Fit a robust GLM where the loss function is a composite function cfunodfun.
# S3 method for formula
irglm(formula, data, weights, offset=NULL, contrasts=NULL,
cfun="ccave", dfun=gaussian(), s=NULL, delta=0.1, fk=NULL, init.family=NULL,
iter=10, reltol=1e-5, theta, x.keep=FALSE, y.keep=TRUE, trace=FALSE, ...)An object with S3 class "irglm", "glm" for various types of models.
the call that produced the model fit
original weights used in the model
weights in the final iteration of the IRGLM algorithm
original input arguments
is offset used?
symbolic description of the model, see details.
argument controlling formula processing
via model.frame.
optional numeric vector of weights.
input matrix, of dimension nobs x nvars; each row is an observation vector
response variable. Quantitative for dfun=1 and -1/1 for classification.
the contrasts corresponding to levels from the
respective models
this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. Currently only one offset term can be included in the formula.
character, type of convex cap (concave) function.
Valid options are:
"hcave"
"acave"
"bcave"
"ccave"
"dcave"
"ecave"
"gcave"
"tcave"
character, type of convex component.
Valid options are:
character value for initial family, one of "clossR","closs","gloss","qloss", which can be used to derive an initial estimator, if the selection is different from the default value
tuning parameter of cfun. s > 0 and can be equal to 0 for cfun="tcave". If s is too close to 0 for cfun="acave", "bcave", "ccave", the calculated weights can become 0 for all observations, thus crash the program.
a small positive number provided by user only if cfun="gcave" and 0 < s <1
predicted values at an iteration in the IRGLM algorithm
number of iteration in the IRGLM algorithm
convergency criteria in the IRGLM algorithm
an overdispersion scaling parameter for family=negbin()
logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value, x is a design matrix of dimension n * p, and x is a vector of observations of length n.
if TRUE, fitting progress is reported
other arguments passing to irglm
Zhu Wang <zwang145@uthsc.edu>
A robust linear, logistic or Poisson regression model is fit by the iteratively reweighted GLM (IRGLM). The output weights_update is a useful diagnostic to the outlier status of the observations.
Zhu Wang (2024) Unified Robust Estimation, Australian & New Zealand Journal of Statistics. 66(1):77-102.
x=matrix(rnorm(100*20),100,20)
g2=sample(c(-1,1),100,replace=TRUE)
fit=irglm(g2~x,data=data.frame(cbind(x, g2)), s=1, cfun="ccave", dfun=gaussian())
fit$weights_update
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