lmrobM: Robust estimators for linear regression with fixed designs

Description

This function computes a robust regression estimator for a linear models with fixed designs.

Usage

lmrobM(
  formula,
  data,
  subset,
  weights,
  na.action,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  singular.ok = TRUE,
  contrasts = NULL,
  offset = NULL,
  control = lmrobM.control()
)

Value

A list with the following components:

coefficients: The estimated vector of regression coefficients
scale: The estimated scale of the residuals
residuals: The vector of residuals associated with the robust fit
converged: Logical value indicating whether IRWLS iterations for the MM-estimator have converged
iter: Number of IRWLS iterations for the MM-estimator
rweights: Robustness weights for the MM-estimator
fitted.values: Fitted values associated with the robust fit
rank: Numeric rank of the fitted linear model
cov: The estimated covariance matrix of the regression estimates
df.residual: The residual degrees of freedom
contrasts: (only where relevant) the contrasts used
xlevels: (only where relevant) a record of the levels of the factors used in fitting
call: the matched call
model: if requested, the model frame used
x: if requested, the model matrix used
y: if requested, the response vector used
na.action: (where relevant) information returned by model.frame on the special handling of NAs

Arguments

formula: a symbolic description of the model to be fit.
data: an optional data frame, list or environment containing the variables in the model. If not found in data, model variables are taken from environment(formula), which usually is the root environment of the current R session.
subset: an optional vector specifying a subset of observations to be used.
weights: an optional vector of weights to be used in the fitting process.
na.action: a function to indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset.
model: logical value indicating whether to return the model frame
x: logical value indicating whether to return the model matrix
y: logical value indicating whether to return the vector of responses
singular.ok: logical value. If FALSE a singular fit produces an error.
contrasts: an optional list. See the contrasts.arg of model.matrix.default.
offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. An offset term can be included in the formula instead or as well, and if both are specified their sum is used.
control: a list specifying control parameters as returned by the function lmrobM.control.

Author

Victor Yohai, vyohai@gmail.com, based on lmrob

Details

This function computes robust regression estimators for linear models with fixed designs. It computes an L1 estimator, and uses it as a starting point to find a minimum of a re-descending M estimator. The scale is set to a quantile of the absolute residuals from the L1 estimator. This function makes use of the functions lmrob.fit, lmrob..M..fit, .vcov.avar1, lmrob.S and lmrob.lar, from robustbase, along with utility functions used by these functions, modified so as to include use of the analytic form of the optimal psi and rho functions (for the optimal psi function , see Section 5.8.1 of Maronna, Martin, Yohai and Salibian Barrera, 2019)

References

http://www.wiley.com/go/maronna/robust

Examples

Run this code

data(shock)
cont <- lmrobM.control(bb = 0.5, efficiency = 0.85, family = "bisquare")
shockrob <- lmrobM(time ~ n.shocks, data = shock, control=cont)
shockrob
summary(shockrob)

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