# ps2D_PartialDeriv: Partial derivative two-dimensional smoothing scattered... In JOPS: Practical Smoothing with P-Splines

 ps2D_PartialDeriv R Documentation

## Partial derivative two-dimensional smoothing scattered (normal) data using P-splines.

### Description

`ps2D_PartialDeriv` provides the partial derivative P-spline surface along `x`, with aniosotripic penalization of tensor product B-splines.

### Usage

``````ps2D_PartialDeriv(
Data,
Pars = rbind(c(min(Data[, 1]), max(Data[, 1]), 10, 3, 1, 2), c(min(Data[, 2]),
max(Data[, 2]), 10, 3, 1, 2)),
XYpred = cbind(Data[, 1], Data[, 2])
)
``````

### Arguments

 `Data` a matrix of 3 columns `x, y, z` of equal length; the response is `z`. `Pars` a matrix of 2 rows, where the first and second row sets the P-spline paramters for `x` and `y`, respectively. Each row consists of: `min max nseg bdeg lambda pord`. The `min` and `max` set the ranges, `nseg` (default 10) is the number of evenly spaced segments between `min` and `max`, `bdeg` is the degree of the basis (default 3 for cubic), `lambda` is the (positive) tuning parameter for the penalty (default 1), `pord` is the number for the order of the difference penalty (default 2). `XYpred` a matrix with two columns `(x, y)` that give the coordinates of (future) prediction; the default is the data locations.

### Details

This is support function for `sim_vcpsr`.

### Value

 `coef` a vector of length `(Pars[1, 3] + Pars[1, 4]) * (Pars[1, 3] + Pars[1, 4]).` of (unfolded) estimated P-spline coefficients. `B` the tensor product B-spline matrix of dimensions `m` by `length(coef)`. `fit` a vector of `length(y)` of smooth estimated means (at the `x, y` locations). `pred` a vector of length `nrow(XYpred)` of (future) predictions. `d_coef` a vector of length `(Pars[1, 3] + Pars[1,4] - 1) * (Pars[1,3]+Pars[1,4]).` of (unfolded) partial derivative estimated P-spline coefficients. `B_d` the tensor product B-spline matrix of dimensions `m` by `lengh(d_coef)`, associated with the partial derivative of the tensor basis. `d_fit` a vector of `length(y)` of partial derivative (along `x`) of the smooth estimated means (at the `x, y` locations). `d_pred` a vector of length `nrow(XYpred)` of partial derivative (future) predictions. `Pars` a matrix of 2 rows, where each the first (second) row sets the P-spline paramters for `x (y)`: `min max nseg bdeg lambda pord`. See the argument above. `cv` root leave-one-out CV or root average PRESS. `XYpred` a matrix with two columns `(x, y)` that give the coordinates of (future) prediction; the default is the data locations.

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

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