Residual Deviance

["Lambert.Winnie" <lambert.winnie@ensco.com>]

S-PLUS 6,  MS Windows XP

 

I am creating several logistic regression equations in which the predictand is binary and the predictors are continuous.  When I use the anova() function to analyze the contribution of each of the predictors, the output includes 'Residual Deviance'.  Of the 4 types of residuals, MASS states that the deviance is the most useful for diagnostic purposes.  My knowledge of residuals does not extend past that for linear regression.  Is it possible to interpret the reduction in the resid deviance as a percent contribution toward explaining the variance in the equation?  e.g.  in one equation the Null residual deviance is 462.5411 with 343 resid degrees of freedom.  The data set has 344 observations for the predictand: 207 1's and 137 0's.  After adding 12 predictors, the resid deviance is now 322.0167 with 332 residual df.  The percent reduction in resid dev is 100*(462.5411 - 322.0167)/322.0167 = 30.4% .....is that an appropriate conclusion?  When I calculate the standard residuals that I am used to, the change goes from 82.4 to 52.4 for a total reduction in the residuals of 36%.  With the second example, am I trying to calculate a linear response to a non-linear process and, therefore, get different percentages for the reduction in the variance of the residuals?

 

I apologize for my ignorance - I appreciate any help in interpreting these values, even if it comes with a scolding

 

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Winifred C. Lambert  Senior Scientist/Meteorologist

ENSCO, Inc.

Aerospace Sciences and Engineering Division

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EMAIL:  lambert.winnie@ensco.com

 

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