# Beginner's Guide to GAM with R # Alain Zuur # www.highstat.com # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. ############################################################## #Load the data Squid <- read.table(file = "SquidNorway.txt", header = TRUE) #Inspect the results str(Squid) names(Squid) ############################################################## #Housekeeping: load packages and support functions library(lattice) #For multi-panel graphs library(mgcv) #For GAMs #Source our library file Highstatlib.R source(file = "HighstatLibV8.R") #It can be dowloaded from the course website. ############################################################## ############################################################## #Section 5.3 Data exploration #Figure 5.1 MyVar <- c("Lat", "Depth", "ML", "d15N") Mydotplot(as.matrix(Squid[,MyVar])) #Collinerity #Figure 5.2 MyVar <- c("d15N" , "Lat", "Depth", "ML") pairs(Squid[,MyVar], lower.panel = panel.cor) #Multipanel scatterplot #Figure 5.3 MyVar <- c("Lat", "Depth", "ML") Myxyplot(Squid, MyVar, "d15N") #For the book chapter we changed the layout #For this we need the xyplot code, and not the #Myxyplot function Y <- Squid\$d15N MyX <- c("Lat", "Depth", "ML") X <- Squid[, MyX] AllX <- as.vector(as.matrix(Squid[,MyX])) AllY <- rep(Squid[,"d15N"] , length(MyX)) AllID <- rep(MyX, each = nrow(Squid)) xyplot(AllY ~ AllX|factor(AllID), col = 1, layout = c(3,1), xlab = list(label="Explanatory variables",cex = 1.5), ylab = list(label = "d15N", cex = 1.5), strip = function(bg='white', ...) strip.default(bg='white', ...), scales = list(alternating = T, x = list(relation = "free"), y = list(relation = "same")), panel=function(x, y){ panel.grid(h=-1, v= 2) panel.points(x, y, col = 1) panel.loess(x, y, col = 1, lwd = 2)}) #Using the Myxyplot is more friendly on the eye! #Have a look at ggplot2...yiu can make similar graphs, #but with easier code. ############################################################## #Section 5.5 Applying the multiple linear regression model #Fit Model M1 M1 <- glm(d15N ~ ML + Lat, data = Squid) #Model validation #Figure 5.4 E1 <- rstandard(M1) F1 <- fitted(M1) par(mfrow = c(1,2), mar = c(5,5,3,3)) plot(x = F1, y = E1, cex.lab = 1.5, xlab = "Fitted values", ylab = "Residuals") abline(h = 0, v = 0) plot(x = Squid\$ML, y = E1, cex.lab = 1.5, xlab = "Mantel length", ylab = "Residuals") abline(h = 0) #Fit a GAM using E1 T1 <- gam(E1 ~ -1 + s(ML), data = Squid) summary(T1) #Figure 5.5 par(mar = c(5,5,3,3)) plot(T1, cex.lab = 1.5) abline(h = 0, lty = 2) ############################################################## #Section 5.6 Applying an additive model #Fit model M2 M2 <- gam(d15N ~ Lat + s(ML), data = Squid) summary(M2) #Figure 5.6 plot(M2, resid = TRUE, pch = 16, cex = 0.5) abline(h = 0, lty = 2) ############################################################# #Model validation #Figure 5.7 E2 <- resid(M2) F2 <- fitted(M2) par(mfrow = c(2,3), mar = c(5,5,3,3)) plot(x = F2, y = E2, xlab = "Fitted values", ylab = "Residuals") abline(h = 0, lty = 2) plot(x = Squid\$ML, y = E2, xlab = "ML", ylab = "Residuals") abline(h = 0, lty = 2) plot(x = Squid\$Lat, y = E2, xlab = "Latitude", ylab = "Residuals") abline(h = 0, lty = 2) plot(x = Squid\$Depth, y = E2, xlab = "Depth", ylab = "Residuals") abline(h = 0, lty = 2) hist(E2, xlab = "", ylab ="", breaks = 10) plot(sort(E2), type = "h", xlab = "Sorted residuals", ylab = "Residuals") ############################################################## #Section 5.7 Testing linearity vs non-linearity #Compare models AIC(M1, M2) anova(M1, M2, test = "F") #Fit model M3 M3 <- gam(d15N ~ Lat + s(ML, bs = "cr"), data = Squid) #5.7.1 Programming a smoother manually rg <- range(Squid\$ML) Squid\$MLsc <- (Squid\$ML - rg[1]) / (rg[2] - rg[1]) probs <- seq(0, 1, length = 5) QD <- quantile(unique(Squid\$MLsc), probs) QD rhs <- function(x, TH) {ifelse(x >= TH, (x-TH)^3,0)} dk <- function(x,TH,K){ (rhs(x,TH) - rhs(x,K)) / (K-TH) } bj <- function(x,TH,K){ dk(x,TH,K) - dk(x,K-1,K)} I1 <- order(Squid\$MLsc) Squid1 <- Squid[I1,] M4 <- lm(d15N ~ 1 + Lat + MLsc + bj(MLsc, QD[2], QD[4]) + bj(MLsc, QD[3], QD[4]) , data = Squid1) X <- model.matrix(M4) head(X) coef(M4) Smooth <- X[,3:5] %*% coef(M4)[3:5] Smooth <-Smooth - mean(Smooth) #Figure 5.8 plot(x = Squid1\$MLsc, y = Squid1\$d15N, xlab = "Scaled ML", type = "n", ylab = "Smoothing function ML", ylim = c(-2.5,2.5), cex = 0.7, pch = 16, col = grey(0.5)) E4 <- resid(M4) lines(Squid1\$MLsc, Smooth, lwd = 5) for (i in 1:5){abline(v = QD[i])} points(Squid1\$MLsc, Smooth+E4) #End Figure 5.8 code #Compare the model with lm results M5 <- lm(d15N ~ Lat + MLsc , data = Squid1) anova(M4, M5, test = "F") #Small differences with the book! ############################################################# #Section 5.8 Consequences of ignoring collinearity in GAM M6 <- gam(d15N ~ s(Lat)+ s(Depth) + s(ML), data = Squid) M6 <- gam(d15N ~ s(Lat, k = 4) + s(Depth, k = 4) + s(ML), data = Squid) summary(M6) ##################End of code ##########################