SMurphy 2020-08-29
Set seed for replication to 123. Import excel data representing
training data of burn severity classes from candidate spectral indices
sampled in-field in composite burn plots.
set.seed(123)
darkwoods_fire_plots_data <- read_excel("3.1.darkwoods_fire_ground_plots.xls")ndbr_lm <- lm(CBI_total_2 ~ NDBR_2016, data = darkwoods_fire_plots_data)
ndbr_lm_resid <- resid(ndbr_lm)
plot(CBI_total_2 ~ NDBR_2016, data = darkwoods_fire_plots_data,
ylab = "Fire severity score of composite burn plots", xlab = "NDBR",
col = "blue")
abline(ndbr_lm, col = "red")
Splitting data 70:30 between training and test subsets according to
distribution of response variable: CBI_total_2.
training.samples <- createDataPartition(darkwoods_fire_plots_data$CBI_total_2,
p = 0.7, list = FALSE)
train.data <- darkwoods_fire_plots_data[training.samples, ]
test.data <- darkwoods_fire_plots_data[-training.samples, ]Training regimes set by 10K-fold cross validation with 10, 5 and no
repeats using repeatedcv and cv parameters.
model_training_10kfold_10repeat <- trainControl(method = "repeatedcv",
number = 10, repeats = 10, savePredictions = TRUE)
model_training_10kfold_3repeat <- trainControl(method = "repeatedcv",
number = 10, repeats = 3, savePredictions = TRUE)
model_training_10kfold <- trainControl(method = "cv", number = 10,
savePredictions = TRUE)
# 10k-fold method
knitr::include_graphics(path = "animation.gif")
Apply 10K-fold-X10 training regime to test prediction of NDBR between
three candidate models including linear, non-linear support vector
machine regressions, randomForest regression tree using svmLinear ,
svmRadial , rf kernels. Data preprocessing included using center
and scale operations.
svm_ndbr_log_linear <- train(CBI_total_2 ~ NDBR_2016, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 10)), metric = "RMSE")
svm_ndbr_log_radial <- train(CBI_total_2 ~ NDBR_2016, data = train.data,
method = "svmRadial", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tunelength = 10)
rf_nndbr_1000trees <- train(CBI_total_2 ~ NDBR_2016, data = train.data,
method = "rf", ntree = 1000, metric = "RMSE", trControl = model_training_10kfold,
importance = TRUE)
# Selected kernel
svm_ndbr_log_linear_full <- train(CBI_total_2 ~ NDBR_2016, data = darkwoods_fire_plots_data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 10)), metric = "RMSE")Compare performance of svmLinear model between training, test, and
full dataset, using absolute and relative MAE, RMSE, and RMSE-ratio
metrics, and TheilU statistic of model bias. Following results table
is taken from manuscript section 2.3.
| Model | R2 | RMSE | RMSEratio | TheilU | C | ε |
| NBR | 0.879*** | 1.05 | 0.46 | 0.035 | 0.336 | 0.10 |
| BAI2-SL | 0.183*** | 2.61 | 1.09 | 0.307 | 1.105 | 0.10 |
| MIRBI | 0.551*** | 1.94 | 1.16 | 0.469 | 0.316 | 0.10 |
