R: M-S regression estimators

lmrob.M.S {robustbase} | R Documentation

## M-S regression estimators

### Description

Computes an M-S-estimator for linear regression using the “M-S” algorithm.

### Usage

    lmrob.M.S(x, y, control, mf,
              split = splitFrame(mf, x, control$split.type))

### Arguments

`x` | numeric matrix (a `model.matrix`) of the predictors.
`y` | numeric vector for the response
`control` | list as returned by `lmrob.control`.
`mf` | a model frame as returned by `model.frame`.
`split` | (optional) list as returned by `splitFrame`.

### Details

This function is used by `lmrob` and not intended to be used on its own (because an M-S-estimator has too low efficiency ‘on its own’).

An M-S estimator is a combination of an S-estimator for the continuous variables and an L1-estimator (i.e. an M-estimator with ψ(t) = sign(t)) for the categorical variables.

The S-estimator is estimated using a subsampling algorithm. If the model includes interactions between categorical (`factor`) and continuous variables, the subsampling algorithm might fail. In this case, one can choose to assign the interaction to the categorical side of variables rather than to the continuous side. This can be accomplished via the control argument `split.type` or by specifying `split`, see `splitFrame`.

Note that the return status `converged` does not refer to the actual convergence status. The algorithm used does not guarantee convergence and thus true convergence is almost never reached. This is, however, not a problem if the estimate is only used as initial estimate part of an MM or SMDM estimate.

The algorithm sometimes produces the warning message “Skipping design matrix equilibration (dgeequ): row ?? is exactly zero.”. This is just an artifact of the algorithm and can be ignored safely.

### Value

A list with components

`coefficients` | numeric vector (length p) of M-S-regression coefficient estimates.
`scale` | the M-S-scale residual estimate
`residuals` | numeric vector (legnth n) of the residuals.
`rweights` | numeric vector (length n) of the robustness weights.
`control` | the same list as the `control` argument.
`converged` | Convergence status (always `TRUE`), needed for `lmrob.fit`.

### Author(s)

Manuel Koller

### References

Maronna, R. A., and Yohai, V. J. (2000). Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference 89, 197–214.

### See Also

`lmrob`; for a description of the available split types, see `splitFrame`.

`lmRob` in package robust uses a version of the M-S algorithm automatically when the formula contains factors. Our version however follows Maronna and Yohai (2000) more closely.

### Examples

    data(education)
    education <- within(education, Region <- factor(Region))
    flm <- lm(Y ~ Region + X1 + X2 + X3, education)
    x <- model.matrix(flm)
    y <- education$Y # == model.response(model.frame(flm))
    set.seed(17)
    f.MS <- lmrob.M.S(x, y, control = lmrob.control(),
                      mf = model.frame(flm))

    ## The typical use of the "M-S" estimator -- as initial estimate :
    fmMS <- lmrob(Y ~ Region + X1 + X2 + X3, education,
                  init = "M-S")

[Package robustbase version 0.93-9 Index]