Below are the solutions to these exercises on “GAMs – Exercises.”

if (!require(mgcv)){install.packages(mgcv, dep=T)} library(mgcv) if (!require(car)){install.packages(car, dep=T)} library(car) ############### # # # Exercise 1 # # # ############### Veg <- read.csv(file.choose()) str(Veg)

## 'data.frame': 58 obs. of 8 variables: ## $ SR : int 8 6 8 8 10 7 6 5 8 6 ... ## $ ROCK : num 27 26 30 18 23 26 39 25 24 21 ... ## $ LITTER : num 30 20 24 35 22 26 19 26 24 16 ... ## $ BARESOIL: num 26 28 30 16 9 23 19 33 29 41 ... ## $ SprTmax : num 15.8 15.2 12.8 14 14.3 ... ## $ Time : int 1958 1962 1967 1974 1981 1994 2002 1958 1962 1967 ... ## $ FallPrec: num 30.2 99.6 43.4 54.9 24.4 ... ## $ Transect: int 1 1 1 1 1 1 1 2 2 2 ...

head(Veg)

## SR ROCK LITTER BARESOIL SprTmax Time FallPrec Transect ## 1 8 27 30 26 15.77 1958 30.22 1 ## 2 6 26 20 28 15.21 1962 99.56 1 ## 3 8 30 24 30 12.76 1967 43.43 1 ## 4 8 18 35 16 14.00 1974 54.86 1 ## 5 10 23 22 9 14.33 1981 24.38 1 ## 6 7 26 26 23 16.91 1994 10.16 1

# Response variable = SR or species richness of plants per transect # Explanatory - Rock content (ROCK) # Explanatory - baresoil (BARESOIL) # Explanatory - Litter (LITTER) # Explanatory - ppt in Autumn (FallPrec) # Explanatory - Max Spring temperature (SprTmax) # Explanatory - Year of transect (Time) # Explanatory - Transect number (Transect) ############### # # # Exercise 2 # # # ############### scatterplot(SR ~ ROCK, data = Veg)

############### # # # Exercise 3 # # # ############### Veg.gam1 <- gam(SR ~ s(ROCK), data = Veg) plot(Veg.gam1)

############### # # # Exercise 4 # # # ############### summary(Veg.gam1)

## ## Family: gaussian ## Link function: identity ## ## Formula: ## SR ~ s(ROCK) ## ## Parametric coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 9.9655 0.3757 26.52 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Approximate significance of smooth terms: ## edf Ref.df F p-value ## s(ROCK) 3.778 4.664 2.285 0.0768 . ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## R-sq.(adj) = 0.126 Deviance explained = 18.4% ## GCV = 8.9217 Scale est. = 8.1867 n = 58

############### # # # Exercise 5 # # # ############### gam.check(Veg.gam1)

## ## Method: GCV Optimizer: magic ## Smoothing parameter selection converged after 5 iterations. ## The RMS GCV score gradient at convergence was 0.0001067967 . ## The Hessian was positive definite. ## Model rank = 10 / 10 ## ## Basis dimension (k) checking results. Low p-value (k-index<1) may ## indicate that k is too low, especially if edf is close to k'. ## ## k' edf k-index p-value ## s(ROCK) 9.00 3.78 1.01 0.47

############### # # # Exercise 6 # # # ############### # plot base graph (with CIs) plot(SR ~ ROCK, data = Veg, pch = 16, xlab = "% ROCK in substrate", ylab = "Species Richness") ############### # # # Exercise 7 # # # ############### # predict across the data x <- seq(min(Veg$ROCK), max(Veg$ROCK), l=100) # 100 steps.... y <- predict(Veg.gam1, data.frame(ROCK = x), se = TRUE) # using standard errors se = TRUE # add lines ############### # # # Exercise 7 # # # ############### lines(x, y$fit) # plots the fitted values lines(x, y$fit + 2 * y$se.fit, lty = 2) # plots a dashed line for 2 * SE above the fit lines(x, y$fit - 2 * y$se.fit, lty = 2) # plots a dashed line for 2 * SE below the fit

## Leave a Reply