| TVI | 0.584*** | 1.88 | 1.16 | 0.432 | 0.474 | 0.10 |
| TVI-SW | 0.241*** | 2.54 | 1.10 | 0.343 | 0.158 | 0.10 |
svm_ndbr_pred_train <- predict(svm_ndbr_log_linear, data = train.data)
svm_ndbr_pred_test <- predict(svm_ndbr_log_linear, data = test.data)
svm_ndbr_pred_full <- predict(svm_ndbr_log_linear_full, data = darkwoods_fire_plots_data)
svm_ndbr_pred_full_r2 <- MLmetrics::R2_Score(svm_ndbr_pred_full,
darkwoods_fire_plots_data$CBI_total_2)
svm_ndbr_pred_train_r2 <- MLmetrics::R2_Score(svm_ndbr_pred_train,
train.data$CBI_total_2)
svm_ndbr_pred_test_r2 <- MLmetrics::R2_Score(svm_ndbr_pred_test,
test.data$CBI_total_2)
svm_ndbr_pred_full_mae <- mae(svm_ndbr_pred_full, darkwoods_fire_plots_data$CBI_total_2)
svm_ndbr_pred_train_mae <- mae(svm_ndbr_pred_train, train.data$CBI_total_2)
svm_ndbr_pred_test_mae <- mae(svm_ndbr_pred_test, test.data$CBI_total_2)
svm_ndbr_pred_full_mae_rel <- (svm_ndbr_pred_full_mae/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_ndbr_pred_train_mae_rel <- (svm_ndbr_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_ndbr_pred_test_mae_rel <- (svm_ndbr_pred_test_mae/mean(test.data$CBI_total_2)) *
100
svm_ndbr_pred_full_rmse <- rmse(svm_ndbr_pred_full, darkwoods_fire_plots_data$CBI_total_2)
svm_ndbr_pred_train_rmse <- rmse(svm_ndbr_pred_train, train.data$CBI_total_2)
svm_ndbr_pred_test_rmse <- rmse(svm_ndbr_pred_test, test.data$CBI_total_2)
svm_ndbr_pred_full_rmse_rel <- (svm_ndbr_pred_full_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_ndbr_pred_train_rmse_rel <- (svm_ndbr_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_ndbr_pred_test_rmse_rel <- (svm_ndbr_pred_test_rmse/mean(test.data$CBI_total_2)) *
100
svm_ndbr_pred_train_rmseRatio <- svm_ndbr_pred_train_rmse/svm_ndbr_pred_test_rmse
svm_ndbr_pred_test_rmseRatio <- svm_ndbr_pred_test_rmse/svm_ndbr_pred_train_rmse
svm_ndbr_full_Ubias_DescTools <- DescTools::TheilU(darkwoods_fire_plots_data$CBI_total_2,
svm_ndbr_pred_full, type = 2)
svm_ndbr_pred_full_r2[1] 0.8822122
svm_ndbr_pred_train_r2[1] 0.9046967
svm_ndbr_pred_test_r2[1] -4.316728
svm_ndbr_pred_full_mae[1] 0.6713043
svm_ndbr_pred_train_mae[1] 0.5238902
svm_ndbr_pred_test_mae[1] 4.022415
svm_ndbr_pred_full_mae_rel[1] 15.93547
svm_ndbr_pred_train_mae_rel[1] 12.64298
svm_ndbr_pred_test_mae_rel[1] 91.56658
svm_ndbr_pred_full_rmse[1] 1.008688
svm_ndbr_pred_train_rmse[1] 0.8607236
svm_ndbr_pred_test_rmse[1] 4.774957
svm_ndbr_pred_full_rmse_rel[1] 23.94431
svm_ndbr_pred_train_rmse_rel[1] 20.77174
svm_ndbr_pred_test_rmse_rel[1] 108.6975
svm_ndbr_pred_train_rmseRatio[1] 0.1802579
svm_ndbr_pred_test_rmseRatio[1] 5.547608
svm_ndbr_full_Ubias_DescTools[1] 0.1963738
svm_ndbr_log_linear_full$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 0.333333333333333
Linear (vanilla) kernel function.
