High Breakdown and High Efficiency Robust Regression

DESCRIPTION:

Performs high breakdown point and high efficiency regression with a test for bias according to a method proposed by Yohai, Stahel and Zamar (1991).

USAGE:

lmRobMM(formula, data=<<see below>>, weights=<<see below>>,
        subset=<<see below>>, na.action=na.fail, model=F, 
        x=F, y=F, contrasts=NULL, ...)

REQUIRED ARGUMENTS:

formula
a formula object, with the response on the left side of the tilde ( ~) operator, and the terms separated by + operators on the right.

OPTIONAL ARGUMENTS:

data
a data frame in which to interpret the variables named in the formula, subset and weights arguments. If data is missing, the variables in the formula should be on your search list. This argument may also be a single number to handle some special cases; see the help file for details.
weights
a vector of observation weights. If supplied, the fitting algorithm minimizes a function of the sum of the weights multiplied by the squared residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is recommended that they be strictly positive, since zero weights are ambiguous. To exclude particular observations from the model, use the subset argument instead of zero weights.
subset
a S-PLUS expression specifying which subset of observations should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), a numeric vector indicating the observation numbers to be included, or a character vector of the observation names that should 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 applied. The default is na.fail, which returns an error if any missing values are found. An alternative is na.exclude, which deletes observations that contain one or more missing values.
model
logical flag: if TRUE, then the model frame is returned in the model component of the fitted object.
x
logical flag: if TRUE, then the model matrix is returned in the x component of the fitted object.
y
logical flag: if TRUE, then the response is returned in the y component of the fitted object.
contrasts
a list giving contrasts for some or all of the factors appearing in the model formula. An element in the list should have the same name as the factor variable it encodes, and it should be either a contrast matrix (any full-rank matrix with as many rows as there are levels in the factor), or a function that computes such a matrix given the number of levels.
...
additional arguments for the fitting routines. Possibilities include the following:
nrep

the number of random subsamples to be drawn. The default is 4.6*2^ncol(x); see Yohai, Stahel, and Zamar (1991) for a justification of this value. If "Exhaustive" resampling is chosen, the value of nrep is ignored. See the help file for a description of different resampling methods.

singular.ok
logical flag: if FALSE, an error is returned when x is singular (i.e., when the model is over-determined). Otherwise, the fitting algorithm continues and returns a model object. By default, singular.ok=TRUE.

qr.out
logical flag: if TRUE, a list representing the QR-decomposition of x is returned. By default, qr.out=TRUE.

robust.control
a list of control parameters to be used in the numerical algorithms. See lmRobMM.robust.control for the available control parameters and their default settings. By default, robust.control=lmRobMM.robust.control.

genetic.control
a list of control parameters to be used in the genetic resampling algorithm, if chosen. See the help file for the available control parameters and their default settings. See lmRobMM.robust.control for a description of different resampling methods.

VALUE:

a list describing the regression. See for a complete description of the returned model object. The solution computed by lmRobMM is an approximation to the true solution based upon a resampling algorithm. Hence, you will obtain (slightly) different answers each time you make the same call.

REFERENCES:

Marazzi, A. (1993). Algorithms, Routines, and S functions for Robust Statistics. Wadsworth & Brooks/Cole, Pacific Grove, CA.

Yohai, V., Stahel, W.A., and Zamar, R.H. (1991). A procedure for robust estimation and inference in linear regression. In Stahel, W.A. and Weisberg, S.W., Eds., Directions in Robust Statistics and Diagnostics, Part II. Springer-Verlag.

SEE ALSO:

, , , .

EXAMPLES:

oil.robust <- lmRobMM(Oil ~ Market, data=oilcity) 
summary(oil.robust)