Various Graphical Methods for Assessing a Logistic Regression Model

- Journal title : Korean Journal of Applied Statistics
- Volume 28, Issue 6, 2015, pp.1191-1208
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2015.28.6.1191

Title & Authors

Various Graphical Methods for Assessing a Logistic Regression Model

Kim, Kyung Jin; Kahng, Myung Wook;

Kim, Kyung Jin; Kahng, Myung Wook;

Abstract

Most statistical methods are dependent on the summary statistic. However, with graphical approaches, it is easier to identify the characteristics of the data and detect information that cannot be obtained by the summary statistic. We present various graphical methods to assess the adequacy of models in logistic regression that include checking log-density ratio, structural dimension, marginal model plot, chi-residual plot, and CERES plot. Through simulation data, we investigate and compare the results of graphical approaches under diverse conditions.

Keywords

binary response plot;CERES plot;chi-residual plot;log-density ratio;marginal model plot;structural dimension;

Language

Korean

References

1.

Atkinson, A. C. (1985). Plots, Transformations and Regression, Oxford University Press, Oxford.

2.

Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression Diagnostics, Wiley, New York.

3.

Cleveland, W. S. and Devlin, D. J. (1988). Locally weighted regression: An approach to regression analysis by local fitting, Journal of the American Statistical Association, 83, 596-610.

5.

Cook, R. D. (1998). Regression Graphics: Idea for Studying Regressions through Graphics, Wiley, New York.

6.

Cook, R. D. and Croos-Dabrera, R. (1998). Partial residual plots in generalized linear models, Journal of the American Statistical Association, 93, 730-739.

7.

Cook, R. D. and Weisberg, S. (1982). Residuals and Inuence in Regression, Chapman & Hall, London.

8.

Cook, R. D. and Weisberg, S. (1994). An Introduction to Regression Graphics, Wiley, New York.

9.

Cook, R. D. and Weisberg, S. (1997). Graphics for assessing the adequacy of regression models, Journal of the American Statistical Association, 92, 490-499.

10.

Cook, R. D. and Weisberg, S. (1999). Applied Regression Including Computing and Graphics, Wiley, New York.

11.

Ezekiel, M. (1924). A method of handling curvilinear correlation for any number of variables, Journal of the American Statistical Association, 19, 431-453.

12.

Kay, R. and Little, S. (1987). Transformations of the explanatory variables in the logistic regression model for binary data, Biometrika, 74, 495-501.

13.

Scrucca, L. (2003). Graphics for studying logistic regression models, Statistical Methods and Applications, 11, 371-394.

14.

Scrucca, L. and Weisberg, S. (2004). A simulation study to investigate the behavior of the log-density ratio under normality, Communication in Statistics Simulation and Computation, 33, 159-178.

15.

Tierney, L. (1990). Lisp-Stat: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics, Wiley, New York.