lmrob.control: Tuning Parameters for lmrob() and Auxiliaries

View source: R/lmrob.MM.R

lmrob.controlR Documentation

Tuning Parameters for lmrob() and Auxiliaries

Description

Tuning parameters for lmrob, the MM-type regression estimator and the associated S-, M- and D-estimators. Using setting="KS2011" sets the defaults as suggested by Koller and Stahel (2011) and analogously for "KS2014".

The .M*.default functions and .M*.defaults lists contain default tuning parameters for all the predefined psi functions, see also Mpsi, etc.

Usage

lmrob.control(setting, seed = NULL, nResample = 500,
              tuning.chi = NULL, bb = 0.5, tuning.psi = NULL,
              max.it = 50, groups = 5, n.group = 400,
              k.fast.s = 1, best.r.s = 2,
              k.max = 200, maxit.scale = 200, k.m_s = 20,
              refine.tol = 1e-7, rel.tol = 1e-7, scale.tol = 1e-10, solve.tol = 1e-7,
              trace.lev = 0,
              mts = 1000, subsampling = c("nonsingular", "simple"),
              compute.rd = FALSE, method = "MM", psi = "bisquare",
              numpoints = 10, cov = NULL,
              split.type = c("f", "fi", "fii"), fast.s.large.n = 2000,
              eps.outlier = function(nobs) 0.1 / nobs,
              eps.x = function(maxx) .Machine$double.eps^(.75)*maxx,
              compute.outlier.stats = method,
              warn.limit.reject = 0.5,
              warn.limit.meanrw = 0.5, ...)

.Mchi.tuning.defaults
.Mchi.tuning.default(psi)
.Mpsi.tuning.defaults
.Mpsi.tuning.default(psi)

Arguments

setting

a string specifying alternative default values. Leave empty for the defaults or use "KS2011" or "KS2014" for the defaults suggested by Koller and Stahel (2011, 2017). See Details.

seed

NULL or an integer vector compatible with .Random.seed: the seed to be used for random re-sampling used in obtaining candidates for the initial S-estimator. The current value of .Random.seed will be preserved if seed is set, i.e. non-NULL; otherwise, as by default, .Random.seed will be used and modified as usual from calls to runif() etc.

nResample

number of re-sampling candidates to be used to find the initial S-estimator. Currently defaults to 500 which works well in most situations (see references).

tuning.chi

tuning constant vector for the S-estimator. If NULL, as by default, sensible defaults are set (depending on psi) to yield a 50% breakdown estimator. See Details.

bb

expected value under the normal model of the “chi” (rather rho) function with tuning constant equal to tuning.chi. This is used to compute the S-estimator.

tuning.psi

tuning constant vector for the redescending M-estimator. If NULL, as by default, this is set (depending on psi) to yield an estimator with asymptotic efficiency of 95% for normal errors. See Details.

max.it

integer specifying the maximum number of IRWLS iterations.

groups

(for the fast-S algorithm): Number of random subsets to use when the data set is large.

n.group

(for the fast-S algorithm): Size of each of the groups above. Note that this must be at least p.

k.fast.s

(for the fast-S algorithm): Number of local improvement steps (“I-steps”) for each re-sampling candidate.

k.m_s

(for the M-S algorithm): specifies after how many unsucessful refinement steps the algorithm stops.

best.r.s

(for the fast-S algorithm): Number of of best candidates to be iterated further (i.e., “refined”); is denoted t in Salibian-Barrera & Yohai(2006).

k.max

(for the fast-S algorithm): maximal number of refinement steps for the “fully” iterated best candidates.

maxit.scale

integer specifying the maximum number of C level find_scale() iterations.

refine.tol

(for the fast-S algorithm): relative convergence tolerance for the fully iterated best candidates.

rel.tol

(for the RWLS iterations of the MM algorithm): relative convergence tolerance for the parameter vector.

scale.tol

(for the scale estimation iterations of the S algorithm): relative convergence tolerance for the scale σ(.).

solve.tol

(for the S algorithm): relative tolerance for inversion. Hence, this corresponds to solve.default()'s tol.

trace.lev

integer indicating if the progress of the MM-algorithm should be traced (increasingly); default trace.lev = 0 does no tracing.

mts

maximum number of samples to try in subsampling algorithm.

subsampling

type of subsampling to be used, a string: "simple" for simple subsampling (default prior to version 0.9), "nonsingular" for nonsingular subsampling. See also lmrob.S.

compute.rd

logical indicating if robust distances (based on the MCD robust covariance estimator covMcd) are to be computed for the robust diagnostic plots. This may take some time to finish, particularly for large data sets, and can lead to singularity problems when there are factor explanatory variables (with many levels, or levels with “few” observations). Hence, is FALSE by default.

method

string specifying the estimator-chain. MM is interpreted as SM. See Details of lmrob for a description of the possible values.

psi

string specifying the type ψ-function used. See Details of lmrob. Defaults to "bisquare" for S and MM-estimates, otherwise "lqq".

numpoints

number of points used in Gauss quadrature.

cov

function or string with function name to be used to calculate covariance matrix estimate. The default is if(method %in% c('SM', 'MM')) ".vcov.avar1" else ".vcov.w". See Details of lmrob.

split.type

determines how categorical and continuous variables are split. See splitFrame.

fast.s.large.n

minimum number of observations required to switch from ordinary “fast S” algorithm to an efficient “large n” strategy.

eps.outlier

limit on the robustness weight below which an observation is considered to be an outlier. Either a numeric(1) or a function that takes the number of observations as an argument. Used in summary.lmrob and outlierStats.

eps.x

limit on the absolute value of the elements of the design matrix below which an element is considered zero. Either a numeric(1) or a function that takes the maximum absolute value in the design matrix as an argument.

compute.outlier.stats

vector of character strings, each valid to be used as method argument. Used to specify for which estimators outlier statistics (and warnings) should be produced. Set to empty string if none are required.

warn.limit.reject

limit of ratio # rejected / # obs in level above (>=) which a warning is produced. Set to NULL to disable warning.

warn.limit.meanrw

limit of the mean robustness per factor level below which (<=) a warning is produced. Set to NULL to disable warning.

