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On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models

Author

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  • Njål Foldnes

    (BI Norwegian Business School)

  • Steffen Grønneberg

    (BI Norwegian Business School)

Abstract

A standard approach for handling ordinal data in covariance analysis such as structural equation modeling is to assume that the data were produced by discretizing a multivariate normal vector. Recently, concern has been raised that this approach may be less robust to violation of the normality assumption than previously reported. We propose a new perspective for studying the robustness toward distributional misspecification in ordinal models using a class of non-normal ordinal covariance models. We show how to simulate data from such models, and our simulation results indicate that standard methodology is sensitive to violation of normality. This emphasizes the importance of testing distributional assumptions in empirical studies. We include simulation results on the performance of such tests.

Suggested Citation

  • Njål Foldnes & Steffen Grønneberg, 2019. "On Identification and Non-normal Simulation in Ordinal Covariance and Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1000-1017, December.
  • Handle: RePEc:spr:psycho:v:84:y:2019:i:4:d:10.1007_s11336-019-09688-z
    DOI: 10.1007/s11336-019-09688-z
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    References listed on IDEAS

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    1. Albert Maydeu-Olivares, 2006. "Limited information estimation and testing of discretized multivariate normal structural models," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 57-77, March.
    2. repec:hrv:faseco:34728615 is not listed on IDEAS
    3. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    4. Njål Foldnes & Steffen Grønneberg, 2015. "How General is the Vale–Maurelli Simulation Approach?," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1066-1083, December.
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    7. Steffen Grønneberg & Njål Foldnes, 2017. "Covariance Model Simulation Using Regular Vines," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1035-1051, December.
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    9. Yoshio Takane & Jan Leeuw, 1987. "On the relationship between item response theory and factor analysis of discretized variables," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 393-408, September.
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    Cited by:

    1. Alessandro Barbiero & Asmerilda Hitaj, 2020. "Goodman and Kruskal’s Gamma Coefficient for Ordinalized Bivariate Normal Distributions," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 905-925, December.
    2. Steffen Grønneberg & Jonas Moss & Njål Foldnes, 2020. "Partial Identification of Latent Correlations with Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 1028-1051, December.

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