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, Volume 17, Issue 2, pp 25–40 | Cite as

A survey of some studies in methods for the structural analysis of multivariate data in the social sciences

  • Roderick P. McDonald
Dominant Themes

Keywords

Social Science Structural Analysis Multivariate Data 
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References

  1. Ahlawat, K. S. (1976).Alternative methods of estimating the parameters of the normal ogive. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  2. Anderson, T. W. (1959). Some scaling models and estimation procedures in the latent class model. In U. Grenander (Ed.),Probability and statistics (the Harold Cramer volume) (pp. 9–38). New York: Wiley.Google Scholar
  3. Anderson, T. W., & Rubin, H. (1956). Statistical inference in factor analysis.Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability 5 111–150.Google Scholar
  4. Bartholomew, D. J. (1980). Factor analysis for categorical data (with discussion).Journal of the Royal Statistical Society Series B 42 293–321.Google Scholar
  5. Bartholomew, D. J. (1985). Foundations of factor analysis: Some practical applications.British Journal of Mathematical and Statistical Psychology 38 1–10.Google Scholar
  6. Boodoo, G. M. (1973).Application of simple structure to factor pattern, factor structure and factor score regression matrices. Unpublished master's thesis, University of Toronto.Google Scholar
  7. Boodoo, G. M. (1977).The structure of binary data. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  8. Browne, M. W. (1974). Generalized least squares estimators in the analysis of covariance structures.South African Statistical Journal 8 1–24. Reprinted in D. J. Aigner & A. S. Goldberger (Eds.),Latent variables in socio-economic models (pp. 205–226). Amsterdam: North Holland.Google Scholar
  9. Browne, M. W. (1986).Robustness of statistical inference in factor analysis and related models (Research Rep.). Department of Statistics, University of South Africa.Google Scholar
  10. Chan, K.-W. (1978).A study of radex theory. Unpublished master's thesis, University of Toronto.Google Scholar
  11. Christofferson, A. (1975). Factor analysis of dichotomized variables.Psychometrika 40 5–22.Google Scholar
  12. Coombs, C. H. (1964).A theory of data. New York: Wiley.Google Scholar
  13. Coughlin, R. (1974).A multidimensional extension of the normal ogive, logistic and linear latent trait models. Unpublished master's thesis, University of Toronto.Google Scholar
  14. Dassa, C. (1979).A factor analytic model for longitudinal data. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  15. de Leeuw, J. (1982). Generalized eigenvalue problems with positive semi-definite matrices.Psychometrika 47 87–93.Google Scholar
  16. Draper, N. R., & Smith, H. (1966)Applied regression analysis. New York: Wiley.Google Scholar
  17. Etezadi-Amoli, J. (1978).Nonlinear factor analysis using spline functions. Unpublished master's thesis, University of Toronto.Google Scholar
  18. Etezadi-Amoli, J. (1981).A general polynomial model for nonlinear factor analysis. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  19. Etezadi-Amoli, J., & McDonald, R. P. (1983). A second generation nonlinear factor analysis.Psychometrika 48 315–342.Google Scholar
  20. Fraser, C. (1980).COSAN: User's guide. Toronto: Department of MECA, Ontario Institute for Studies in Education.Google Scholar
  21. Fraser, C. (1981).NOHARM II: A Fortran program for fitting unidimensional and multidimensional normal ogive models of latent trait theory. Armidale, Australia: Centre for Behavioural Studies, The University of New England.Google Scholar
  22. Ghartey-Tagoe, A. (1973).An investigation into Ledermann structure in the oblique factor model. Unpublished master's thesis, University of Toronto.Google Scholar
  23. Gorsuch, R. L. (1983).Factor analysis. Hillsdale, NJ: Erlbaum Associates.Google Scholar
  24. Guttman, L. (1941). The quantification of a class of attributes. In P. Horst (Ed.),The prediction of personal adjustment. New York: Social Science Research Council.Google Scholar
  25. Ishizuka, T. (1976).Weighting multicategory data to fit the common factor model. Unpublished master's thesis, University of Toronto.Google Scholar
  26. Jennrich, R. I., & Robinson, S. M. (1969). A Newton-Raphson algorithm for maximum likelihood factor analysis.Psychometrika 34 111–123.Google Scholar
  27. Jöreskog, K. G. (1970). A general method for the analysis of covariance structures.Biometrika 57 239–251.Google Scholar
  28. Jöreskog, K. G. (1973). A general method for estimating a linear structural equation system. In A. S. Goldberger & O. D. Duncan (Eds.),Structural equation models in the social sciences. New York: Seminar Press.Google Scholar
