R: Compute M-estimators of regression

lmrob..M..fit {robustbase} | R Documentation

## Compute M-estimators of regression

### Description

This function performs RWLS iterations to find an M-estimator of regression. When started from an S-estimated `beta.initial`, this results in an MM-estimator.

### Usage

    lmrob..M..fit(x, y, beta.initial, scale, control, obj,
                  mf = obj$model, method = obj$control$method)

### Arguments

`x` | design matrix (n x p) typically including a column of `1`s 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.
`control` | list of control parameters, as returned by `lmrob.control`. Currently, the components `c("max.it", "rel.tol","trace.lev", "psi", "tuning.psi", "mts", "subsampling")` are accessed.
`obj` | an optional `lmrob`-object. If specified, this is typically used to set values for the other arguments.
`mf` | (optional) a model frame as returned by `model.frame`, used only to compute outlier statistics, see `outlierStats`.
`method` | optional; the `method` used for obj computation.

### Details

This function is used by `lmrob.fit` (and `anova(<lmrob>, type = "Deviance")`) and typically not to be used on its own.

### 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

### Author(s)

Matias Salibian-Barrera and Martin Maechler

### References

Yohai, 1987

### See Also

`lmrob.fit`, `lmrob`; `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$scale, method = "SM",
                        control = lmrob.control(tuning.psi = 1.6, psi = 'bisquare'))
    ## no 'method' (nor 'obj'):
    m1. <- lmrob..M..fit(X, y, beta.initial = coef(m0), scale = m0$scale,
                         control = m1$control)
    stopifnot(all.equal(m1, m1., tol = 1e-15)) # identical {call *not* stored!}

    cbind(m0$coef, m1$coef)
    ## the scale is kept fixed:
    stopifnot(identical(unname(m0$scale), m1$scale))

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

    ## Manually add M-step to SMD-estimate (=> equivalent to "SMDM"):
    m2 <- lmrob(stack.loss ~ ., data = stackloss, method = 'SMD')
    m3 <- lmrob..M..fit(obj = m2)

    ## Simple function that allows custom initial estimates
    ## (Deprecated; use init argument to lmrob() instead.) %% MM: why deprecated?
    lmrob.custom <- function(x, y, beta.initial, scale, terms) {
      ## initialize object
      obj <- list(control = lmrob.control("KS2011"),
                  terms = terms) ## terms is needed for summary()
      ## M-step
      obj <- lmrob..M..fit(x, y, beta.initial, scale, obj = obj)
      ## D-step
      obj <- lmrob..D..fit(obj, x)
      ## Add some missing elements
      obj$cov <- TRUE ## enables calculation of cov matrix
      obj$p <- obj$qr$rank
      obj$degree.freedom <- length(y) - obj$p
      ## M-step
      obj <- lmrob..M..fit(x, y, obj=obj)
      obj$control$method <- ".MDM"
      obj
    }

    m4 <- lmrob.custom(X, y, m2$init$init.S$coef,
                       m2$init$scale, m2$terms)
    stopifnot(all.equal(m4$coef, m3$coef))

    ## Start from ltsReg:
    m5 <- ltsReg(stack.loss ~ ., data = stackloss)
    m6 <- lmrob.custom(m5$X, m5$Y, coef(m5), m5$scale, m5$terms)

[Package robustbase version 0.92-7 Index]