Number of Support Vectors : 57
Objective Function Value : -5.0484
Training error : 0.116535
# model 2 - NDBR-SW
svm_ndbr_sw_linear <- train(CBI_total_2 ~ NDBR_SW2_2, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 20)))
# model 3 - BAI2
svm_bai2_linear <- train(CBI_total_2 ~ BAI2_2016, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 20)))
# model 4 - MIRBI
svm_mirbi_linear <- train(CBI_total_2 ~ MIRBI_2016, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 20)))
# model 5 - MSAV
svm_msav_linear <- train(CBI_total_2 ~ MSAV_2016, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 20)))
# model 6 - TVI
svm_tvi_linear <- train(CBI_total_2 ~ VIT2_2016, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 20)))
# model 7 - TVI-SW
svm_tvi_sw_linear <- train(CBI_total_2 ~ VIRSW2_201, data = train.data,
method = "svmLinear", trControl = model_training_10kfold,
preProcess = c("center", "scale"), tuneGrid = expand.grid(C = seq(0,
3, length = 20)))# model 2 - NDBRSW results
summary(lm(predict(svm_ndbr_sw_linear) ~ train.data$CBI_total_2))Call:
lm(formula = predict(svm_ndbr_sw_linear) ~ train.data$CBI_total_2)
Residuals:
Min 1Q Median 3Q Max
-2.1946 -0.7337 -0.1164 0.6918 2.1474
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.40877 0.21770 15.658 <2e-16 ***
train.data$CBI_total_2 0.08340 0.04359 1.913 0.0601 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.002 on 66 degrees of freedom
Multiple R-squared: 0.05255, Adjusted R-squared: 0.03819
F-statistic: 3.661 on 1 and 66 DF, p-value: 0.06005
svm_ndbr_sw_pred_train <- predict(svm_ndbr_sw_linear, data = train.data)
svm_ndbr_sw_pred_train_mae <- mae(svm_ndbr_sw_pred_train, train.data$CBI_total_2)
svm_ndbr_sw_pred_train_mae[1] 2.294951
svm_ndbr_sw_pred_train_mae_rel <- (svm_ndbr_sw_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_ndbr_sw_pred_train_mae_rel[1] 55.38379
svm_ndbr_sw_pred_train_rmse <- rmse(svm_ndbr_sw_pred_train, train.data$CBI_total_2)
svm_ndbr_sw_pred_train_rmse[1] 2.767207
svm_ndbr_sw_pred_train_rmse_rel <- (svm_ndbr_sw_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_ndbr_sw_pred_train_rmse_rel[1] 66.78068
svm_ndbr_sw_pred_train_R2 <- R2(svm_ndbr_sw_pred_train, train.data$CBI_total_2)
svm_ndbr_sw_pred_train_R2[1] 0.05254919
TheilU(train.data$CBI_total_2, svm_ndbr_sw_pred_train, type = 2)[1] 0.5540623
svm_ndbr_sw_train_Ubias <- DescTools::TheilU(train.data$CBI_total_2,
svm_ndbr_sw_pred_train, type = 2)
svm_ndbr_sw_train_Ubias <- ((svm_ndbr_sw_pred_train_mae) * 68)/((svm_ndbr_sw_pred_train_mae)^2)
svm_ndbr_sw_train_Ubias[1] 29.63026
svm_ndbr_sw_pred_test <- predict(svm_ndbr_sw_linear, data = darkwoods_fire_plots_data)
svm_ndbr_sw_pred_test_rmse <- rmse(svm_ndbr_sw_pred_test, darkwoods_fire_plots_data$CBI_total_2)
svm_ndbr_sw_pred_test_rmse[1] 2.913245
svm_ndbr_sw_pred_test_rmse_rel <- (svm_ndbr_sw_pred_test_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_ndbr_sw_pred_test_rmse_rel[1] 69.15485
svm_ndbr_sw_pred_train_rmse/svm_ndbr_sw_pred_test_rmse[1] 0.9498709
svm_ndbr_sw_pred_test_rmse/svm_ndbr_sw_pred_train_rmse[1] 1.052775
svm_ndbr_sw_linearSupport Vector Machines with Linear Kernel
68 samples
1 predictor
Pre-processing: centered (1), scaled (1)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 61, 62, 61, 61, 61, 62, ...
