# Two-dimensional smoothing scattered (normal) data using P-splines. ps2DNormal is used to smooth scattered (normal) data, with anisotropic penalization of tensor product P-splines. ```r ps2DNormal( 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 = expand.grid(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. ## Returns - **coef**: a vector of length `(Pars[1,3]+Pars[1,4])*(Pars[2,3]+Pars[2,4])` of (unfolded) estimated P-spline coefficients. - **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. - **Pars**: the design and tuning parameters (see arguments above). - **cv**: leave-one-out standard error of prediction or root average PRESS. - **h**: "hat" diagonals of tensor P-spline fit. - **B**: tensor product B-spline basis used for fitting. ## Details Support functions needed: `pspline_fitter`, `bbase`, and `pspline_2dchecker`. ## Examples ```r library(fields) library(spam) library(JOPS) # Get the data data(ethanol) x <- ethanol$C y <- ethanol$E z <- ethanol$NOx # Set parameters for domain xlo <- 7 xhi <- 19 ylo <- 0.5 yhi <- 1.25 # Set P-spline parameters, fit and compute surface xpars <- c(xlo, xhi, 10, 3, 3, 1) ypars <- c(ylo, yhi, 10, 3, 3, 1) Pars1 <- rbind(xpars, ypars) fit <- ps2DNormal(cbind(x, y, z), Pars = Pars1) plot(fit, xlab = "C", ylab = "E") ``` ## 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. ## See Also ps2DGLM ## Author(s) Paul Eilers and Brian Marx

ps2DNormal function