robustbase (version 0.5-0-1)

lmrob..M..fit: Compute M-estimators of regression

Description

This function performs RWLS iterations to find an M-estimator of regression with Tukey's bisquare psi-function. When started from an S-estimated beta.initial, this results in an MM-estimator.

Usage

lmrob..M..fit(x, y, beta.initial, scale, c.psi, control)

Arguments

x

design matrix ($n \times p$) typically including a column of 1s for the intercept.

y

numeric response vector (of length $n$).

beta.initial

numeric vector (of length $p$) of initial estimate. Usually the result of an S-regression estimator.

scale

robust residual scale estimate. Usually an S-scale estimator.

c.psi

the tuning constant of the $\psi /$ psi-function of the M-estimator used.

control

list of control parameters, as returned by lmrob.control. Currently, only the components c("max.it", "rel.tol","trace.lev") are accessed.

Value

• A list with the following elements:
• coef
  the M-estimator (or MM-estim.) of regression
• control
  the control list input used
• scale
  The residual scale estimate
• seed
  The random number generator seed
• converged
  TRUE if the RWLS iterations converged, FALSE otherwise

Details

This function is used by lmrob.fit.MM and typically not to be used on its own.

References

Yohai, 1987

See Also

lmrob.fit.MM, lmrob; for M-estimators with more flexibility, e.g., choice of rho/psi: rlm from package MASS.

Examples

data(stackloss)
X <- model.matrix(stack.loss ~ . , data = stackloss)
y <- stack.loss
## Compute manual MM-estimate:
## 1) initial LTS:
m0 <- ltsReg(X[,-1], y)
## 2) M-estimate started from LTS:
m1 <- lmrob..M..fit(X, y, beta.initial = coef(m0),
                    scale = m0$scale, c.psi = 1.6,
                    control = lmrob.control())
cbind(m0$coef, m1$coef)
## the scale is kept fixed:
stopifnot(identical(unname(m0$scale), m1$scale))

##  robustness weights: are
r.s <- with(m1, resid/scale) # scaled residuals
m1.wts <- robustbase:::tukeyPsi1(r.s, cc = 1.6) / r.s
summarizeRobWeights(m1.wts)
##--> outliers 1,3,4,13,21
which(m0$lts.wt == 0) # 1,3,4,21 but not 13