Updated #R Code: GAM exercise using mgcv package

Dear friends,

The previous GAM post was based on only one year dataset. I have added another four year dataset in to the system and unfortunately it needed several adjustment, especially for the knot (k) value.

So the following is the updated R code. I am sure someone can come up with more efficient code.

Cheers,
Erwin

Note: 
We can use (x,y) coordinate as one of the predictor, as tensor function using "te()".
We can also include character-type column as the predictor.

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#--- # title : MGCV package tryout # author: Dasapta Erwin Irawan^1 and Farzina Akter^2 # affiliation^1: Institut Teknologi Bandung (Indonesia) # affiliation^2: University of Sydney (Australia) # date : 22 July 2014 #--- # This code is following http://www3.nd.edu/~mclark19/learn/GAMS.pdf # Load library and data require("mgcv") data <- read.csv("alldata23.csv") ########################## ##### GAM ANALYSIS ####### ########################## # load library and data require("mgcv") data <- read.csv("alldata23.csv") group1 <- data[,c("x","y","ec","elv","aq","ph","hard","tds","temp","eh","Q")] group2 <- data[,c("x","y","ec","Ca","Mg","Fe","Mn","K","Na")] group3 = data[,c("x","y","ec","CO3","HCO3","CO2","Cl","SO4","NO2", "NO3","SiO2")] # GAM models (check, all predictors must be numeric) ################## FAMILY = GAUSSIAN ##################### ## ols (k=10 default changed to k=5, to avoid smoothing error) k1<-3 # change the knot (k) value to avoid this error message # ... basis dimension, k, increased to minimum possible ... # k=10 (default) gam11<-gam(ec ~ s(x,k=k1) + s(y,k=k1) + s(elv,k=k1) + s(ph,k=k1) + s(hard,k=k1) + s(tds,k=k1) + s(temp,k=k1) + s(eh,k=k1) + s(Q,k=k1), data=group1) # [dropping "Mg"] # I've tested each variables to avoid these error messages # ... max not meaningful for factors ... k2<-3 # (if you don't change it, then R will use previous k value) gam12<-gam(ec ~ s(x,k=k2) + s(y,k=k2) + s(Ca,k=k2) + s(Fe,k=k2) + s(K,k=k2) + s(Na,k=k2) + s(Mn,k=k2), data=group2) k3<-3 # (if you don't change it, then R will use previous k value) gam13<-gam(ec ~ s(x,k=k3) + s(y,k=k3) + s(CO3,k=k3) + s(HCO3,k=k3) + s(CO2,k=k3) + s(Cl,k=k3) + s(SO4,k=k3) + s(NO2,k=k3) + s(NO3,k=k3) + + s(SiO2,k=k3), data=group3) ## smoothing=thin plate smoothing #k1<-3 gam21<-gam(ec ~ s(x,k=k1,bs="tp") + s(y,k=k1,bs="tp") + s(elv,k=k1,bs="tp") + s(ph,k=k1,bs="tp") + s(hard,k=k1,bs="tp") + s(tds,k=k1,bs="tp") + s(temp,k=k1,bs="tp") + s(eh,k=k1,bs="tp") + s(Q,k=k1,bs="tp"), data=group1) #k2<-3 xxxxxxxxxxxx gam22<-gam(ec ~ s(x,k=k2,bs="tp") + s(y,k=k2,bs="tp") + s(Ca,k=k2,bs="tp") + s(Fe,k=k2,bs="tp") + s(Mn,k=k2,bs="tp") + s(K,k=k2,bs="tp") + s(Na,k=k2,bs="tp"), data=group2) #k3<-5 gam23<-gam(ec ~ s(x,k=k3,bs="tp") + s(y,k=k3,bs="tp") + s(CO3,k=k3,bs="tp") + s(HCO3,k=k3,bs="tp") + s(CO2,k=k3,bs="tp") + s(Cl,k=k3,bs="tp") + s(SO4,k=k3,bs="tp") + s(NO2,k=k3,bs="tp") + s(NO3,k=k3,bs="tp") + + s(SiO2,k=k3,bs="tp"), data=group3) ## smoothing=thin shrinkage #k1<-5 