Applying R 2 -Type measures to ordered categorical data

The concentration and entropy measures for categorical data tend to be highly dependent on the choice of response categories. If the categorization of the response variable is arbitiary but it is reasonable to assume an underlying continuous distribution, then an adaptation of the regression R 2 measure can be useful for describing multiple association.

[1]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.

[2]  J. Landis,et al.  Catanova for multidimensional contingency tables: ordinal-scale resfqnse , 1980 .

[3]  H. Theil On the Estimation of Relationships Involving Qualitative Variables , 1970, American Journal of Sociology.

[4]  Barry H. Margolin,et al.  An Analysis of Variance for Categorical Data, II: Small Sample Comparisons with Chi Square and other Competitors , 1974 .

[5]  V. P. Bhapkar,et al.  On the analysis of contingency tables with a quantitative response. , 1968, Biometrics.

[6]  Leo A. Goodman,et al.  Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories , 1981 .

[7]  R. N. Kackar,et al.  Off-line quality control in integrated circuit fabrication using experimental design , 1983 .

[8]  B. Efron Regression and ANOVA with Zero-One Data: Measures of Residual Variation , 1978 .

[9]  G. Koch,et al.  Linear Models Methods for Some Rank Function Analyses of Ordinal Categorical Data , 1983 .

[10]  P. McCullagh Regression Models for Ordinal Data , 1980 .

[11]  L. A. Goodman Simple Models for the Analysis of Association in Cross-Classifications Having Ordered Categories , 1979 .

[12]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[13]  Stephen E. Fienberg,et al.  The analysis of cross-classified categorical data , 1980 .

[14]  L. A. Goodman,et al.  Measures of Association for Cross Classifications, IV: Simplification of Asymptotic Variances , 1972 .

[15]  A. Agresti Analysis of Ordinal Categorical Data , 1985 .

[16]  S. Haberman Analysis of Dispersion of Multinomial Responses , 1982 .

[17]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[18]  Jay Magidson,et al.  Qualitative variance, entropy, and correlation ratios for nominal dependent variables , 1981 .

[19]  Bhapkar Vp,et al.  On the analysis of contingency tables with a quantitative response. , 1968 .

[20]  Louis N. Gray,et al.  Goodman and Kruskal's Tau b: Multiple and Partial Analogs , 1981 .

[21]  James E. Grizzle,et al.  Analysis of Contingency Tables Having Ordered Response Categories , 1972 .