Resampling results across tuning parameters:
C RMSE Rsquared MAE
0.0000000 NaN NaN NaN
0.1578947 2.718691 0.2040276 2.324704
0.3157895 2.725407 0.2040276 2.331462
0.4736842 2.756288 0.2040276 2.333996
0.6315789 2.756288 0.2040276 2.333996
0.7894737 2.756288 0.2040276 2.334002
0.9473684 2.756245 0.2040276 2.333969
1.1052632 2.756269 0.2040276 2.333993
1.2631579 2.756266 0.2040276 2.333990
1.4210526 2.756229 0.2040276 2.333963
1.5789474 2.756267 0.2040276 2.333989
1.7368421 2.756269 0.2040276 2.333988
1.8947368 2.753512 0.2040276 2.332823
2.0526316 2.749483 0.2040276 2.330864
2.2105263 2.747695 0.2040276 2.329871
2.3684211 2.747683 0.2040276 2.329866
2.5263158 2.747683 0.2040276 2.329866
2.6842105 2.747668 0.2040276 2.329859
2.8421053 2.747742 0.2040276 2.329917
3.0000000 2.747683 0.2040276 2.329871
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was C = 0.1578947.
plot(svm_ndbr_sw_linear)
densityplot(svm_ndbr_sw_linear)
svm_ndbr_sw_linear$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 0.157894736842105
Linear (vanilla) kernel function.
Number of Support Vectors : 66
Objective Function Value : -7.77
Training error : 0.970576
# model 3 - BAI2 results
summary(lm(predict(svm_bai2_linear) ~ train.data$CBI_total_2))Call:
lm(formula = predict(svm_bai2_linear) ~ train.data$CBI_total_2)
Residuals:
Min 1Q Median 3Q Max
-3.7708 -0.2785 0.2322 0.9280 1.9086
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.48741 0.28138 12.394 < 2e-16 ***
train.data$CBI_total_2 0.23558 0.05634 4.181 8.72e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.295 on 66 degrees of freedom
Multiple R-squared: 0.2094, Adjusted R-squared: 0.1975
F-statistic: 17.48 on 1 and 66 DF, p-value: 8.719e-05
svm_bai2_pred_train <- predict(svm_bai2_linear, data = train.data)
svm_bai2_pred_train_mae <- mae(svm_bai2_pred_train, train.data$CBI_total_2)
svm_bai2_pred_train_mae[1] 2.080891
svm_bai2_pred_train_mae_rel <- (svm_bai2_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_bai2_pred_train_mae_rel[1] 50.2179
svm_bai2_pred_train_rmse <- rmse(svm_bai2_pred_train, train.data$CBI_total_2)
svm_bai2_pred_train_rmse[1] 2.504634
svm_bai2_pred_train_rmse_rel <- (svm_bai2_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_bai2_pred_train_rmse_rel[1] 60.44403
svm_bai2_pred_train_R2 <- R2(svm_bai2_pred_train, train.data$CBI_total_2)
svm_bai2_pred_train_R2[1] 0.2094349
TheilU(train.data$CBI_total_2, svm_bai2_pred_train, type = 2)[1] 0.5014887
svm_bai2_train_Ubias <- ((svm_bai2_pred_train_mae) * 68)/((svm_bai2_pred_train_mae)^2)
svm_bai2_train_Ubias[1] 32.67831
svm_bai2_pred_test <- predict(svm_bai2_linear, data = darkwoods_fire_plots_data)
svm_bai2_pred_test_rmse <- rmse(svm_bai2_pred_test, darkwoods_fire_plots_data$CBI_total_2)
svm_bai2_pred_test_rmse[1] 3.261599
svm_bai2_pred_test_rmse_rel <- (svm_bai2_pred_test_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_bai2_pred_test_rmse_rel[1] 77.4241
svm_bai2_pred_train_rmse/svm_bai2_pred_test_rmse[1] 0.7679159
svm_bai2_pred_test_rmse/svm_bai2_pred_train_rmse[1] 1.302226
svm_bai2_linearSupport Vector Machines with Linear Kernel
68 samples
1 predictor
Pre-processing: centered (1), scaled (1)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 62, 63, 62, 60, 60, 62, ...