bsm<-"ts" gam31<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), data=group1) #k2<-3 xxxxxxxxxxxx bsm<-"ts" gam32<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), data=group2) #k3<-5 bsm<-"ts" gam33<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), data=group3) # smoothing=cubic regression spline #k1<-5 bsm<-"cr" gam41<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), data=group1) #k2<-3 xxxxxxxxxxxx gam42<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), data=group2) #k3<-5 gam43<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), data=group3) # smoothing=cubic shrinkage version bsm<-"cs" #k1<-5 gam51<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), data=group1) #k2<-3 xxxxxxxxxxxx gam52<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), data=group2) #k3<-5 gam53<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), data=group3) # smoothing=cyclic cubic regression spline k1<-5 [changed from 3 to 5] bsm<-"cc" gam61<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), data=group1) k2<-8 xxxxxxxxxxxxx gam62<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), data=group2) k3<-5 gam63<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), data=group3) # Dropping "cc" model, causing error, don't have cyclic pattern ################## FAMILY = GAMMA ##################### ## link=log, default smoothing #k1<-5 # k=10 (default) gam71<-gam(ec ~ s(x,k=k1) + s(y,k=k1) + s(elv,k=k1) + s(ph,k=k1) + s(hard,k=k1) + s(tds,k=k1) + s(temp,k=k1) + s(eh,k=k1) + s(Q,k=k1), Gamma (link="log"), data=group1) #k2<-3 xxxxxxxxxxxxx gam72<-gam(ec ~ s(x,k=k2) + s(y,k=k2) + s(Ca,k=k2) + s(Fe,k=k2) + s(Mn,k=k2) + s(K,k=k2) + s(Na,k=k2), Gamma (link="log"), data=group2) #k3<-5 gam73<-gam(ec ~ s(x,k=k3) + s(y,k=k3) + s(CO3,k=k3) + s(HCO3,k=k3) + s(CO2,k=k3) + s(Cl,k=k3) + s(SO4,k=k3) + s(NO2,k=k3) + s(NO3,k=k3) + + s(SiO2,k=k3), Gamma (link="log"), data=group3) ## smoothing=thin plate smoothing #k1<-5 gam81<-gam(ec ~ s(x,k=k1,bs="tp") + s(y,k=k1,bs="tp") + s(elv,k=k1,bs="tp") + s(ph,k=k1,bs="tp") + s(hard,k=k1,bs="tp") + s(tds,k=k1,bs="tp") + s(temp,k=k1,bs="tp") + s(eh,k=k1,bs="tp") + s(Q,k=k1,bs="tp"), Gamma (link="log"), data=group1) #k2<-3 xxxxxxxxxxxxx gam82<-gam(ec ~ s(x,k=k2,bs="tp") + s(y,k=k2,bs="tp") + s(Ca,k=k2,bs="tp") + s(Fe,k=k2,bs="tp") + s(Mn,k=k2,bs="tp") + s(K,k=k2,bs="tp") + s(Na,k=k2,bs="tp"), Gamma (link="log"), data=group2) #k3<-5 gam83<-gam(ec ~ s(x,k=k3,bs="tp") + s(y,k=k3,bs="tp") + s(CO3,k=k3,bs="tp") + s(HCO3,k=k3,bs="tp") + s(CO2,k=k3,bs="tp") + s(Cl,k=k3,bs="tp") + s(SO4,k=k3,bs="tp") + s(NO2,k=k3,bs="tp") + s(NO3,k=k3,bs="tp") + + s(SiO2,k=k3,bs="tp"), Gamma (link="log"), data=group3) ## smoothing=thin shrinkage #k1<-5 bsm<-"ts" gam91<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), Gamma (link="log"), data=group1) #k2<-3 xxxxxxxxxxxxx bsm<-"ts" gam92<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), Gamma (link="log"), data=group2) #k3<-5 bsm<-"ts" gam93<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), Gamma (link="log"), data=group3) # Family=gaussian, smoothing=cubic