A new explanatory index for evaluating the binary logistic regression based on the sensitivity of the estimated model

We propose a new explanatory index for evaluating the binary logistic regression model based on the sensitivity of the estimated model. We previously formalized the idea of sensitivity and established the principles a statistic should comply with to be considered a sensitivity index. We apply the results to a practical example and compare the results with those obtained utilizing other indices.

[1]  N. Nagelkerke,et al.  A note on a general definition of the coefficient of determination , 1991 .

[2]  C. Metz.  Basic principles of ROC analysis. , 1978, Seminars in nuclear medicine.

[3]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[4]  P. Schmidt,et al.  Limited-Dependent and Qualitative Variables in Econometrics. , 1984 .

[5]  David R. Cox.  The analysis of binary data , 1970 .

[6]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[7]  Tue Tjur,et al.  Coefficients of Determination in Logistic Regression Models—A New Proposal: The Coefficient of Discrimination , 2009 .

[8]  Robert H. Somers,et al.  A new asymmetric measure of association for ordinal variables. , 1962 .

[9]  Frank Windmeijer,et al.  Goodness-of-fit measures in binary choice models 1 , 1995 .

[10]  R. McKelvey,et al.  A statistical model for the analysis of ordinal level dependent variables , 1975 .

[11]  H. Dalton.  The Measurement of the Inequality of Incomes , 1920 .

[12]  F. Windmeijer,et al.  An R-squared measure of goodness of fit for some common nonlinear regression models , 1997 .

[13]  Roger Newson,et al.  Parameters behind “Nonparametric” Statistics: Kendall's tau, Somers’ D and Median Differences , 2002 .

[14]  David W. Hosmer,et al.  Applied Logistic Regression , 1991 .

[15]  J. Shao,et al.  PSEUDO-R 2 IN LOGISTIC REGRESSION MODEL , 2006 .

[16]  Thomas J. Smith,et al.  A Comparison of Logistic Regression Pseudo R 2 Indices , 2013 .

[17]  J. G. Cragg,et al.  The Demand for Automobiles , 1970 .