R: Derivative for a P-spline fit of scattered (normal) data.

psNormal_Deriv {JOPS}

R Documentation

Derivative for a P-spline fit of scattered (normal) data.

Description

psNormal_Deriv provides the derivative P-spline fit along x.

Usage

psNormal_Deriv(
  x,
  y,
  xl = min(x),
  xr = max(x),
  nseg = 10,
  bdeg = 3,
  pord = 2,
  lambda = 1,
  wts = rep(1, length(y)),
  xgrid = x
)

Arguments

`x`	the vector for the continuous regressor of `length(y)` and the abcissae of fit.
`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, or 3 (defalult).
`pord`	the number of the order of the difference penalty, usually 1, 2 (defalult), or 3.
`lambda`	the positive tuning parameter (default 1).
`wts`	the vector of weights, default is 1; 0/1 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`).

Details

This is also a support function needed for sim_psr and sim_vcpsr. SISR (Eilers, Li, Marx, 2009).

Value

`coef`	a vector of `length(nsegs + bdeg)` of estimated P-spline coefficients.
`B`	The B-spline matrix of dimensions `m` by `length(coef)`.
`fit`	a vector of `length(y)` of smooth estimated means (at the `x` locations).
`pred`	a vector of `length(xgrid)` of (future) predictions.
`d_coef`	a vector of `length(nsegs + bdeg - 1)` of differenced (derivative) estimated P-spline coefficients.
`B_d`	The first derivative B-spline matrix of dimensions `m` by `lengh(d_coef)`.
`d_fit`	a vector of `length(y)` of partial derivative (along `x`) of the smooth estimated means (at the `x` locations).
`d_pred`	a vector of length `lenght(xgrid)` of partial derivative (future) predictions.
`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, or 3 (default).
`pord`	the number of the order of the difference penalty, usually 1, 2 (default), or 3.
`lambda`	the positive tuning parameter (default 1).

Author(s)

Paul Eilers and Brian Marx

References

Marx, B. D. (2015). Varying-coefficient single-index signal regression. Chemometrics and Intelligent Laboratory Systems, 143, 111–121.

Eilers, P.H.C., B. Li, B.D. Marx (2009). Multivariate calibration with single-index signal regression, Chemometrics and Intellegent Laboratory Systems, 96(2), 196-202.

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