IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v40y2015i4p402-423.html
   My bibliography  Save this article

Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations Among Latent Variables

Author

Listed:
  • Jolynn Pek

    (York University)

  • R. Philip Chalmers

    (York University)

  • Bethany E. Kok

    (Max Planck Institute for Human Cognitive and Brain Sciences)

  • Diane Losardo

    (Amplify Education)

Abstract

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural equation models to add SEMM to their toolkit of exploratory analytic options. We describe how the SEMM captures potential nonlinearity between latent variables, and how confidence bands (CBs; point wise and simultaneous) for the recovered latent function are constructed and interpreted. We then illustrate the usefulness of CBs for inference with an empirical example on the effect of emotions on cognitive processing. We also introduce a visualization tool that automatically generates plots of the latent regression and their CBs to promote user accessibility. Finally, we conclude with a discussion on the use of this SPM for exploratory research.

Suggested Citation

  • Jolynn Pek & R. Philip Chalmers & Bethany E. Kok & Diane Losardo, 2015. "Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations Among Latent Variables," Journal of Educational and Behavioral Statistics, , vol. 40(4), pages 402-423, August.
  • Handle: RePEc:sae:jedbes:v:40:y:2015:i:4:p:402-423
    DOI: 10.3102/1076998615589129
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998615589129
    Download Restriction: no

    File URL: https://libkey.io/10.3102/1076998615589129?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Conor Dolan & Han Maas, 1998. "Fitting multivariage normal finite mixtures subject to structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 227-253, September.
    2. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    3. Kamel Jedidi & Harsharanjeet S. Jagpal & Wayne S. DeSarbo, 1997. "Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity," Marketing Science, INFORMS, vol. 16(1), pages 39-59.
    4. Gerhard Arminger & Petra Stein & Jörg Wittenberg, 1999. "Mixtures of conditional mean- and covariance-structure models," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 475-494, December.
    5. Leemis, Lawrence M. & McQueston, Jacquelyn T., 2008. "Univariate Distribution Relationships," The American Statistician, American Statistical Association, vol. 62, pages 45-53, February.
    6. Steven Boker & Michael Neale & Hermine Maes & Michael Wilde & Michael Spiegel & Timothy Brick & Jeffrey Spies & Ryne Estabrook & Sarah Kenny & Timothy Bates & Paras Mehta & John Fox, 2011. "OpenMx: An Open Source Extended Structural Equation Modeling Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 306-317, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Dylan Molenaar, 2015. "Heteroscedastic Latent Trait Models for Dichotomous Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 625-644, September.
    3. Williams, John & Temme, Dirk & Hildebrandt, Lutz, 2002. "A Monte Carlo study of structural equation models for finite mixtures," SFB 373 Discussion Papers 2002,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    5. Temme, Dirk & Williams, John R. & Hildebrandt, Lutz, 2002. "Structural equation models for finite mixtures: Simulation results and empirical applications," SFB 373 Discussion Papers 2002,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Johan Oud & Manuel Voelkle, 2014. "Do missing values exist? Incomplete data handling in cross-national longitudinal studies by means of continuous time modeling," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3271-3288, November.
    7. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    8. Bacci, Silvia & Bartolucci, Francesco & Pieroni, Luca, 2012. "A causal analysis of mother’s education on birth inequalities," MPRA Paper 38754, University Library of Munich, Germany.
    9. Eisenbeiss, Maik & Blechschmidt, Boris & Backhaus, Klaus & Freund, Philipp Alexander, 2012. "“The (Real) World Is Not Enough:” Motivational Drivers and User Behavior in Virtual Worlds," Journal of Interactive Marketing, Elsevier, vol. 26(1), pages 4-20.
    10. Sy-Miin Chow & Guangjian Zhang, 2013. "Nonlinear Regime-Switching State-Space (RSSS) Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 740-768, October.
    11. Hong-Tu Zhu & Sik-Yum Lee, 2001. "A Bayesian analysis of finite mixtures in the LISREL model," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 133-152, March.
    12. Zhou, Min & Zhao, Lindu & Kong, Nan & Campy, Kathryn S. & Xu, Ge & Zhu, Guiju & Cao, Xianye & Wang, Song, 2020. "Understanding consumers’ behavior to adopt self-service parcel services for last-mile delivery," Journal of Retailing and Consumer Services, Elsevier, vol. 52(C).
    13. Fokoué, Ernest, 2005. "Mixtures of factor analyzers: an extension with covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 370-384, August.
    14. Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.
    15. Hao Wu & Ryne Estabrook, 2016. "Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1014-1045, December.
    16. Terry Elrod & Gerald Häubl & Steven Tipps, 2012. "Parsimonious Structural Equation Models for Repeated Measures Data, with Application to the Study of Consumer Preferences," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 358-387, April.
    17. Wayne S. DeSarbo & Alexandru M. Degeratu & Michel Wedel & M. Kim Saxton, 2001. "The Spatial Representation of Market Information," Marketing Science, INFORMS, vol. 20(4), pages 426-441, June.
    18. 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).
    19. Liat Ayalon, 2018. "Perceived Age Discrimination: A Precipitator or a Consequence of Depressive Symptoms?," The Journals of Gerontology: Series B, The Gerontological Society of America, vol. 73(5), pages 860-869.
    20. Steven Andrew Culpepper & Herman Aguinis & Justin L. Kern & Roger Millsap, 2019. "High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 285-309, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:jedbes:v:40:y:2015:i:4:p:402-423. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.