irglmreg function

Fit a robust penalized generalized linear models

Fit a robust penalized GLM where the loss function is a composite function cfunodfun + penalty. This is the wrapper function of irglmreg_fit

## S3 method for class 'formula'
irglmreg(formula, data, weights, offset=NULL, contrasts=NULL, ...)
## S3 method for class 'matrix'
irglmreg(x, y, weights, offset=NULL, ...)
## Default S3 method:
irglmreg(x,  ...)

Arguments

• formula: symbolic description of the model, see details.
• data: argument controlling formula processing via model.frame.
• weights: optional numeric vector of weights. If standardize=TRUE, weights are renormalized to weights/sum(weights). If standardize=FALSE, weights are kept as original input
• x: input matrix, of dimension nobs x nvars; each row is an observation vector
• y: response variable. Quantitative for rfamily="clossR" and -1/1 for classification.
• offset: Not implemented yet
• contrasts: the contrasts corresponding to levels from the respective models
• ...: Other arguments passing to irglmreg_fit

Details

The computing is done by the iteratively reweighted penalized GLM, an application of the iteratively reweighted convex optimization (IRCO). Here convex is the loss function induced by dfun, not the penalty function. The output weights_update is a useful diagnostic to the outlier status of the observations. The regularization path is computed for the lasso (or elastic net penalty), scad (or snet) and mcp (or mnet penalty), at a grid of values for the regularization parameter lambda. The sequence of robust models implied by lambda is fit by the IRCO along with coordinate descent. Note that the objective function is

if standardize=FALSE and

if standardize=TRUE.

Returns

An object with S3 class "irglmreg" for the various types of models. - call: the call that produced this object

• b0: Intercept sequence of length length(lambda)

• beta: A nvars x length(lambda) matrix of coefficients.

• lambda: The actual sequence of lambda values used

• nobs: number of observations

• risk: if type.path="nonactive", a matrix with number of rows iter and number of columns nlambda, loss values along the regularization path. If type.path="fast", a vector of length nlambda, loss values along the regularization path

• pll: if type.path="nonactive", a matrix with number of rows iter and number of columns nlambda, penalized loss values along the regularization path. If type.path="fast", a vector of length nlambda, penalized loss values along the regularization path

• fitted.values: predicted values depending on standardize, internal use only

References

Zhu Wang (2024) Unified Robust Estimation, Australian & New Zealand Journal of Statistics. 66(1):77-102.

Author(s)

Zhu Wang zwang145@uthsc.edu

See Also

print, predict, coef and plot methods, and the cv.irglmreg function.

Examples

#binomial
x=matrix(rnorm(100*20),100,20)
g2=sample(c(-1,1),100,replace=TRUE)
fit1=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="active",
              decreasing=TRUE,type.init="bst")
#fit1$risk
## Not run:

### different solution paths via a combination of type.path, decreasing and type.init
fit1=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="active",
           decreasing=TRUE,type.init="bst")
fit2=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="active",
           decreasing=FALSE,type.init="bst")
fit3=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="nonactive",
           decreasing=TRUE,type.init="bst")
fit4=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="nonactive",
           decreasing=FALSE,type.init="bst")
fit5=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="active",
           decreasing=TRUE,type.init="co")
fit6=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="active",
           decreasing=FALSE,type.init="co")
fit7=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="nonactive",
           decreasing=TRUE,type.init="co")
fit8=irglmreg(x,g2,s=1,cfun="ccave",dfun="gaussian",type.path="nonactive",
           decreasing=FALSE,type.init="co")
## End(Not run)