On Wed, 2009-09-16 at 14:10 -0700, Chris Martin wrote: > Dear list members, > > I am a looking for a function that can calculate a "surface" from at least > four predictor variables and one response variable. I would then like to > calculate the first derivative of a specific point on this surface. > > I have looked at many packages for nonparametric smoothing and kernel > density estimation but have been unable to find any that fulfill both these > criteria. For example, loess can handle multivariate data, but I do not how > to extract the derivative from the resulting fit? Many smoothing splines > offer predict functions to extract the derivative, but these functions can > only handle univariate data (e.g. smooth.spline). Ideally, I would like to > use local estimates of the surface (i.e. loess).
Depending upon how many observations you have (i.e. not very large numbers) you could estimate this model using mgcv::gam which allows multivariate smooths. You can then compute the derivatives for this smooth using finite differences using the predict.gam method as a basis from which to work (using type = "lpmatrix"). The trick is to get the bits from the model that you need. This code snippet uses data from the semiPar package. I produced the script as I was reading the text that semiPar is support for. Simon Wood, author of the mgcv package, kindly helped me with the code to compute the derivatives: ## Example from Ruppert, Wand and Carroll 2003 pp 156-8 ## Semiparametric regression ## Cambridge University Press ## ## Data for the strontium example are in package SemiPar, support ## software for the book above. require(SemiPar) require(mgcv) # '` require(nlme) ## load the Strontium data data(fossil) mod1 <- gamm(strontium.ratio ~ s(age), data = fossil) ## Compute derivatives ############################################### ## where to evaluate derivatives x.age <- with(fossil, seq(min(age), max(age), length = 200)) newd <- data.frame(age = x.age) X0 <- predict(mod1$gam, newd, type = "lpmatrix") eps <- 1e-7 ## finite difference interval x.age <- x.age + eps ## shift the evaluation points newd <- data.frame(age = x.age) X1 <- predict(mod1$gam, newd, type = "lpmatrix") Xp <- (X1 - X0) / eps ## maps coefficients to (fd approx.) derivatives colnames(Xp) Xi <- Xp*0 Xi[, 2:10] <- Xp[,2:10] ## Xi\%*\%coef(b) = smooth deriv i ## you'll need to change 2:10 in the above to match the cols for your ## smoother ## ith smooth derivative df <- Xi %*% coef(mod1$gam) ## cheap diag(Xi\%*\%b$Vp\%*\%t(Xi))^.5 df.sd <- rowSums(Xi %*% mod1$gam$Vp * Xi)^.5 ## SE of deriv I haven't used this approach to compute the derivatives of a multivariate smooth, but it should work as long as you can identify the columns of X0 and X1 that arise from predict.gam. HTH G > > I would appreciate any suitable functions or advice on where to look for > functions that fulfill both these criteria. > > Thank you very much for your time. > > best wishes, > Chris Martin > Population Biology Graduate Group '12 > University of California, Davis > > [[alternative HTML version deleted]] > > _______________________________________________ > R-sig-ecology mailing list > R-sig-ecology@r-project.org > https://stat.ethz.ch/mailman/listinfo/r-sig-ecology -- %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% Dr. Gavin Simpson [t] +44 (0)20 7679 0522 ECRC, UCL Geography, [f] +44 (0)20 7679 0565 Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/ UK. WC1E 6BT. [w] http://www.freshwaters.org.uk %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