regression spline #k1<-5 bsm<-"cr" gam101<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), Gamma (link="log"), data=group1) #k2<-3 xxxxxxxxxxxxx gam102<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), Gamma (link="log"), data=group2) #k3<-5 gam103<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), Gamma (link="log"), data=group3) # smoothing=cubic shrinkage version bsm<-"cs" #k1<-5 gam111<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), Gamma (link="log"), data=group1) #k2<-3 xxxxxxxxxxxxx gam112<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), Gamma (link="log"), data=group2) #k3<-5 gam113<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), Gamma (link="log"), data=group3) # smoothing=cyclic cubic regression spline # k1<-5 bsm<-"cc" gam121<-gam(ec ~ s(x,k=k1,bs=bsm) + s(y,k=k1,bs=bsm) + s(elv,k=k1,bs=bsm) + s(ph,k=k1,bs=bsm) + s(hard,k=k1,bs=bsm) + s(tds,k=k1,bs=bsm) + s(temp,k=k1,bs=bsm) + s(eh,k=k1,bs=bsm) + s(Q,k=k1,bs=bsm), Gamma (link="log"), data=group1) #k2<-3 xxxxxxxxxxxxx gam122<-gam(ec ~ s(x,k=k2,bs=bsm) + s(y,k=k2,bs=bsm) + s(Ca,k=k2,bs=bsm) + s(Fe,k=k2,bs=bsm) + s(Mn,k=k2,bs=bsm) + s(K,k=k2,bs=bsm) + s(Na,k=k2,bs=bsm), Gamma (link="log"), data=group2) #k3<-5 gam123<-gam(ec ~ s(x,k=k3,bs=bsm) + s(y,k=k3,bs=bsm) + s(CO3,k=k3,bs=bsm) + s(HCO3,k=k3,bs=bsm) + s(CO2,k=k3,bs=bsm) + s(Cl,k=k3,bs=bsm) + s(SO4,k=k3,bs=bsm) + s(NO2,k=k3,bs=bsm) + s(NO3,k=k3,bs=bsm) + + s(SiO2,k=k3,bs=bsm), Gamma (link="log"), data=group3) ######### GAM EVALUATION ################ # Gaussian AIC.gsdef<-AIC(gam11,gam12,gam13) AIC.gstp<-AIC(gam21,gam22,gam23) AIC.gsts<-AIC(gam31,gam32,gam33) AIC.gscr<-AIC(gam41,gam42,gam43) AIC.gscs<-AIC(gam51,gam52,gam53) AIC.gscc<-AIC(gam61,gam62,gam63) print(AIC.gsdef) ; print(AIC.gstp) # lowestAIC=gam13(3300.728) and gam23(3300.728) print(AIC.gsts) ; print(AIC.gscr) # lowestAIC=gam33(3296.121) and gam43(3295.407) print(AIC.gscs) ; print(AIC.gscc) # lowest AIC=gam53(3290.296) and gam63(3307.973) summary(gam13) # R-sq=0.359, GCV=24394, scale=22925, Dev=39.5% # signif pars=CO3, HCO3, CO2, Cl, NO2 gam.check(gam13) summary(gam23) # R-sq=0.359, GCV=24394, scale=22925, Dev=39.5% # sigpar=CO3, HCO3, CO2, Cl, NO2 gam.check(gam23) summary(gam33) # R-sq=0.358, GCV=23906, scale=22956, Dev=38.1% # sigpar=CO3, HCO3, CO2, Cl, NO2 gam.check(gam33) summary(gam43) # R-sq=0.372, GCV=23888, scale=22465, Dev=40.7% # sigpar=CO3, HCO3, CO2, Cl, NO2, SiO2 gam.check(gam43) summary(gam53) # R-sq=0.374, GCV=23369, scale=22403, Dev=39.7% # sigpar=CO3, HCO3, CO2, Cl, NO2 gam.check(gam53) # Gamma # using AIC AIC.gmdef<-AIC(gam71,gam72,gam73) AIC.gmtp<-AIC(gam81,gam82,gam83) AIC.gmts<-AIC(gam91,gam92,gam93) AIC.gmcr<-AIC(gam101,gam102,gam103) AIC.gmcs<-AIC(gam111,gam112,gam113) AIC.gmcc<-AIC(gam121,gam122,gam123) print(AIC.gmdef) ; print(AIC.gmtp) # lowestAIC=gam71(3137.232) and gam81(3137.232) print(AIC.gmts) ; print(AIC.gmcr) # lowestAIC=gam91(3133.663) and gam101(3138.866) print(AIC.gmcs) ; print(AIC.gmcc) # lowestAIC=gam111(3135.529) and gam121(3163.347)