 2012. "qgraph: Network Visualizations of Relationships in Psychometric Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i04).
    2. Edgar Merkle & Jinyan Fan & Achim Zeileis, 2014. "Testing for Measurement Invariance with Respect to an Ordinal Variable," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 569-584, October.
    3. Hansen, Bruce E, 1997. "Approximate Asymptotic P Values for Structural-Change Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 60-67, January.
    4. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    5. Seibold Heidi & Hothorn Torsten & Zeileis Achim, 2016. "Model-Based Recursive Partitioning for Subgroup Analyses," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 45-63, May.
    6. Sacha Epskamp & Mijke Rhemtulla & Denny Borsboom, 2017. "Generalized Network Psychometrics: Combining Network and Latent Variable Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 904-927, December.
    7. Carolin Strobl & Julia Kopf & Achim Zeileis, 2015. "Rasch Trees: A New Method for Detecting Differential Item Functioning in the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 289-316, June.
    8. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    9. Hothorn, Torsten & Hornik, Kurt & van de Wiel, Mark A. & Zeileis, Achim, 2006. "A Lego System for Conditional Inference," The American Statistician, American Statistical Association, vol. 60, pages 257-263, August.
    10. Edgar Merkle & Achim Zeileis, 2013. "Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 59-82, January.
    11. Mair, Patrick & de Leeuw, Jan, 2010. "A General Framework for Multivariate Analysis with Optimal Scaling: The R Package aspect," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i09).
    12. Carolin Strobl & Florian Wickelmaier & Achim Zeileis, 2011. "Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning," Journal of Educational and Behavioral Statistics, , vol. 36(2), pages 135-153, April.
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