Resampling results across tuning parameters:
C RMSE Rsquared MAE
0.0000000 NaN NaN NaN
0.1578947 2.497105 0.3535304 2.151404
0.3157895 2.496210 0.3535304 2.147108
0.4736842 2.495418 0.3535304 2.145369
0.6315789 2.496022 0.3535304 2.139129
0.7894737 2.496032 0.3535304 2.139131
0.9473684 2.496022 0.3535304 2.139129
1.1052632 2.496013 0.3535304 2.139081
1.2631579 2.510650 0.3535304 2.156239
1.4210526 2.510635 0.3535304 2.156236
1.5789474 2.510635 0.3535304 2.156236
1.7368421 2.510635 0.3535304 2.156236
1.8947368 2.510680 0.3535304 2.156271
2.0526316 2.510635 0.3535304 2.156236
2.2105263 2.510635 0.3535304 2.156236
2.3684211 2.510810 0.3535304 2.156590
2.5263158 2.511150 0.3535304 2.157354
2.6842105 2.511137 0.3535304 2.157346
2.8421053 2.511137 0.3535304 2.157346
3.0000000 2.511137 0.3535304 2.157346
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was C = 0.4736842.
plot(svm_bai2_linear)
densityplot(svm_bai2_linear)
svm_bai2_linear$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 0.473684210526316
Linear (vanilla) kernel function.
Number of Support Vectors : 66
Objective Function Value : -20.8218
Training error : 0.795124
plot(svm_bai2_linear)
# model 4 - MIRBI results
summary(lm(predict(svm_mirbi_linear) ~ train.data$CBI_total_2))Call:
lm(formula = predict(svm_mirbi_linear) ~ train.data$CBI_total_2)
Residuals:
Min 1Q Median 3Q Max
-4.2389 -0.8579 0.3350 0.9567 2.8901
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.93938 0.30551 6.348 2.3e-08 ***
train.data$CBI_total_2 0.54280 0.06117 8.873 7.3e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.406 on 66 degrees of freedom
Multiple R-squared: 0.544, Adjusted R-squared: 0.5371
F-statistic: 78.74 on 1 and 66 DF, p-value: 7.298e-13
svm_mirbi_pred_train <- predict(svm_mirbi_linear, data = train.data)
svm_mirbi_pred_train_mae <- mae(svm_mirbi_pred_train, train.data$CBI_total_2)
svm_mirbi_pred_train_mae[1] 1.3871
svm_mirbi_pred_train_mae_rel <- (svm_mirbi_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_mirbi_pred_train_mae_rel[1] 33.47472
svm_mirbi_pred_train_rmse <- rmse(svm_mirbi_pred_train, train.data$CBI_total_2)
svm_mirbi_pred_train_rmse[1] 1.883277
svm_mirbi_pred_train_rmse_rel <- (svm_mirbi_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_mirbi_pred_train_rmse_rel[1] 45.4489
svm_mirbi_pred_train_R2 <- R2(svm_mirbi_pred_train, train.data$CBI_total_2)
svm_mirbi_pred_train_R2[1] 0.5440053
TheilU(train.data$CBI_total_2, svm_mirbi_pred_train, type = 2)[1] 0.377078
svm_mirbi_train_Ubias <- ((svm_mirbi_pred_train_mae) * 68)/((svm_mirbi_pred_train_mae)^2)
svm_mirbi_train_Ubias[1] 49.02314
svm_mirbi_pred_test <- predict(svm_mirbi_linear, data = darkwoods_fire_plots_data)
svm_mirbi_pred_test_rmse <- rmse(svm_mirbi_pred_test, darkwoods_fire_plots_data$CBI_total_2)
svm_mirbi_pred_test_rmse[1] 3.421022
svm_mirbi_pred_test_rmse_rel <- (svm_mirbi_pred_test_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_mirbi_pred_test_rmse_rel[1] 81.2085
svm_mirbi_pred_train_rmse/svm_mirbi_pred_test_rmse[1] 0.5505013
svm_mirbi_pred_test_rmse/svm_mirbi_pred_train_rmse[1] 1.816526
svm_mirbi_linearSupport Vector Machines with Linear Kernel
68 samples
1 predictor
Pre-processing: centered (1), scaled (1)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 61, 60, 60, 62, 60, 60, ...
