Deviance residuals

Call gam(formula = Loss s(AirFlow) + s(waterTemp) +s(AcidConc), data = stack, control = gam.control(bf.maxit = 50)) Deviance Residuals ... 

Figure 5.26 Top plot is observed data and fitted models for the nausea and vomiting data in Table 5.22 using AUC as the predictor for both males and females. Bottom plot is an index plot of deviance residuals.

While in the regression case the optimization criterion was based on residual sum of squares, this would not be meaningful in the classification case. A usual error function in the context of neural networks is the cross entropy or deviance, defined as... 

Type stack < -data.frame(cbind (stack.x,stack, loss) ) (note stack.x and stack.loss are S-Plus built-in data sets) The following is a single command names (stack) < -c( AirFlow , waterTemp , AcidConc , Loss ) System responds with Call gam(formula = Loss s(AirFlow) + s(waterTemp) + s(AcidConc), data = stack, control = gam.control(bf.maxit = 50)) Degrees of Freedom 21 total 8.00097 Residual Residual Deviance 67.79171 ... 

Residual Deviance 67.79171 on 8.00097 degrees of freedom Number of Local Scoring Iterations 1 DF for Terms and F-values for Nonparametric... 

If multiple observations are available on each sampling unit, such as a subject in a clinical trial, a plot of residuals versus subject number may be informative at detecting systematic deviations between subjects. Each subject s residuals should be centered around zero with approximately the same variance. Subjects that show systematic deviance from the model will tend to have all residuals above or below the zero line. This plot becomes more useful as the number of observations per subject increases because with a small number of... 

A variety of diagnostics for examining individual observations for extreme deviance and extreme influence can be derived using Hp Four are chosen here. The following developments [except Eq. (57)] are given by or derived from the work of Belsley et al. (1980). The first diagnostic, the standardized residual for the ith observation, is... 

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