...

further arguments to be added as list components to the result, e.g., those to be used in .vcov.w().

Details

The option setting="KS2011" alters the default arguments. They are changed to method = "SMDM", psi = "lqq", max.it = 500, k.max = 2000, cov = ".vcov.w". The defaults of all the remaining arguments are not changed.

The option setting="KS2014" builds upon setting="KS2011". More arguments are changed to best.r.s = 20, k.fast.s = 2, nResample = 1000. This setting should produce more stable estimates for designs with factors.

By default, and in .Mpsi.tuning.default() and .Mchi.tuning.default(), tuning.chi and tuning.psi are set to yield an MM-estimate with breakdown point 0.5 and efficiency of 95% at the normal.

If numeric tuning.chi or tuning.psi are specified, say cc, for psi = "ggw" or "lqq", .psi.const(cc, psi) is used, see its help page.

To get the defaults, e.g., .Mpsi.tuning.default(psi) is equivalent to but more efficient than the formerly widely used lmrob.control(psi = psi)$tuning.psi.

These defaults are:

psi tuning.chi tuning.psi
bisquare1.54764 4.685061
welsh 0.5773502 2.11
ggw c(-0.5, 1.5, NA, 0.5) c(-0.5, 1.5, 0.95, NA)
lqq c(-0.5, 1.5, NA, 0.5) c(-0.5, 1.5, 0.95, NA)
optimal 0.4047 1.060158
hampel c(1.5, 3.5, 8)*0.2119163 c(1.5, 3.5, 8)*0.9014

The values for the tuning constant for the ggw and lqq psi functions are specified differently here by a vector with four elements: minimal slope, b (controlling the bend at the maximum of the curve), efficiency, breakdown point. Use NA for an unspecified value of either efficiency or breakdown point, see examples in the tables (above and below). For these table examples, the respective “inner constants” are stored precomputed, see .psi.lqq.findc for more.

The constants for the "hampel" psi function are chosen to have a redescending slope of -1/3. Constants for a slope of -1/2 would be

psi tuning.chi tuning.psi
"hampel"c(2, 4, 8) * 0.1981319 c(2, 4, 8) * 0.690794

Alternative coefficients for an efficiency of 85% at the normal are given in the table below.

psi tuning.psi
bisquare 3.443689
welsh 1.456
ggw, lqqc(-0.5, 1.5, 0.85, NA)
optimal 0.8684
hampel (-1/3) c(1.5, 3.5, 8)* 0.5704545
hampel (-1/2) c( 2, 4, 8) * 0.4769578

Value

.Mchi.tuning.default(psi) and .Mpsi.tuning.default(psi) return a short numeric vector of tuning constants which are defaults for the corresponding psi-function, see the Details. They are based on the named lists .Mchi.tuning.defaults and .Mpsi.tuning.defaults, respectively.

lmrob.control() returns a named list with over twenty components, corresponding to the arguments, where tuning.psi and tuning.chi are typically computed, as .Mpsi.tuning.default(psi) or .Mchi.tuning.default(psi), respectively.

Author(s)

Matias Salibian-Barrera, Martin Maechler and Manuel Koller

References

Koller, M. and Stahel, W.A. (2011) Sharpening Wald-type inference in robust regression for small samples. Computational Statistics & Data Analysis 55(8), 2504–2515.

Koller, M. and Stahel, W.A. (2017) Nonsingular subsampling for regression S~estimators with categorical predictors, Computational Statistics 32(2): 631–646. doi: 10.1007/s00180-016-0679-x. Referred as "KS2014" everywhere in robustbase; A shorter first version, Koller (2012) has been available from https://arxiv.org/abs/1208.5595.

See Also

Mpsi, etc, for the (fast!) psi function computations; lmrob, also for references and examples.

Examples

## Show the default settings:
str(lmrob.control())

## Artificial data for a  simple  "robust t test":
set.seed(17)
y <- y0 <- rnorm(200)
y[sample(200,20)] <- 100*rnorm(20)
gr <- as.factor(rbinom(200, 1, prob = 1/8))
lmrob(y0 ~ 0+gr)

## Use  Koller & Stahel(2011)'s recommendation but a larger  'max.it':
str(ctrl <- lmrob.control("KS2011", max.it = 1000))

str(.Mpsi.tuning.defaults)
stopifnot(identical(.Mpsi.tuning.defaults,
                   sapply(names(.Mpsi.tuning.defaults),
                          .Mpsi.tuning.default)))
## Containing (names!) all our (pre-defined) redescenders:
str(.Mchi.tuning.defaults)

## Difference between settings:
C11 <- lmrob.control("KS2011")
C14 <- lmrob.control("KS2014")
str(C14)
## Apart from `setting` itself, they only differ in three places:
diffC <- names(which(!mapply(identical, C11,C14, ignore.environment=TRUE)))
cbind(KS11 = unlist(C11[diffC[-1]]),
      KS14 = unlist(C14[diffC[-1]]))
##           KS11 KS14
## nResample  500 1000
## best.r.s     2   20
## k.fast.s     1    2

robustbase documentation built on April 3, 2022, 1:05 a.m.