Resampling results across tuning parameters:
C RMSE Rsquared MAE
0.0000000 NaN NaN NaN
0.1578947 1.802346 0.6379662 1.427605
0.3157895 1.803264 0.6379662 1.431911
0.4736842 1.802172 0.6379662 1.430893
0.6315789 1.801566 0.6379662 1.430789
0.7894737 1.801634 0.6379662 1.430857
0.9473684 1.801739 0.6379662 1.430971
1.1052632 1.800109 0.6379662 1.428635
1.2631579 1.800231 0.6379662 1.428716
1.4210526 1.802228 0.6379662 1.430441
1.5789474 1.801768 0.6379662 1.430125
1.7368421 1.804024 0.6379662 1.434333
1.8947368 1.804169 0.6379662 1.434657
2.0526316 1.804120 0.6379662 1.434612
2.2105263 1.804156 0.6379662 1.434646
2.3684211 1.804120 0.6379662 1.434590
2.5263158 1.804213 0.6379662 1.434691
2.6842105 1.804163 0.6379662 1.434650
2.8421053 1.804576 0.6379662 1.434907
3.0000000 1.808693 0.6379662 1.437331
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was C = 1.105263.
plot(svm_mirbi_linear)
densityplot(svm_mirbi_linear)
svm_mirbi_linear$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 1.10526315789474
Linear (vanilla) kernel function.
Number of Support Vectors : 62
Objective Function Value : -30.2531
Training error : 0.449547
plot(svm_mirbi_linear)
# model 5 - MSAV results
summary(lm(predict(svm_msav_linear) ~ train.data$CBI_total_2))Call:
lm(formula = predict(svm_msav_linear) ~ train.data$CBI_total_2)
Residuals:
Min 1Q Median 3Q Max
-1.6722 -0.9243 -0.0853 0.6957 3.3895
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.6308 0.2362 15.370 < 2e-16 ***
train.data$CBI_total_2 0.1739 0.0473 3.676 0.000477 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.087 on 66 degrees of freedom
Multiple R-squared: 0.17, Adjusted R-squared: 0.1574
F-statistic: 13.51 on 1 and 66 DF, p-value: 0.000477
svm_msav_pred_train <- predict(svm_msav_linear, data = train.data)
svm_msav_pred_train_mae <- mae(svm_msav_pred_train, train.data$CBI_total_2)
svm_msav_pred_train_mae[1] 2.24269
svm_msav_pred_train_mae_rel <- (svm_msav_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_msav_pred_train_mae_rel[1] 54.12257
svm_msav_pred_train_rmse <- rmse(svm_msav_pred_train, train.data$CBI_total_2)
svm_msav_pred_train_rmse[1] 2.548744
svm_msav_pred_train_rmse_rel <- (svm_msav_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_msav_pred_train_rmse_rel[1] 61.50855
svm_msav_pred_train_R2 <- R2(svm_msav_pred_train, train.data$CBI_total_2)
svm_msav_pred_train_R2[1] 0.1699657
TheilU(train.data$CBI_total_2, svm_msav_pred_train, type = 2)[1] 0.5103207
svm_msav_train_Ubias <- ((svm_msav_pred_train_mae) * 68)/((svm_msav_pred_train_mae)^2)
svm_msav_train_Ubias[1] 30.32073
svm_msav_pred_test <- predict(svm_msav_linear, data = darkwoods_fire_plots_data)
svm_msav_pred_test_rmse <- rmse(svm_msav_pred_test, darkwoods_fire_plots_data$CBI_total_2)
svm_msav_pred_test_rmse[1] 3.091682
svm_msav_pred_test_rmse_rel <- (svm_msav_pred_test_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_msav_pred_test_rmse_rel[1] 73.3906
svm_msav_pred_train_rmse/svm_msav_pred_test_rmse[1] 0.8243875
svm_msav_pred_test_rmse/svm_msav_pred_train_rmse[1] 1.213022
svm_msav_linearSupport Vector Machines with Linear Kernel
68 samples
1 predictor
Pre-processing: centered (1), scaled (1)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 61, 62, 61, 61, 61, 61, ...
