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Multilevel Structural Equation Modeling

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Handbook of Multilevel Analysis

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References

  1. A. Agresti. Categorical Data Analysis. Wiley, New York, 1990.

    MATH  Google Scholar 

  2. M. Aitkin and N. Longford. Statistical modelling issues in school effectiveness studies. Journal of the Royal Statistical Society, Series A, 149:1–43, 1986. (with discussion)

    Article  Google Scholar 

  3. H. Akaike. Factor analysis and AIC. Psychometrika, 52:317–332, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  4. T. W. Anderson. An Introduction to Multivariate Statistical Analysis, 2nd edition. Wiley, New York, 1984.

    Google Scholar 

  5. R. E. Bargmann. Matrices and determinants. In R. C. Weast and S. M. Selby, editors, C.R.C. Handbook of Tables in Mathematics, 4th edition, pages 507–534. Chemical Rubber, Cleveland, OH, 1975.

    Google Scholar 

  6. R. D. Bock. Within-subject experimentation in psychiatric research. In R. D. Gibbons and M. W. Dysken, editors, Statistical and Methodological Advances in Psychiatric Research, pages 59–90. Spectrum, New York, 1983.

    Google Scholar 

  7. H. Bozdogan. Model selection and Akaike’s Information Criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52:345–370, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. W. Browne. Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 8:1–24, 1974. (Reprinted in D. J. Aigner and A. S. Goldberger, editors, Latent Variables in Socio-Economic Models, pages 205–226, North-Holland, Amsterdam, 1977.)

    MathSciNet  Google Scholar 

  9. M. W. Browne and R. Cudeck. Alternative ways of assessing model fit. In K. A. Bollen and J. S. Long, editors, Testing Structural Equation Models, pages 136–162. Sage, Thousand Oaks, CA, 1993.

    Google Scholar 

  10. M. W. Browne and S. H. C. Du Toit. Automated fitting of nonstandard models for mean vectors and covariance matrices. Multivariate Behavioral Research, 27:269–300, 1992.

    Article  Google Scholar 

  11. A. S. Bryk and S. W. Raudenbush. Hierarchical Linear Models: Applications and Data Analysis Methods. Sage, Newbury Park, CA, 1992.

    Google Scholar 

  12. J. de Leeuw and I. G. G. Kreft. Random coefficient models for multilevel analysis. Journal of Educational Statistics, 11:57–85, 1986.

    Article  Google Scholar 

  13. A. P. Dempster, D. B. Rubin, and R. K. Tsutakawa. Estimation in covariance components models. Journal of the American Statistical Association, 76: 341–353, 1981.

    Google Scholar 

  14. M. Du Toit. The Analysis of Hierarchical and Unbalanced Complex Survey Data using Multilevel Models. PhD thesis, University of Pretoria, Pretoria, South Africa, 1995.

    Google Scholar 

  15. M. Du Toit and S. H. C. Du Toit. Interactive LISREL: User’s Guide. Scientific Software International, Chicago, 2002.

    Google Scholar 

  16. R. D. Gibbons and R. D. Bock. Trend in correlated proportions. Psychometrika, 52:113–124, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  17. P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization. Academic Press, London, 1981.

    MATH  Google Scholar 

  18. H. Goldstein. Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73:43–56, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  19. H. Goldstein and R. P. McDonald. A general model for the analysis of multilevel data. Psychometrika, 53:455–467, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  20. D. Holt, A. J. Scott, and P. D. Ewings. Chi-squared tests with survey data. Journal of the Royal Statistical Society, Series A, 143:303–320, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. J. Hox. Factor analysis of multilevel data: Gauging the Muthèn model. In J. H. L. Oud and R. A. W. van Blokland-Vogelesang, editors, Advances in Longitudinal and Multivariate Analysis in the Behavioral Sciences, pages 141–156. ITS, Nijmegen, The Netherlands, 1993.

    Google Scholar 

  22. R. I. Jennrich and P. F. Sampson. Application of stepwise regression to nonlinear estimation. Technometrics, 10:63–72, 1968.

    Article  MathSciNet  Google Scholar 

  23. K. G. Jöreskog. Structural equation models in the social sciences: Specification, estimation and testing. In P. R. Krishnaiah, editor, Applications of Statistics, pages 265–287. North-Holland, Amsterdam, 1977.

