Fit a Robust Generalized Linear Model

DESCRIPTION:

Produces an object of class glmRob which is a Robust Generalized Linear Model fit.

USAGE:

glmRob(formula = formula(data), family = binomial, data = sys.parent(),  
subset, na.action = na.fail, start = eta, fit.method = "cubif", 
model = F, x = F, y = T, contrasts = NULL, 
cubif.control = glmRob.cubif.control(...), 
mallows.control = glmRob.mallows.control(...),
misclass.control = glmRob.misclass.control(...),
method = "glmRob.fit", estim = "mcd", robust.cov.control =
covRob.control(estim = estim, quan = 0.75, ...), ...) 

REQUIRED ARGUMENTS:

formula
a formula expression as for other regression models, of the form response ~ predictors. See the documentation of lm and formula for details.

OPTIONAL ARGUMENTS:

family
a family object - only binomial and poisson are implemented. See the documentation of glm for details.
data
an optional data frame in which to interpret the variables occuring in the formula.
subset
expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.
na.action
a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.exclude, which deletes observations that contain one or more missing values.
start
a vector of initial values on the scale of the linear predictor.
fit.method
a character vector indicating the fitting method. Conditionally unbiased bounded influence estimators are obtained with this argument equal to "cubif", Mallow's leverage downweighting estimates are fit with fit.method = "mallows" and "misclass" fits a consistent estimate based on the misclassification model. The last two estimators are only defined for logistic regression models with a Bernoulli response variable.
model
logical flag: if TRUE, the model.frame is returned. If this argument is itself a model.frame, then the formula and data arguments are ignored, and model is used to define the model.
x
logical flag: if TRUE, the model.matrix is returned.
y
logical flag: if TRUE, the response variable is returned (default is TRUE).
contrasts
a list of contrasts to be used for some or all of the factors appearing as variables in the model formula. The names of the list should be the names of the corresponding variables, and the elements should either be contrast-type matrices (matrices with as many rows as levels of the factor and with columns linearly independent of each other and of a column of one's), or else they should be functions that compute such contrast matrices.
cubif.control
a list of iteration and algorithmic constants to control the conditionally unbiased bounded influence robust fit. See glmRob.cubif.control for their names and default values. These can also be set as arguments of glmRob itself.
mallows.control
a list of iteration and algorithmic constants to control the Mallows leverage downweighted robust fit. See glmRob.mallows.control for their names and default values. These can also be set as arguments of glmRob itself.
misclass.control
a list of iteration and algorithmic constants to control the robust fit based on the misclassification model. See glmRob.misclass.control for their names and default values. These can also be set as arguments of glmRob itself.
estim
the robust covariance estimator used in the initial step of the "cubif" method. The choices are the same as those for covRob.
robust.cov.control
a list of parameters affecting the robust covariance estimation during the initial step of the "cubif" method.
...
control arguments maybe given directly. See the documentation of glmRob.cubif.control, glmRob.mallows.control or glmRob.misclass.control for details.

VALUE:

an object of class glmRob that contains the Robust Generalized Linear Model fit.

REFERENCES:

Copas, J. B. (1988). Binary Regression Models for Contaminated Data. JRSS \fB50\fR, 225-265.
Kunsch, L., Stefanski L. and Carroll, R. (1989). Conditionally Unbiased Bounded-Influence Estimation in General Regression Models, with Applications to Generalized Linear Models. JASA \fB84\fR, 460-466.
Carroll, R. J. and Pederson, S. (1993). On Robustness in the Logistic Regression Model. JRSS \fB55\fR, 693-706.
Marazzi, A. (1993). Algorithms, routines and S functions for robust statistics. Wadsworth & Brooks/Cole, Pacific Grove, CA.

SEE ALSO:

, , , , , .

EXAMPLES:

glmRob(sumY~Age10+Base4*Trt, family=poisson, data=breslow.dat, fit.method =
"cubif")