project {gss}

Projecting Smoothing Spline ANOVA Fits for Model Diagnostics

Description

Calculate Kullback-Leibler projection of smoothing spline ANOVA fits for model diagnostics.

Usage

project(object, ...)
## S3 method for class 'ssanova'
project(object, include, ...)
## S3 method for class 'ssanova9'
project(object, include, ...)
## S3 method for class 'gssanova'
project(object, include, ...)
## S3 method for class 'ssden'
project(object, include, mesh=FALSE, ...)
## S3 method for class 'ssden1'
project(object, include, drop1=FALSE, ...)
## S3 method for class 'sscden'
project(object, include, ...)
## S3 method for class 'sscden1'
project(object, include, ...)
## S3 method for class 'sshzd'
project(object, include, mesh=FALSE, ...)
## S3 method for class 'sscox'
project(object, include, ...)
## S3 method for class 'sshzd1'
project(object, include, ...)
## S3 method for class 'ssllrm'
project(object, include, ...)

Arguments

object

Object of class "ssanova", "gssanova", "ssden", "ssden1", "sscden", "sscden1", "sshzd", "sshzd1", or "ssllrm".

...

Additional arguments. Ignored in project.x.

include

List of model terms to be included in the reduced model space. The partial and offset terms, if present, are to be specified by "partial" and "offset", respectively.

mesh

Flag indicating whether to return evaluations of the projection.

drop1

If TRUE, calculate p<-length(include) projections with include[-i], i=1,...,p.

Details

The entropy KL(fit0,null) can be decomposed as the sum of KL(fit0,fit1) and KL(fit1,null), where fit0 is the fit to be projected, fit1 is the projection in the reduced model space, and null is the constant fit. The ratio KL(fit0,fit1)/KL(fit0,null) serves as a diagnostic of the feasibility of the reduced model.

For regression fits, smoothness safe-guard is used to prevent interpolation, and KL(fit0,fit1)+KL(fit1,null) may not match KL(fit0,null) perfectly.

For mixed-effect models from ssanova and gssanova, the estimated random effects are treated as offset.

Value

The functions return a list consisting of the following elements.

ratio

KL(fit0,fit1)/KL(fit0,null); the smaller the value, the more feasible the reduced model is.

kl

KL(fit0,fit1).

For regression fits, the list also contains the following element.

check

KL(fit0,fit1)/KL(fit0,null)+KL(fit1,null)/KL(fit0,null); a value closer to 1 is preferred.

For density and hazard fits, the list may contain the following optional element.

mesh

The evaluations of the projection.

Note

project.ssden1, project.sscden1, and project.sshzd1 calculates square error projections.

References

Gu, C. (2004), Model diagnostics for smoothing spline ANOVA models. The Canadian Journal of Statistics, 32, 347–358.

See Also

Fitting functions ssanova, gssanova, ssden, sshzd, and sshzd1.