lmrobdet.control {RobStatTM}

Tuning parameters for lmrobdetMM and lmrobdetDCML

Description

This function sets tuning parameters for the MM estimator implemented in lmrobdetMM and the Distance Constrained Maximum Likelihood regression estimators computed by lmrobdetDCML.

Usage

lmrobdet.control(
  bb = 0.5,
  efficiency = 0.95,
  family = "mopt",
  tuning.psi,
  tuning.chi,
  compute.rd = FALSE,
  corr.b = TRUE,
  split.type = "f",
  initial = "S",
  max.it = 100,
  refine.tol = 1e-07,
  rel.tol = 1e-07,
  refine.S.py = 1e-07,
  refine.PY = 10,
  solve.tol = 1e-07,
  trace.lev = 0,
  psc_keep = 0.5,
  resid_keep_method = "threshold",
  resid_keep_thresh = 2,
  resid_keep_prop = 0.2,
  py_maxit = 20,
  py_eps = 1e-05,
  mscale_maxit = 50,
  mscale_tol = 1e-06,
  mscale_rho_fun = "bisquare"
)

Arguments

bb

tuning constant (between 0 and 1/2) for the M-scale used to compute the initial S-estimator. It determines the robusness (breakdown point) of the resulting MM-estimator, which is bb. Defaults to 0.5.

efficiency

desired asymptotic efficiency of the final regression M-estimator. Defaults to 0.95.

family

string specifying the name of the family of loss function to be used (current valid options are "bisquare", "opt" and "mopt"). Incomplete entries will be matched to the current valid options. Defaults to "mopt".

tuning.psi

tuning parameters for the regression M-estimator computed with a rho function as specified with argument family. If missing, it is computed inside lmrobdet.control to match the value of efficiency according to the family of rho functions specified in family. Appropriate values for tuning.psi for a given desired efficiency for Gaussian errors can be constructed using the functions bisquare, mopt and opt.

tuning.chi

tuning constant for the function used to compute the M-scale used for the initial S-estimator. If missing, it is computed inside lmrobdet.control to match the value of bb according to the family of rho functions specified in family.

compute.rd

logical value indicating whether robust leverage distances need to be computed.

corr.b

logical value indicating whether a finite-sample correction should be applied to the M-scale parameter bb.

split.type

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

initial

string specifying the initial value for the M-step of the MM-estimator. Valid options are 'S', for an S-estimator and 'MS' for an M-S estimator which is appropriate when there are categorical explanatory variables in the model.

max.it

maximum number of IRWLS iterations for the MM-estimator

refine.tol

relative convergence tolerance for the S-estimator

rel.tol

relative convergence tolerance for the IRWLS iterations for the MM-estimator

refine.S.py

relative convergence tolerance for the local improvements of the Pena-Yohai candidates for the S-estimator

refine.PY

number of refinement steps for the Pen~a-Yohai candidates

solve.tol

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

trace.lev

positive values (increasingly) provide details on the progress of the MM-algorithm

psc_keep

For pyinit, proportion of observations to remove based on PSCs. The effective proportion of removed observations is adjusted according to the sample size to be prosac*(1-p/n). See pyinit.

resid_keep_method

For pyinit, how to clean the data based on large residuals. If "threshold", all observations with scaled residuals larger than C.res will be removed, if "proportion", observations with the largest prop residuals will be removed. See pyinit.

resid_keep_thresh

See parameter resid_keep_method above. See pyinit.

resid_keep_prop

See parameter resid_keep_method above. See pyinit.

py_maxit

Maximum number of iterations. See pyinit.

py_eps

Relative tolerance for convergence. See pyinit.

mscale_maxit

Maximum number of iterations for the M-scale algorithm. See pyinit and mscale.

mscale_tol

Convergence tolerance for the M-scale algorithm. See mscale and mscale.

mscale_rho_fun

String indicating the loss function used for the M-scale. See pyinit.

Details

The argument family specifies the name of the family of loss function to be used. Current valid options are "bisquare", "opt", "mopt", "optV0" and "moptV0". "mopt" is a modified version of the optimal psi function to make it strictly increasing close to 0, and to make the corresponding weight function non-increasing.

Value

A list with the necessary tuning parameters.

Choice of Rho Loss Function

As of RobStatTM Versopm 1.0.7, the opt and mopt rhos functions are calculated using polynomials, rather than using the standard normal error function (erf) as in versions of RobStatTM prior to 1.0.7. The numerical results one now gets with the opt or mopt choices will differ by small amounts from those in earlier RobStatTM versions. Users who wish to replicate results from releases prior to 1.0.7 may do so using the family arguments family = "optV0" or family = "moptV0". Note that the derivative of the rho loss function, known as the "psi" function, is not the derivative of the rho polynomial,instead it is still the analytic optimal psi function whose formula is given in the second of the Vignettes referenced just below.

Related Vignettes

For further details, see the Vignettes "Polynomial Opt and mOpt Rho Functions", and "Optimal Bias Robust Regression Psi and Rho".

Author(s)

Matias Salibian-Barrera, [e-mail]

See Also

pyinit, mscale.

Examples

data(coleman, package='robustbase')
m2 <- lmrobdetMM(Y ~ ., data=coleman, control=lmrobdet.control(refine.PY=50))
m2
summary(m2)