Showing posts with label generalised additive model. Show all posts
Showing posts with label generalised additive model. Show all posts

05 August 2014

Preliminary "mgcv" result

Dear friends,

I managed to add some other predictors: anions, cumulative monthly rain, and lagged-1 monthly rain.

The following table shows the updated result.
Based on the table, I made a conceptual model about the water flow and the interaction between predictors in the system. As I've mentioned before, the surficial processes have stronger control to water chemistry than lithology. Hopefully the following sketch can give more spatial sense of the area. The strongest process detected by mgcv is NO3 enrichment in the river water as it gains water from groundwater flow. The other process is dilution  effect by river water as shown by decreasing pattern for elements like Cl, SO4, and Mn towards river.



New results

GAM Predictant Predictors Significance Family Residuals AIC Deviance GCV Rsq Pattern TrendRiver
10 logEC te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, Y gamma good 3794.627 16.200 0.448 0.140 clear decreasing
11 logCO3 te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, N gaussian poor 886.045 25.800 1.171 0.229 clear decreasing
12 logHCO3 te(x,y), elv, lithology, cumRain, lagRain N, Y, N, N, Y gaussian good 778.806 40.300 0.819 0.362 not clear
13 logCO2 te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, Y, N gaussian poor 1035.771 14.200 1.950 0.111 clear decreasing
14 logCl te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, Y gaussian good 814.054 31.000 0.922 0.267 not clear
15 logSO4 te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, N gaussian good 1129.933 32.700 2.686 0.296 clear decreasing
16 logNO2 te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, Y gaussian good 778.314 62.200 0.819 0.589 clear decreasing
17 logNO3 te(x,y), elv, lithology, cumRain, lagRain Y, N, N, Y, N gaussian good 1168.619 42.500 3.062 0.399 clear increasing
18 logFe te(x,y), elv, lithology, cumRain, lagRain Y, N, N, N, N gaussian good 649.973 12.300 0.528 0.083 clear decreasing
19 logCa te(x,y), elv, lithology, cumRain, lagRain N, Y, N, N, Y gaussian good 785.075 30.300 0.833 0.281 not clear
20 logMg te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, Y gaussian good 730.692 41.600 0.696 0.371 not clear
21 logMn te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, N gaussian poor -72.300 79.100 0.046 0.774 clear decreasing
22 logNa te(x,y), elv, lithology, cumRain, lagRain Y, Y, N, N, Y gaussian good 641.144 39.500 0.514 0.353 clear decreasing
23 logK te(x,y), elv, lithology, cumRain, lagRain N, N, N, N, N gaussian good 592.524 18.400 0.434 0.166 not clear






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Previous post

This post would be the continuation of the previous serial posts on GAM using mgcv package. As I have posted before, I am looking for predictors that explain the interaction between groundwater and river water in Cikapundung watershed (Bandung, West Java, Indonesia).

The following table is the preliminary result. I'll make further explanation.




GAM Predictant Predictors Significance Family Residuals AIC Deviance (%) Notes Trend
10 EC (x,y), elv, lithology yes, yes, no gamma good 3805.445 10.6 clear pattern, decreasing trend towards river E-W
11 logCO3 (x,y), elv, lithology yes, yes, no gaussian poor 889.724 24.5 clear pattern, decreasing trend towards river E-W
13 logCO2 (x,y), elv, lithology yes, yes, no gaussian poor 1046.908 11.8 clear pattern, decreasing trend towards river NE-SW
15 logSO4 (x,y), elv, lithology yes, yes, no gaussian poor 1132.996 32.9 clear pattern, decreasing trend towards river NW-SE
17 NO3 (x,y), elv, lithology yes, no, no gaussian poor 1388.982 8.38 clear pattern, decreasing trend towards river NW-SE
20 logMg (x,y), elv, lithology no, yes, no gaussian poor 780.82 26.4 clear pattern, decreasing trend towards river E-W
21 Mn (x,y), elv, lithology yes, yes, no gaussian poor -971.85 74.4 clear pattern, decreasing trend towards river N-S, NE-SW
16 logNO2 (x,y), elv, lithology yes, no, no gaussian poor 1183.261 43.3 clear pattern, increasing trend towards river NE, SE
18 Fe (x,y), elv, lithology no, no, no gaussian poor -70.72 2.44 clear pattern, increasing trend towards river NW-SE
22 logNa (x,y), elv, lithology yes, yes, no gamma good 649.918 33.3 clear pattern, increasing trend towards river E-W
12 logHCO3 (x,y), elv, lithology no, yes, no gaussian good 847.1502 22.8 no clear pattern
14 logCl (x,y), elv, lithology yes, yes, no gaussian good 828.088 27.4 no clear pattern
19 logCa (x,y), elv, lithology no, yes, no gaussian poor 838 17.6 no clear pattern
23 logK (x,y), elv, lithology no, yes, no gaussian good 594.923 18.3 no clear pattern
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31 July 2014

Looking at the predictors to water quality: using GAM



Dear friends,

Continuing my analysis on water quality, on this post I try to look at the predictors that control water quality. I am still using GAM with mgcv package. We can use (x,y) coordinate as one of the predictor, as tensor function using "te()" command. Character-type column can also be used as the predictor without "s()" command. In the following code, I am putting the:
  • EC (electro-conductivity) and concentrations of CO3, HCO3, CO2, Cl, SO4, NO2, NO3, Fe (in mg/L) as predictant
  • Spatial distribution "te(x,y)" + geology "(data$aq) column" and + elevation "s(elevation)" as predictors
One of the result from "plot(gam.., pages=1)" command will look something like the above image. I will elaborate more on the results and the workaround later on. The following is the sample code.


 

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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  : 01 Aug 2014
#---

##########################
##### 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", "elv", "aq", "Ca", "Mg", 
                  "Fe", "Mn", "K", "Na")]
group3 = data[,c("x", "y", "ec", "elv", "aq", "CO3","HCO3",
                 "CO2","Cl","SO4","NO2",
                 "NO3","SiO2")]


################## FAMILY = GAUSSIAN #####################

# smoothing=cubic shrinkage version ########################
k1<-10
bsm<-"cs"
Gcr10 <- gam(ec ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group1)       
plot(Gcr10, pages=1)
gam.check(Gcr10)
summary(Gcr10)

Gcr11 <- gam(CO3 ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr11, pages=1)
gam.check(Gcr11)               
summary(Gcr11)

Gcr12 <- gam(HCO3 ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr12, pages=1)
gam.check(Gcr12)               
summary(Gcr12)

Gcr13 <- gam(CO2 ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr13, pages=1)
gam.check(Gcr13)               
summary(Gcr13)

Gcr14 <- gam(Cl ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr14, pages=1)
gam.check(Gcr14)               
summary(Gcr14)

Gcr15 <- gam(SO4 ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr15, pages=1)
gam.check(Gcr15)               
summary(Gcr15)

Gcr16 <- gam(NO2 ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr16, pages=1)
gam.check(Gcr16)               
summary(Gcr16)

Gcr17 <- gam(NO3 ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group3) 
plot(Gcr17, pages=1)
gam.check(Gcr17)               
summary(Gcr17)

Gcr18 <- gam(Fe ~ te(x, y, k=k1, bs=bsm) +
            s(elv, k=k1, bs=bsm) + 
            (data$aq),
            data=group2) 
plot(Gcr18, pages=1)
gam.check(Gcr18)               
summary(Gcr18)

AIC(Gcr10, Gcr11, Gcr12)
AIC(Gcr13, Gcr14, Gcr15)
AIC(Gcr16, Gcr17, Gcr18)
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24 July 2014

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)
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