loess                 package:stats                 R Documentation

_L_o_c_a_l _P_o_l_y_n_o_m_i_a_l _R_e_g_r_e_s_s_i_o_n _F_i_t_t_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     Fit a polynomial surface determined by one or more numerical
     predictors, using local fitting.

_U_s_a_g_e:

     loess(formula, data, weights, subset, na.action, model = FALSE,
           span = 0.75, enp.target, degree = 2,
           parametric = FALSE, drop.square = FALSE, normalize = TRUE,
           family = c("gaussian", "symmetric"),
           method = c("loess", "model.frame"),
           control = loess.control(...), ...)

_A_r_g_u_m_e_n_t_s:

 formula: a formula specifying the numeric response and one to four
          numeric predictors (best specified via an interaction, but
          can also be specified additively).  Will be coerced to a
          formula if necessary.

    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 'loess' is called.

 weights: optional weights for each case.

  subset: an optional specification of a subset of the data to be used.

na.action: the action to be taken with missing values in the response
          or predictors.  The default is given by
          'getOption("na.action")'.

   model: should the model frame be returned?

    span: the parameter alpha which controls the degree of smoothing.

enp.target: an alternative way to specify 'span', as the approximate
          equivalent number of parameters to be used.

  degree: the degree of the polynomials to be used, normally 1 or 2.
          (Degree 0 is also allowed, but see the 'Note'.)

parametric: should any terms be fitted globally rather than locally? 
          Terms can be specified by name, number or as a logical vector
          of the same length as the number of predictors.

drop.square: for fits with more than one predictor and 'degree=2',
          should the quadratic term be dropped for particular
          predictors?  Terms are specified in the same way as for
          'parametric'.

normalize: should the predictors be normalized to a common scale if
          there is more than one?  The normalization used is to set the
          10% trimmed standard deviation to one.  Set to false for
          spatial coordinate predictors and others know to be a common
          scale.

  family: if '"gaussian"' fitting is by least-squares, and if
          '"symmetric"' a re-descending M estimator is used with
          Tukey's biweight function.

  method: fit the model or just extract the model frame.

 control: control parameters: see 'loess.control'.

     ...: control parameters can also be supplied directly.

_D_e_t_a_i_l_s:

     Fitting is done locally.  That is, for the fit at point x, the fit
     is made using points in a neighbourhood of x, weighted by their
     distance from x (with differences in 'parametric' variables being
     ignored when computing the distance).  The size of the
     neighbourhood is controlled by alpha (set by 'span' or
     'enp.target').  For alpha < 1, the neighbourhood includes
     proportion alpha of the points, and these have tricubic weighting
     (proportional to (1 - (dist/maxdist)^3)^3.  For alpha > 1, all
     points are used, with the 'maximum distance' assumed to be
     alpha^1/p times the actual maximum distance for p explanatory
     variables.

     For the default family, fitting is by (weighted) least squares. 
     For 'family="symmetric"' a few iterations of an M-estimation
     procedure with Tukey's biweight are used.  Be aware that as the
     initial value is the least-squares fit, this need not be a very
     resistant fit.

     It can be important to tune the control list to achieve acceptable
     speed.  See 'loess.control' for details.

_V_a_l_u_e:

     An object of class '"loess"'.

_N_o_t_e:

     As this is based on 'cloess', it is similar to but not identical
     to the 'loess' function of S.  In particular, conditioning is not
     implemented.

     The memory usage of this implementation of 'loess' is roughly
     quadratic in the number of points, with 1000 points taking about
     10Mb.

     'degree = 0', local constant fitting, is allowed in this
     implementation but not documented in the reference.  It seems very
     little tested, so use with caution.

_A_u_t_h_o_r(_s):

     B. D. Ripley, based on the 'cloess' package of Cleveland, Grosse
     and Shyu (currently available as 'dloess' at <URL:
     http://www.netlib.org/a>: the R implementation is based on an 1998
     version).

_R_e_f_e_r_e_n_c_e_s:

     W. S. Cleveland, E. Grosse and W. M. Shyu (1992) Local regression
     models. Chapter 8 of _Statistical Models in S_ eds J.M. Chambers
     and T.J. Hastie, Wadsworth & Brooks/Cole.

_S_e_e _A_l_s_o:

     'loess.control', 'predict.loess'.

     'lowess', the ancestor of 'loess' (with different defaults!).

_E_x_a_m_p_l_e_s:

     cars.lo <- loess(dist ~ speed, cars)
     predict(cars.lo, data.frame(speed = seq(5, 30, 1)), se = TRUE)
     # to allow extrapolation
     cars.lo2 <- loess(dist ~ speed, cars,
       control = loess.control(surface = "direct"))
     predict(cars.lo2, data.frame(speed = seq(5, 30, 1)), se = TRUE)