Collapsibility and Suppression for Cumulative Logistic Model

Hong, Chong-Sun;Kim, Kil-Tae

  • 발행 : 2005.08.01


In this paper, we discuss suppression for logistic regression model. Suppression for linear regression model was defined as the relationship among sums of squared for regression as well as correlation coefficients of. variables. Since it is not common to obtain simple correlation coefficient for binary response variable of logistic model, we consider cumulative logistic models with multinomial and ordinal response variables rather than usual logistic model. As number of category of a response variable for the cumulative logistic model gets collapsed into binary, it is found that suppressions for these logistic models are changed. These suppression results for cumulative logistic models are discussed and compared with those of linear model.


Coefficient of determination;Log-linear model;Logit model


  1. Cohen, J. and Cohen, P.(1975). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences, New Jersey: Lawrence Erlbaum Associates
  2. Conger, A. J.(1975). A Revised Definition for Suppressor Variables: A Guide to Their Identification and Interpretation, Educational and Psychological Measurement, 34, 35-46
  3. Cox, D. R and Snell, E. J.(1989). Analysis of Binary Data, Chapman and Hall
  4. Hamilton, D.(1987). Sometimes $R^2\;>\;r^2_{yx_1}+R^2_{yx_2}$ Correlated Variables are not Always Redundant, The American Statistician, 41, 129-132
  5. Horst, P.(1941). The Role of Prediction Variables Which are Independent of the Criterion, in The Prediction Adjustment, ed. P. Horst, New York: Social Science Research Council
  6. Hong, C. S.(2004). Suppression and Collapsibility for Log-linear Model, The Korean Communication in Statistics, 11, 3, 519-527
  7. Lynn, H. S.(2003). Suppression and Confounding in Action, The American Statistician, 57, 58-61
  8. McCullagh, P.(1980), Regression Models for Ordinal Data (with discussion), Journal of Royal Statistical Society, Ser. B, 42, 109-142
  9. Menard, S.(2000). Coefficients of Determination for Multiple Logistic Regression Analysis, The American Statistician, 54, 17-24
  10. Mittlebock, M. and Schemper, M.(1996). Explained Variation for Logistic Regression, Statistics in Medicine, 15, 1987-1997<1987::AID-SIM318>3.0.CO;2-9
  11. Schey, H. M.(1993). The Relationship Between the Magnitudes of SSR($X_2$) and SSR($X_2IX_1$): A Geometric Description, The American Statistician, 47, 26-30
  12. Sharpe, N. R., and Roberts, R. A.(1997). The Relationship Among Sums of Squares, Correlation Coefficients, and Suppression, The American Statistician, 51, 46-48
  13. Walker. S. H. and Duncan, D. B.(1967). Estimation of the Probability of an Event as a Function of Several Independent Variables. Biometrika. 54, 167-179
  14. Nagelkerke, N. J. D.(1991). A Note on a General Definition of the Coefficient of Determination. Biometrika. 78: 691-692
  15. Murad, H., Fleischman, A., Sadetzki, S., Geyer, O., and Freedman, L. S.(2003). Small Samples and Ordered Logistic Regression: Does it Help to Collapse Categories of Outcome?' The American Statistician. 57, 3, 155-160
  16. Velicer, W. F.(1978). Suppressor Variables and the Sernipartial Correlation Coefficient. Educational and Psychological Measurement, 38: 953-958