Local Regression, Likelihood and Density Estimation.
locfit.raw(x, y, weights=1, cens=NULL, base=0,
scale=F, alpha=0.7, deg=2, kern="tcub", kt="sph", acri="none", basis=list(NULL),
ev="tree", flim, mg=10, cut=0.8,
maxk=100, itype="default", mint=20, maxit=20, debug=0,
locfit.raw is an interface to Locfit using numeric vectors
(for a model-formula based interface, use locfit).
Although this function has a large number of arguments, most users
are likely to need only a small subset.
The first set of arguments (x, y, weights,
cens, and base) specify the regression
variables and associated quantities.
Another set (scale, alpha, deg, kern,
kt, acri and basis) control the amount of smoothing:
bandwidth, smoothing weights and the local model.
deriv and dc relate to derivative (or local slope)
family and link specify the likelihood family.
xlim and renorm may be used in density estimation.
ev, flim, mg and cut
control the set of evaluation points.
maxk, itype, mint, maxit and debug
control the Locfit algorithms, and will be rarely used.
geth and sty are used by other functions calling
locfit.raw, and should not be used directly.
Vector (or matrix) of the independent variable(s).
Response variable for regression models. For density families,
y can be omitted.
Prior weights for observations (reciprocal of variance, or sample size).
Censoring indicators for hazard rate or censored regression. The coding
is 1 (or TRUE) for a censored observation, and
0 (or FALSE) for uncensored observations.
Baseline parameter estimate. If provided, the local regression model is
fitted as Y_i = b_i + m(x_i) + \epsilon_i, with Locfit estimating
the m(x) term. For regression models, this effectively subtracts
b_i from Y_i. The advantage of the base formulation
is that it extends to likelihood regression models.
A scale to apply to each variable. This is especially important for
multivariate fitting, where variables may be measured in
non-comparable units. It is also used to specify the frequency
for ang terms. If scale=F (the default) no scaling
is performed. If scale=T, marginal standard deviations are used.
Alternatively, a numeric vector can provide scales for the
Smoothing parameter. A single number (e.g. alpha=0.7)
is interpreted as a nearest neighbor fraction. With two
componentes (e.g. alpha=c(0.7,1.2)), the first component
is a nearest neighbor fraction, and the second component is
a fixed component. A third component is the penalty term in locally
Degree of local polynomial. Default: 2 (local quadratic). Degrees
0 to 3 are supported by almost all parts of the Locfit code. Higher
degrees may work in some cases.
Weight function, default = "tcub".
Other choices are "rect", "trwt", "tria",
"epan", "bisq" and "gauss". Choices may be restricted
when derivatives are required; e.g. for confidence bands and some
Kernel type, "sph" (default); "prod".
In multivariate problems, "prod" uses a
simplified product model which speeds up computations.
- Criterion for adaptive bandwidth selection.
- User-specified basis functions. See
lfbas for more details on this argument.
Derivative estimation. If deriv=1, the returned fit will be
estimating the derivative (or more correctly, an estimate of the
local slope). If deriv=c(1,1) the second order derivative
is estimated. deriv=2 is for the partial derivative, with
respect to the second variable, in multivariate settings.
- Derivative adjustment.
Local likelihood family; "gaussian";
"binomial"; "poisson"; "gamma" and "geom".
Density and rate estimation families are "dens", "rate" and
"hazard" (hazard rate). If the family is preceded by a 'q'
(for example, family="qbinomial"), quasi-likelihood variance
estimates are used. Otherwise, the residual variance (rv)
is fixed at 1. The default family is "qgauss" if a response
y is provided; "density" if no response is provided.
Link function for local likelihood fitting. Depending on the family,
choices may be "ident", "log", "logit",
"inverse", "sqrt" and "arcsin".
For density estimation, Locfit allows the density to be supported on
a bounded interval (or rectangle, in more than one dimension).
The format should be c(ll,ul) where ll is a vector of
the lower bounds and ur the upper bounds. Bounds such as
[0,\infty) are not supported, but can be effectively
implemented by specifying a very large upper bound.
- Local likelihood density estimates may not integrate
exactly to 1. If renorm=T, the integral will be estimated
numerically and the estimate rescaled. Presently this is implemented
only in one dimension.
Evaluation Structure, default = "tree". Also available are
"phull", "data", "grid", "kdtree",
"kdcenter" and "crossval". ev="none" gives no
evaluation points, effectively producing the global parametric fit.
A vector or matrix of evaluation points can also be provided.
A vector of lower and upper bounds for the evaluation structure,
specified as c(ll,ur). This should not be confused with
xlim. It defaults to the data range.
For the "grid" evaluation structure, mg specifies the
number of points on each margin. Default 10. Can be either a single
number or vector.
Refinement parameter for adaptive partitions. Default 0.8; smaller
values result in more refined partitions.
Controls space assignment for evaluation structures.
For the adaptive evaluation structures, it is impossible to be sure
in advance how many vertices will be generated. If you get
warnings about `Insufficient vertex space', Locfit's default assigment
can be increased by increasing maxk. The default is maxk=100.
Integration type for density estimation. Available methods include
"prod", "mult" and "mlin"; and "haz" for
hazard rate estimation problems. The available integration methods
depend on model specification (e.g. dimension, degree of fit). By
default, the best available method is used.
Points for numerical integration rules. Default 20.
Maximum iterations for local likelihood estimation. Default 20.
- If > 0; prints out some debugging information.
- Don't use!
- Style for special terms (left,
ang e.t.c.). Do not try to set this directly;
call locfit instead.
An object with class "locfit". A standard set of methods for printing, ploting, etc. these objects is provided.
Consult the Web page http://cm.bell-labs.com/stat/project/locfit/.
Built: Sat Aug 4 07:44:53 EDT 2001
Copyright © 2000, Lucent Technologies
Author: Catherine Loader