    Google Scholar 

  24. K. G. Jöreskog and D. Sörbom. Advances in Factor Analysis and Structural Equation Models. Abt Books, Cambridge, MA, 1979.

    MATH  Google Scholar 

  25. K. G. Jöreskog and D. Sörbom. LISREL 8: Structural Equation Modeling with the SIMPLIS Command Language. Scientific Software International, Chicago, 1993.

    Google Scholar 

  26. K. G. Jöreskog and D. Sörbom. LISREL 8 User's Reference Guide. Scientific Software International, Chicago, 1996.

    Google Scholar 

  27. C. G. Khatri. A note on a MANOVA model applied to problems in growth curves. Annals of the Institute of Statistical Mathematics, 181:75–86, 1966.

    Article  MathSciNet  Google Scholar 

  28. S.-Y. Lee. Multilevel analysis of structural equation models. Biometrika, 77:763–772, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  29. S.-Y. Lee and W.-Y. Poon. Analysis of two-level structural equation models via EM type algorithms. Statistica Sinica, 8:749–766, 1998.

    MATH  MathSciNet  Google Scholar 

  30. J. Liang and P. M. Bentler. An EM algorithm for fitting two-level structural equation models. Psychometrika, 69:101–122, 2004.

    Article  MathSciNet  Google Scholar 

  31. N. T. Longford. A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects. Biometrika, 74:817–827, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  32. W. M. Mason, G. Y. Wong, and B. Entwisle. Contextual analysis through the multilevel linear model. Sociological Methodology, 14:72–103, 1983.

    Article  Google Scholar 

  33. J. J. McArdle and R. P. McDonald. Some algebraic properties of the Reticular Action Model for moment structures. British Journal of Mathematical and Statistical Psychology, 37:234–251, 1984.

    MATH  Google Scholar 

  34. R. P. McDonald. A general model for two-level data with responses missing at random. Psychometrika, 58:575–585, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  35. R. P. McDonald. The Bilevel Reticular Action Model for path analysis with latent variables. Sociological Methods & Research, 22:399–413, 1994.

    Article  Google Scholar 

  36. R. P. McDonald and H. Goldstein. Balanced versus unbalanced designs for linear structural relations in two-level data. British Journal of Mathematical and Statistical Psychology, 42:215–232, 1989.

    MATH  MathSciNet  Google Scholar 

  37. P. Mortimore, P. Sammons, L. Stoll, D. Lewis, and R. Ecob. School Matters, the Junior Years. Open Books, Wells, UK, 1988.

    Google Scholar 

  38. B. O. Muthén. Mean and covariance structure analysis of hierarchical data. UCLA Statistics Preprint 62, UCLA, Department of Statistics, Los Angeles, 1990.

    Google Scholar 

  39. B. O. Muthén. Multilevel factor analysis of class and student achievement com-ponents. Journal of Educational Measurement, 28:338–354, 1991.

    Article  Google Scholar 

  40. B. O. Muthén. Multilevel covariance structure analysis. Sociological Methods & Research, 22:376–398, 1994.

    Article  Google Scholar 

  41. S. W. Raudenbush. Maximum likelihood estimation for unbalanced multilevel covariance structure models via the EM algorithm. British Journal of Mathematical and Statistical Psychology, 48:359–370, 1995.

    MATH  Google Scholar 

  42. S. W. Raudenbush and A. S. Bryk. A hierarchical model for studying school effects. Sociology of Education, 59:1–17, 1986.

    Article  Google Scholar 

  43. J. H. Steiger. Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research, 25:173–180, 1990.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Scientific Software International, Lincolnwood, IL 60712-1747, USA

    Stephen H. C. du Toit & Mathilda du Toit

Authors
  1. Stephen H. C. du Toit
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  2. Mathilda du Toit
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Editor information

Editors and Affiliations

  1. Department of Statistics, University of California at Los Angeles, Los Angeles, CA 90095-1554, USA

    Jan de Leeuw

  2. RAND Corporation, 1776 Main St, PO Box 2138, Santa Monica, CA 90407-2138, USA

    Erik Meijer

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du Toit, S.H., Toit, M.d. (2008). Multilevel Structural Equation Modeling. In: Leeuw, J.d., Meijer, E. (eds) Handbook of Multilevel Analysis. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73186-5_12

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