lmrob               package:robustbase               R Documentation

_M_M-_E_s_t_i_m_a_t_o_r_s _f_o_r _L_i_n_e_a_r _R_e_g_r_e_s_s_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Computes fast MM-estimators for linear (regression) models.

_U_s_a_g_e:

     lmrob(formula, data, subset, weights, na.action,
           model = TRUE, x = !control$compute.rd, y = FALSE, singular.ok = TRUE,
           contrasts = NULL, offset = NULL, control = lmrob.control(...), ...)

_A_r_g_u_m_e_n_t_s:

 formula: a symbolic description of the model to be fit.  See 'lm' and
          'formula' for more details.

    data: an optional data frame, list or environment (or object
          coercible by 'as.data.frame' to a data frame) containing the
          variables in the model.  If not found in 'data', the
          variables are taken from 'environment(formula)', typically
          the environment from which 'lmrob' is called.

  subset: an optional vector specifying a subset of observations to be
          used in the fitting process.

 weights: an optional vector of weights to be used in the fitting
          process.  

na.action: a function which indicates what should happen when the data
          contain 'NA's.  The default is set by the 'na.action' setting
          of 'options', and is 'na.fail' if that is unset.  The
          "factory-fresh" default is 'na.omit'.  Another possible value
          is 'NULL', no action.  Value 'na.exclude' can be useful.

model, x, y: logicals.  If 'TRUE' the corresponding components of the
          fit (the model frame, the model matrix, the response) are
          returned.

singular.ok: logical. If 'FALSE' (the default in S but not in R) a
          singular fit is an error.

contrasts: an optional list.  See the 'contrasts.arg' of
          'model.matrix.default'.

  offset: this can be used to specify an _a priori_ known component to
          be included in the linear predictor during fitting.  An
          'offset' term can be included in the formula instead or as
          well, and if both are specified their sum is used.

 control: a 'list' specifying control parameters; use the function
          'lmrob.control(.)' and see its help page.

     ...: can be used to specify control parameters directly instead of
          via 'control'.

_D_e_t_a_i_l_s:

     This function computes an MM-regression estimator as described in
     Yohai (1987).  It uses a bi-square re-desceding score function,
     and by default it returns a highly robust and highly efficient
     estimator (with 50% breakdown point and 95% asymptotic efficiency
     for normal errors).  The computation is carried out by a call to
     'lmrob.MM()'.

     It uses an S-estimator (Rousseeuw and Yohai, 1984) for the errors
     which is also computed with a bi-square score function. The
     S-estimator is computed using the Fast-S algorithm of
     Salibian-Barrera and Yohai (2006), calling the function 'lmrob.S'.

     Standard errors are computed using the formulas of Croux, Dhaene
     and Hoorelbeke (2003).

_V_a_l_u_e:

     An object of class 'lmrob'. A list that includes the following
     components: 

coefficients: The MM-estimator of the coefficient vector

initial.coefficients: the S-estimator

   scale: The scale as returned by S-estimator and used in the M one.

     cov: The estimated covariance matrix of the regression
          coefficients

residuals: Residuals associated with the MM-estimator

fitted.values: Fitted values associated with the MM-estimator

 weights: the "robustness weights" psi(r_i/S) / (r_i/S).

converged: 'TRUE' if the IRWLS iterations have converged

_A_u_t_h_o_r(_s):

     Matias Salibian-Barrera

_R_e_f_e_r_e_n_c_e_s:

     Croux, C., Dhaene, G. and Hoorelbeke, D. (2003) _Robust standard
     errors for robust estimators_, Discussion Papers Series 03.16,
     K.U. Leuven, CES.

     Rousseeuw, P.J. and Yohai, V.J. (1984) Robust regression by means
     of S-estimators, In _Robust and Nonlinear Time Series_, J. Franke,
     W. H\"ardle and R. D. Martin (eds.). Lectures Notes in Statistics
     26, 256-272, Springer Verlag, New York.

     Salibian-Barrera, M. and Yohai, V.J. (2006) A fast algorithm for
     S-regression estimates, _Journal of Computational and Graphical
     Statistics_, in press. 

     Yohai, V.J. (1987) High breakdown-point and high efficiency
     estimates for regression. _The Annals of Statistics_ *15*, 642-65.

_S_e_e _A_l_s_o:

     'lmrob.control'; for the algorithms 'lmrob.S' and 'lmrob.MM'; and
     for methods, 'summary.lmrob', 'print.lmrob', and 'plot.lmrob'.

_E_x_a_m_p_l_e_s:

     data(coleman)
     summary( m1 <- lmrob(Y ~ ., data=coleman) )

     data(starsCYG, package = "robustbase")
     ## Plot simple data and fitted lines
     plot(starsCYG)
      lmST <-    lm(log.light ~ log.Te, data = starsCYG)
     (RlmST <- lmrob(log.light ~ log.Te, data = starsCYG))
     abline(lmST, col = "red")
     abline(RlmST, col = "blue")
     summary(RlmST)

