Today, we will work with daily water temperature and air temperature data observed for 31 rivers in Spain. The goal of this tutorial is to identify the best model for predicting the maximum water temperature given the maximum air temperature. In the preview below, W
represents the daily maximum water temperature and A
represents the daily maximum air temperature. The data contains almost a full year of data for each of the 31 different rivers.
## # A tibble: 6 × 8
## JULIAN_DAY YEAR L W A TIME MONTH DAY
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 2003 103 14.2 21.2 1 1 1
## 2 2 2003 103 14.4 16.8 2 1 2
## 3 3 2003 103 14.4 15.4 3 1 3
## 4 4 2003 103 10.9 10.8 4 1 4
## 5 5 2003 103 10.8 11.7 5 1 5
## 6 6 2003 103 10.7 12.4 6 1 6
Please modify the code chunk to visualize the relationship between A
and W
with scatterplot (set alpha=0.3
) and smooth line.
ggplot(data=DATA) +
geom_point(aes(x=A,y=W),alpha=0.3)+
geom_smooth(aes(x=A,y=W)) +
theme_minimal()
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
WAPLOT.func=function(Location){
DATA %>% filter(L == Location) %>%
ggplot()+
geom_point(aes(x=A,y=W),alpha=0.3)+
geom_smooth(aes(x=A,y=W)) +
theme_minimal()
}
WAPLOT.func(103)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
WAPLOT.func(105)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
WAPLOT.func(918)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
set.seed(216)
TEST.LOCATIONS=sample(x=unique(DATA$L),size=3,replace=F)
TRAIN = anti_join(DATA,tibble(L=TEST.LOCATIONS),by="L")
TEST = semi_join(DATA,tibble(L=TEST.LOCATIONS),by="L")
WAPLOT2.func=function(DATA){
ggplot(data=DATA)+
geom_point(aes(x=A,y=W),alpha=0.3)+
geom_smooth(aes(x=A,y=W)) +
theme_minimal()
}
WAPLOT2.func(TRAIN)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
WAPLOT2.func(TEST)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
linmod=lm(W~A,data=TRAIN)
summary(linmod)
##
## Call:
## lm(formula = W ~ A, data = TRAIN)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.1495 -2.1024 -0.1857 1.8851 16.8637
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.394990 0.087161 38.95 <0.0000000000000002 ***
## A 0.649422 0.004101 158.36 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.075 on 8866 degrees of freedom
## (1371 observations deleted due to missingness)
## Multiple R-squared: 0.7388, Adjusted R-squared: 0.7388
## F-statistic: 2.508e+04 on 1 and 8866 DF, p-value: < 0.00000000000000022
TRAIN2 = TRAIN %>% add_predictions(linmod,var="linpred")
TEST2 = TEST %>% add_predictions(linmod,var="linpred")
TruevsPred = function(test_data, train_data, col_name){
SPLIT = c(rep("TEST",dim(test_data)[1]),rep("TRAIN",dim(train_data)[1]))
cbind(rbind(test_data,train_data),SPLIT) %>%
ggplot()+geom_point(aes(x=W,y=get(col_name),
color=factor(SPLIT,levels=c("TRAIN","TEST"))),alpha=0.2) +
theme_minimal() + geom_abline(intercept=0,slope=1) +
guides(color=guide_legend(title="Dataset")) + xlab("True Value") +
ylab("Predicted Value Under MODEL")
}
TruevsPred(TEST2, TRAIN2, 'linpred')
TRAIN3 = TRAIN2 %>% add_residuals(linmod,var="linres")
TEST3 = TEST2 %>% add_residuals(linmod,var="linres")
MSEandMAE = function(test_data, col_name){
residual = unlist(test_data[col_name])
MAE = mean(abs(residual),na.rm=T)
MSE = mean((residual)^2,na.rm=T)
result = matrix(c(MAE,MSE),1,2)
colnames(result) = c("MAE","MSE")
rownames(result) = c("Loss")
return(result)
}
MSEandMAE(TEST3,'linres')
## MAE MSE
## Loss 2.750323 11.23319
poly2mod=lm(W~A+I(A^2),data=TRAIN)
poly3mod=lm(W~A+I(A^2)+I(A^3),data=TRAIN)
poly4mod=lm(W~A+I(A^2)+I(A^3)+I(A^4),data=TRAIN)
anova(linmod,poly2mod,poly3mod,poly4mod,test="Chisq")
## Analysis of Variance Table
##
## Model 1: W ~ A
## Model 2: W ~ A + I(A^2)
## Model 3: W ~ A + I(A^2) + I(A^3)
## Model 4: W ~ A + I(A^2) + I(A^3) + I(A^4)
## Res.Df RSS Df Sum of Sq Pr(>Chi)
## 1 8866 83855
## 2 8865 83553 1 302.01 0.00000001284 ***
## 3 8864 82840 1 713.09 < 0.00000000000000022 ***
## 4 8863 82730 1 109.48 0.0006152 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TRAIN4 =TRAIN3 %>%
add_predictions(poly2mod,var="poly2pred") %>%
add_predictions(poly3mod,var="poly3pred") %>%
add_predictions(poly4mod,var="poly4pred")
TEST4 =TEST3 %>%
add_predictions(poly2mod,var="poly2pred") %>%
add_predictions(poly3mod,var="poly3pred") %>%
add_predictions(poly4mod,var="poly4pred")
TruevsPred(TEST4, TRAIN4, 'poly2pred')
TruevsPred(TEST4, TRAIN4, 'poly3pred')
TruevsPred(TEST4, TRAIN4, 'poly4pred')
TRAIN5 =TRAIN4 %>%
add_residuals(poly2mod,var="poly2res") %>%
add_residuals(poly3mod,var="poly3res") %>%
add_residuals(poly4mod,var="poly4res")
TEST5 =TEST4 %>%
add_residuals(poly2mod,var="poly2res") %>%
add_residuals(poly3mod,var="poly3res") %>%
add_residuals(poly4mod,var="poly4res")
MSEandMAE(TEST5,'poly2res')
## MAE MSE
## Loss 2.732399 11.18813
MSEandMAE(TEST5,'poly3res')
## MAE MSE
## Loss 2.706833 11.0815
MSEandMAE(TEST5,'poly4res')
## MAE MSE
## Loss 2.715366 11.14699
The function save.image()
in R can be used to save all objects in the global environment. This is very helpful when you want work off your results without rerunning all previous R code. The name of the exported information should contain the file extension .Rdata. These files can be extremely large depending how much RAM was utilized in your R session. The function load()
can be used to import a previous workspace.
For more information on .Rdata file types, see https://fileinfo.com/extension/rdata for help.
save.image("Tutorial.Rdata")