Borrowing Strength from Images to Facilitate Exploratory Structural Analysis of Binary Variables

  • Robert M. Pruzek
Conference paper


This paper concerns exploratory structural analysis of relations among binary variables. Some new methods are described and illustrated, methods that appear to hold promise for general improvements in binary structural analysis. Standard common factor theory and methods, including image analysis, are used in combination with methods for data smoothing, to construct an alternative data system at the outset of analysis. Most of the new algorithms are relatively fast, easy to explain and to program, and appear to work as intended, at least for initial applications with real and simulated data. Given various advances in statistical theory and methods for prediction, as well as increasingly powerful and convenient computing facilities, there are a number of ways to extend the methods discussed here beyond the current framework.


Binary Variable Coefficient Matrice Factor Coefficient Tetrachoric Correlation Apply Psychological Measurement 


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  1. Bock RD, Lieberman M. (1970). Fitting a response curve model for dichotomously scored items. Psychometrika, 35, 179–198.CrossRefGoogle Scholar
  2. Bock, R. D., Gibbons, R., and Muraki, E. (1988) Full-information item factor analysis. Applied Psychological Measurement, 12, 261–280.CrossRefGoogle Scholar
  3. Chen, C. (1979) Bayesian inference for a normal dispersion matrix and its applications to stochastic multiple regression. Journal of the Royal Statistical Society, Series B, 41, 235 —248.Google Scholar
  4. Guttman, L. (1953) Image theory for the structure of quantitative variates. Psychometricka, 18, 273–285.MathSciNetGoogle Scholar
  5. Harris, C.W. (1962). Some Rao-Guttman relationships. Psychometrika, 27, 247 –263.Google Scholar
  6. Knol, D.L. and Berger, M.P.F. (1991). Empirical comparison between factor analysis and multidimensional item response models. ivvlultivariate Behavioral Research, 26, 457–477.CrossRefGoogle Scholar
  7. Mislevy R.J. (1986) Recent developments in the factor analysis of categorical variables. Journal of Educational Statistics, 11, 3–31.CrossRefGoogle Scholar
  8. Muthén, B. (1978) Contributions to factor analysis of dichotomized variables. Psychometrika, 43, 551–560.MathSciNetCrossRefMATHGoogle Scholar
  9. Parry C.D. and McArdle J. J. (1991) An applied comparison of methods for least-squares factor analysis of dichotomous variables. Applied Psychological Measurement, 15, 35–46.CrossRefGoogle Scholar
  10. Pruzek, R.M. and Lepak, G. (1992) Weighted structural regression: A broad class of adaptive methods for improving linear prediction. Multivariate Behavioral Research, 27, 95 – 129.Google Scholar
  11. Rabinowitz, S.N., Rule, D. and Pruzek, R.M. (1998) Some new regression methods for predictive and construct validation. Social Indicators Research, 45, 201– 231.Google Scholar
  12. Tucker, L. R. (1983) Searching for structure in binary data. In H. Wainer and S. Messick (Eds.), Principals of Modern Psychological Measurement, 215 – 235. Erlbaum and Associates, Hillsdale, N.J.Google Scholar
  13. Wailer, N. (2000) MicroFACT user’s manual 2.0. Assessment Systems Corp., St. Paul.Google Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Robert M. Pruzek
    • 1
  1. 1.State University of New York at AlbanyUSA

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