  29. Kestelman, H. (1952). The fundamental equation of factor analysis.British Journal of Psychology, Statistics Section 5 1–6.Google Scholar
  30. Krane, W. R. (1977).Unrestricted common factor analysis by Newton's method. Unpublished doctoral dissertation, York University, Toronto.Google Scholar
  31. Krane, W. R., & McDonald, R. P. (1978). Scale-invariant estimators in common factor analysis and related models.British Journal of Mathematical and Statistical Psychology 31 218–228.Google Scholar
  32. Kruskal, J. B., & Wish, M. (1978).Multidimensional scaling. Beverly Hills, CA: Sage.Google Scholar
  33. Leong, K.-S. (1975).A comprehensive model for covariance structure analysis. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  34. Long, J. S. (1983).Covariance structure models: An introduction to LISREL. Beverly Hills, CA: Sage.Google Scholar
  35. Lord, F. M. (1980).Applications of item response theory to practical testing problems. Hillsdale, NJ: Erlbaum Associates.Google Scholar
  36. Lord, F. M., & Novick, M. R. (1968).Statistical theories of mental test scores: With contributions by Alan Birnbaum. Reading, MA: Addison-Wesley.Google Scholar
  37. Macrae, E. C. (1974). Matrix derivatives with an application to an adaptive linear decision problem.Annals of Statistics 2 337–346.Google Scholar
  38. Martin, J. K., & McDonald, R. P. (1975). Bayesian estimation in unrestricted factor analysis: A treatment for Heywood cases.Psychometrika 40 505–517.Google Scholar
  39. McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the reticular action model for moment structures.British Journal of Mathematical and Statistical Psychology 37 234–251.Google Scholar
  40. McDonald, R. P. (1962a). A general approach to nonlinear factor analysis.Psychometrika 27 397–415.Google Scholar
  41. McDonald, R. P. (1962b). A note on the derivation of the general latent class model.Psychometrika 27 203–206.Google Scholar
  42. McDonald, R. P. (1967a). Factor interaction in nonlinear factor analysis.British Journal of Mathematical and Statistical Psychology 20 205–215.Google Scholar
  43. McDonald, R. P. (1967b). Nonlinear factor analysis.Psychometric Monograph, No. 15.Google Scholar
  44. McDonald, R. P. (1967c). Numerical methods for polynomial models in nonlinear factor analysis.Psychometrika 32 77–112.Google Scholar
  45. McDonald, R. P. (1968). A unified treatment of the weighting problem.Psychometrika 33 351–381.Google Scholar
  46. McDonald, R. P. (1969a). The common factor analysis of multicategory data.British Journal of Mathematical and Statistical Psychology 22 165–175.Google Scholar
  47. McDonald, R. P. (1969b). A generalized common factor analysis based on residual covariance matrices of prescribed structure.British Journal of Mathematical and Statistical Psychology 22 149–163.Google Scholar
  48. McDonald, R. P. (1970a). The theoretical foundations of common factor analysis, principal factor analysis, and alpha factor analysis.British Journal of Mathematical and Statistical Psychology 23 1–21.Google Scholar
  49. McDonald, R. P. (1970b). Three common factor models for groups of variables.Psychometrika 35 111–128.Google Scholar
  50. McDonald, R. P. (1974). Testing pattern hypotheses for covariance matrices.Psychometrika 39 189–201.Google Scholar
  51. McDonald, R. P. (1975). Testing pattern hypotheses for correlation matrices.Psychometrika 40 253–255.Google Scholar
  52. McDonald, R. P. (1976). The McDonald-Swaminathan calculus: Clarifications, extensions and illustrations.General Systems 21 87–94.Google Scholar
  53. McDonald, R. P. (1978). A simple comprehensive model for the analysis of covariance structures.British Journal of Mathematical and Statistical Psychology 31 59–72.Google Scholar
  54. McDonald, R. P. (1979a). The simultaneous estimation of factor loadings and scores.British Journal of Mathematical and Statistical Psychology 32 212–228.Google Scholar
  55. McDonald, R. P. (1979b). The structure of multivariate data: A sketch of a general theory.Multivariate Behavioral Research 14 21–28.Google Scholar
  56. McDonald, R. P. (1980). A simple comprehensive model for the analysis of covariance structures: Some remarks on applications.British Journal of Mathematical and Statistical Psychology 33 161–183.Google Scholar
  57. McDonald, R. P. (1981). The dimensionality of tests and items.British Journal of Mathematical and Statistical Psychology 34 100–117.Google Scholar
  58. McDonald, R. P. (1982a). A note on the investigation of local and global identifiability.Psychometrika 47 101–103.Google Scholar
  59. McDonald, R. P. (1982b). Linear versus nonlinear models in item response theory.Applied Psychological Measurement 6 379–396.Google Scholar
