Diagnosing and revising logistic regression models

Purpose – This study aims to apply a systematic statistical approach, including several plot indexes, to diagnose the goodness of fit of a logistic regression model, and then to detect the outliers and influential observations of the data from experimental data.Design/methodology/approach – The proposed statistical approach is applied to analyze some experimental data on internal solitary wave propagation.Findings – A suitable logistic regression model in which the relationship between the response variable and the explanatory variables is found. The problem of multicollinearity is tested. It was found that certain observations would not have the problem of multicollinearity. The P‐values for both the Pearson and deviance χ2 tests are greater than 0.05. However, the Pearson χ2 value is larger than the degrees of freedom. This finding indicates that although this model fits the data, it has a slight overdispersion. After three outliers and influential observations (cases 11, 27, and 49) are removed from th...

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

[2]  D. Pregibon.  Logistic Regression Diagnostics , 1981 .

[3]  B. Tabachnick,et al.  Using Multivariate Statistics , 1983 .

[4]  D. Pregibon,et al.  Graphical Methods for Assessing Logistic Regression Models , 1984 .

[5]  Dennis E. Jennings.  Judging Inference Adequacy in Logistic Regression , 1986 .

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

[7]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[8]  D. Hosmer,et al.  Applied Logistic Regression , 1991 .

[9]  D. Collett,et al.  Modeling Binary Data. , 1993 .

[10]  Hans C. Jessen,et al.  Applied Logistic Regression Analysis , 1996 .

[11]  Jack Shostak,et al.  Common Statistical Methods for Clinical Research With SAS> Examples , 1997 .

[12]  Paul D. Allison,et al.  Logistic Regression Using the SAS System : Theory and Application , 1999 .

[13]  S. Menard.  Applied Logistic Regression Analysis , 1996 .

[14]  D. Cacchione,et al.  The Shaping of Continental Slopes by Internal Tides , 2002, Science.

[15]  Bayo Lawal,et al.  Categorical Data Analysis With Sas and Spss Applications , 2003 .

[16]  Chen-Yuan Chen,et al.  Interaction between internal waves and a permeable seabed , 2005 .

[17]  Chen-Yuan Chen,et al.  Laboratory Observations on Internal Solitary Wave Evolution over a Submarine Ridge , 2006 .

[18]  Chen-Yuan Chen.  An experimental study of stratified mixing caused by internal solitary waves in a two-layered fluid system over variable seabed topography , 2007 .

[19]  Chen-Yuan Chen,et al.  An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes , 2007 .

[20]  Cheng-Wu Chen,et al.  Analysis of experimental data on internal waves with statistical method , 2007 .

[21]  Chen-Yuan Chen,et al.  Laboratory observations on internal solitary wave evolution on steep and inverse uniform slopes , 2007 .