Skip to main content
Log in

Structural equation modeling with ordinal variables: a large sample case study

  • Published:
Quality & Quantity Aims and scope Submit manuscript

Abstract

In the behavioral sciences, response variables are often non-continuous, ordinal variables. Conventional structural equation models (SEMs) have been generalized to accommodate ordinal responses. In this study, three different estimation methods on real data were performed with ordinal variables. Empirical results obtained from the different estimation methods on given real large sample educational data were investigated and compared to recent simulation results. As a result, even very large sample is available, model estimations and fits for ordinal data are affected from inconvenient estimation methods thus it is concluded that asymptotically distribution free estimation method specialized for ordinal variables is more convenient way to model ordinal variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aish A.M., Joreskog K.G.: A panel model for political efficacy and responsiveness: an application of LISREL 7 with weighted least squares. Qual. Quant. 24, 405–426 (1990)

    Article  Google Scholar 

  • Browne M.W.: Covariance structures. In: Hawkins, D.M. (ed.) Topics in Applied Multivariate Analysis, pp. 72–141. Cambridge University Press, Cambridge (1982)

    Chapter  Google Scholar 

  • Browne M.W.: Asymptotically distribution-free methods for the analysis of covariance structures. Br. J. Math. Stat. Psychol. 37, 62–83 (1984)

    Article  Google Scholar 

  • Chamberlain G.: Multivariate regression models for panel data. J. Econom. 18, 5–46 (1982)

    Article  Google Scholar 

  • Chou, C.P., Bentler, P.M., Satorra, A.: Scaled test statistics and robust standard errors for nonnormal data in covariance structure analysis: a monte carlo study. Technical report, University of California, Los Angeles (1989)

  • Ferguson T.S.: A method of generating best asymptotically normal estimates with application to the estimation of bacterial densities. Ann. Math. Stat. 29, 1046–1062 (1958)

    Article  Google Scholar 

  • Fuller W.A., Schnell D., Sullivan G., Kennedy W.J.: Survey variance computations on the personal computer. Paper delivered at the 46th Session of the International Statistical Institute, Tokyo (1987)

    Google Scholar 

  • Jöreskog K.G.: Latent variable modeling with ordinal variables. In: Haagen, K., Barthholomew, D.J., Deistler, M. (eds) Statistical Modelling and Latent Variables, pp. 163–171. Elsevier, Amsterdam (1993)

    Google Scholar 

  • Jöreskog K.G., Sörbom D.: LISREL 7: A Guide to the Program and Applications. SPSS Publications, Chicago (1989)

    Google Scholar 

  • Lee S.Y., Poon W.-Y., Bentler P.M.: A three stage estimation procedure for structural equation models with polytomous variables. Psychometrika 49, 115–132 (1990)

    Google Scholar 

  • Lei P.W.: Evaluating estimation methods for ordinal data in structural equation modeling. Qual. Quant. 43, 495–507 (2009)

    Article  Google Scholar 

  • Magnus J., Neudecker H.: Matrix Differential Calculus. Wiley, New York (1988)

    Google Scholar 

  • Muthén B.: Latent variable structural equation modeling with categorical data. J. Econom. 22, 48–65 (1983)

    Article  Google Scholar 

  • Muthén B.: A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika 49, 115–132 (1984)

    Article  Google Scholar 

  • Muthén, B.: LISCOMP analysis of linear structural equations with a comprehensive measurement model. Theoretical Integration and User’s Guide. Scientific Software, Mooresville (1987)

  • Muthén B., Kaplan D.: A comparison of some methodologies for the factor analysis of nonnormal likert variables. Br. J. Math. Stat. Psychol. 38, 171–189 (1985)

    Article  Google Scholar 

  • Muthén B., Kaplan D.: A comparison of some methodologies for the factor analysis of non-normal likert variables: a note on the size of the model. Br. J. Math. Stat. Psychol. 45, 19–30 (1992)

    Article  Google Scholar 

  • Muthén B., Satorra A.: Complex sample data in structural equation modeling. In: Marsden, P.V. (ed.) Sociological Methodology, pp. 267–316. American Sociological Association, Washington (1995)

    Google Scholar 

  • Olsson U.: On the robustness of factor analysis against crude classification of the observations. Multivar. Behav. Res. 14, 485–500 (1979)

    Article  Google Scholar 

  • Satorra A.: Alternative test criteria in covariance structure analysis: a unified approach. Psychometrika 54, 131–151 (1989)

    Article  Google Scholar 

  • Satorra A.: Robustness issues in structural equation modeling: a review of recent developments. Qual. Quant. 24, 367–386 (1990)

    Article  Google Scholar 

  • Satorra A.: Asymptotic robust inferences in the analysis of mean and covariance structures. In: Marsden, P. (ed.) Sociological Methodology, pp. 249–278. Blackwell, Oxford (1992)

    Google Scholar 

  • Satorra, A., Bentler, P.M.: Scaling corrections for chi-square test statistics in covariance structure analysis. In: Proceedings of the Business and Economic Statistics Section of the American Statistical Association, 308–311 (1988)

  • Satorra A., Bentler P.M.: Model conditions for asymptotic robustness in the analysis of linear relations. Comput. Stat. Data Anal. 10, 235–249 (1990)

    Article  Google Scholar 

  • Satorra A., Bentler P.M.: Corrections to test statistics and standard errors in covariance structure analysis. In: Eye, A., Clogg, C.C. (eds) Latent Variables Analysis: Applications for Developmental Research, pp. 399–419. Sage, Thousand Oaks (1994)

    Google Scholar 

  • Şimşek G.G., Noyan F.: The effect of perceived instructional effectiveness on student loyalty: a multilevel structural equation model. Hacettepe Univ. J. Educ. 36, 109–118 (2009)

    Google Scholar 

  • Skrondral, A., Rabe-Hesketh, S.: Structural equation modeling: categorical variables. Entry for the encyclopedia of statistics in behavioral science, Wiley (2005)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gülhayat Gölbaşı Şimşek.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Şimşek, G.G., Noyan, F. Structural equation modeling with ordinal variables: a large sample case study. Qual Quant 46, 1571–1581 (2012). https://doi.org/10.1007/s11135-011-9467-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11135-011-9467-4

Keywords

Navigation