  60. McDonald, R. P. (1982c). Some alternative approaches to the improvement of measurement in education and psychology: Fitting latent trait models. In D. Spearritt (Ed.),The improvement of measurement in education and psychology. Victoria: Australian Council for Educational Research.Google Scholar
  61. McDonald, R. P. (1982d, July).Unidimensional and multidimensional models in item response theory. Paper presented at the IR T/CA T conference, Minneapolis, MN.Google Scholar
  62. McDonald, R. P. (1983a). Alternative weights and invariant parameters in optimal scaling.Psychometrika 48 377–391.Google Scholar
  63. McDonald, R. P. (1983b). Exploratory and confirmatory nonlinear factor analysis. In H. Wainer & S. Messick (Eds.),Principals of modern psychological measurement: A festschrift for Frederic M. Lord. Hillsdale, NJ: Erlbaum Associates.Google Scholar
  64. McDonald, R. P. (1984). Confirmatory models for nonlinear structural analysis. In E. Diday et al. (Eds.),Data analysis and informatics III. New York: Elsevier Science Publishers.Google Scholar
  65. McDonald, R. P. (1985).Factor analysis and related methods. Hillsdale, NJ: Erlbaum Associates.Google Scholar
  66. McDonald, R. P. (1985). Comments on O. J. Bartholomew's “Foundations of factor analysis: Some practical applications.”British Journal of Mathematical and Statistical Psychology 38 134–137.Google Scholar
  67. McDonald, R. P., & Ahlawat, K. S. (1974). Difficulty factors in binary data.British Journal of Mathematical and Statistical Psychology 27 82–99.Google Scholar
  68. McDonald, R. P., & Krane, W. R. (1977). A note on local identifiability and degrees of freedom in the asymptotic likelihood ratio test.British Journal of Mathematical and Statistical Psychology 30 198–203.Google Scholar
  69. McDonald, R. P., & Krane, W. R. (1979). A Monte Carlo study of local identifiability and degrees of freedom in the asymptotic likelihood ratio test.British Journal of Mathematical and Statistical Psychology 32 121–132.Google Scholar
  70. McDonald, R. P., & Mulaik, S. A. (1979). Determinacy of common factors: A non-technical review.Psychological Bulletin 86 297–306.Google Scholar
  71. McDonald, R. P., & Swaminathan, H. (1972).The structural analysis of dispersion matrices based on a very general model with a rapidly convergent procedure for the estimation of parameters. Toronto: Department of Measurement and Evaluation, Ontario Institute for Studies in Education.Google Scholar
  72. McDonald, R. P., & Swaminathan, H. (1973). A simple matrix calculus with applications to multivariate analysis.General Systems 18 37–54.Google Scholar
  73. McDonald, R. P., Torii, Y., & Nishisato, S. (1979). Some results on proper eigenvalues and eigenvectors with applications to scaling.Psychometrika 44 211–227.Google Scholar
  74. Mulaik, S. A. (1972).The foundations of factor analysis. New York: McGraw Hill.Google Scholar
  75. Nishisato, S. (1980).Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press.Google Scholar
  76. Rao, C. R., & Mitra, B. K. (1971).Generalized inverse of matrices and its applications. New York: Wiley.Google Scholar
  77. Shapiro, A., & Browne, M. W. (1983). On the investigation of local identifiability: A counterexample.Psychometrika 48 303–304.Google Scholar
  78. Swaminathan, H. (1976). Matrix calculus for functions of partitioned matrices.General Systems 21 95–99.Google Scholar
  79. Thomson, G. H. (1950).The factorial analysis of human ability. London: University of London Press.Google Scholar
  80. Torii, Y. (1977).Generalizations of optimal scaling. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  81. Tracy, D. S., & Dwyer, P. S. (1969). Multivariate maxima and minima with matrix derivatives.Journal of the American Statistical Association 64 1576–1594.Google Scholar
  82. Trahan, M. (1974).An investigation of multicategory data factor analysis. Unpublished doctoral dissertation, University of Toronto.Google Scholar
  83. Van Driel, O. P. (1978). On various causes of improper solutions in maximum likelihood factor analysis.Psychometrika 43 225–243.Google Scholar
  84. Wald, A. (1950). Note on the identification of economic relations. In T. C. Koopmans (Ed.),Statistical inference in dynamic economic models (pp. 238–257). (Cowles Commission Monograph Number 10). New York: Wiley.Google Scholar
  85. Wingersky, M. S., & Lord, F. M. (1973).A computer program for estimating examinee ability and item characteristic curve parameters when there are omitted responses (RM-73-2). Princeton, NJ: Educational Testing Service.Google Scholar
  86. Young, F. W., de Leeuw, J., & Takane, Y. (1979). Quantifying qualitative data. In H. Feger (Ed.),Similarity and choice. New York: Academic Press.Google Scholar

Copyright information

© The Ontario Institute for Studies in Education 1986

Authors and Affiliations

  • Roderick P. McDonald
    • 1
  1. 1.Macquarie University

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