psNormal: Smoothing scattered (normal) data using P-splines.

In JOPS: Practical Smoothing with P-Splines

Smoothing scattered (normal) data using P-splines.

Description

psNormal is used to smooth scattered (normal) data using P-splines (with identity link function).

Usage

psNormal(
  x,
  y,
  xl = min(x),
  xr = max(x),
  nseg = 10,
  bdeg = 3,
  pord = 2,
  lambda = 1,
  wts = NULL,
  xgrid = 100
)

Arguments

x	the vector for the continuous regressor of length(y) and the abcissae used to build the B-spline basis.
y	the response vector, usually continuous data.
xl	the number for the min along x (default is min(x)) .
xr	the number for the max along x (default is max(x)).
nseg	the number of evenly spaced segments between xl and xr.
bdeg	the number of the degree of the basis, usually 1, 2 (default), or 3.
pord	the number of the order of the difference penalty, usually 1, 2, or 3 (defalult).
lambda	the (positive) number for the tuning parameter for the penalty (default 1).
wts	the vector of general weights, default is 1; zero allowed.
xgrid	a scalar or a vector that gives the x locations for prediction, useful for plotting. If a scalar (default 100) is used then a uniform grid of this size along (xl, xr).

Value

pcoeff	a vector of length n of estimated P-spline coefficients.
muhat	a vector of length m of smooth estimated means.
B	a matrix of dimension m by n for the B-spline basis matrix.
wts	a vector of length m of weights.
effdim	estimated effective dimension.
ed_resid	approximate df residual.
sigma	square root of MSE.
cv	standard error of leave-one-out prediction or root average PRESS.
nseg	the number of B-spline segments.
bdeg	the degree of the B-spline basis.
pord	the order of the difference penalty.
lambda	the positive tuning parameter.
xgrid	gridded x values, useful for plotting.
ygrid	gridded fitted mean values, useful for plotting.
se_eta	gridded standard errors for the fitted mean values, useful for plotting.
P	"half" of the penalty, such that P'P= lambda D'D.

Author(s)

Paul Eilers and Brian Marx

References

Eilers, P.H.C. and Marx, B.D. (2021). Practical Smoothing, The Joys of P-splines. Cambridge University Press.

Eilers, P.H.C., Marx, B.D., and Durban, M. (2015). Twenty years of P-splines, SORT, 39(2): 149-186.

Examples

library(JOPS)
library(MASS)
data(mcycle)
x <- mcycle$times
y <- mcycle$accel
fit1 <- psNormal(x, y, nseg = 20, bdeg = 3, pord = 2, lambda = .8)
plot(fit1, se = 2, xlab = "Time (ms)", ylab = "Acceleration")

JOPS documentation built on Sept. 8, 2023, 5:42 p.m.