Resampling results across tuning parameters:
C RMSE Rsquared MAE
0.0000000 NaN NaN NaN
0.1578947 2.543568 0.28233 2.295357
0.3157895 2.544848 0.28233 2.303846
0.4736842 2.544848 0.28233 2.303846
0.6315789 2.544934 0.28233 2.302252
0.7894737 2.544934 0.28233 2.302252
0.9473684 2.547667 0.28233 2.303020
1.1052632 2.547667 0.28233 2.303020
1.2631579 2.547667 0.28233 2.303020
1.4210526 2.547667 0.28233 2.303020
1.5789474 2.547667 0.28233 2.303020
1.7368421 2.547667 0.28233 2.303020
1.8947368 2.547667 0.28233 2.303020
2.0526316 2.547667 0.28233 2.303020
2.2105263 2.547667 0.28233 2.303020
2.3684211 2.547667 0.28233 2.303020
2.5263158 2.547667 0.28233 2.303020
2.6842105 2.547667 0.28233 2.303020
2.8421053 2.547667 0.28233 2.303020
3.0000000 2.547667 0.28233 2.303020
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was C = 0.1578947.
plot(svm_msav_linear)
densityplot(svm_msav_linear)
svm_msav_linear$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 0.157894736842105
Linear (vanilla) kernel function.
Number of Support Vectors : 65
Objective Function Value : -7.6244
Training error : 0.823377
plot(svm_msav_linear)
# model 6 - TVI results
summary(lm(predict(svm_tvi_linear) ~ train.data$CBI_total_2))Call:
lm(formula = predict(svm_tvi_linear) ~ train.data$CBI_total_2)
Residuals:
Min 1Q Median 3Q Max
-2.2991 -0.8968 -0.1297 0.7738 4.0474
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.23292 0.28653 7.793 6.22e-11 ***
train.data$CBI_total_2 0.50138 0.05737 8.739 1.26e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.319 on 66 degrees of freedom
Multiple R-squared: 0.5364, Adjusted R-squared: 0.5294
F-statistic: 76.38 on 1 and 66 DF, p-value: 1.264e-12
svm_tvi_pred_train <- predict(svm_tvi_linear, data = train.data)
svm_tvi_pred_train_mae <- mae(svm_tvi_pred_train, train.data$CBI_total_2)
svm_tvi_pred_train_mae[1] 1.64125
svm_tvi_pred_train_mae_rel <- (svm_tvi_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_tvi_pred_train_mae_rel[1] 39.60809
svm_tvi_pred_train_rmse <- rmse(svm_tvi_pred_train, train.data$CBI_total_2)
svm_tvi_pred_train_rmse[1] 1.910272
svm_tvi_pred_train_rmse_rel <- (svm_tvi_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_tvi_pred_train_rmse_rel[1] 46.10036
svm_tvi_pred_train_R2 <- R2(svm_tvi_pred_train, train.data$CBI_total_2)
svm_tvi_pred_train_R2[1] 0.5364397
TheilU(train.data$CBI_total_2, svm_tvi_pred_train, type = 2)[1] 0.3824829
svm_tvi_train_Ubias <- ((svm_tvi_pred_train_mae) * 68)/((svm_tvi_pred_train_mae)^2)
svm_tvi_train_Ubias[1] 41.43184
svm_tvi_pred_test <- predict(svm_tvi_linear, data = darkwoods_fire_plots_data)
svm_tvi_pred_test_rmse <- rmse(svm_tvi_pred_test, darkwoods_fire_plots_data$CBI_total_2)
svm_tvi_pred_test_rmse[1] 3.439511
svm_tvi_pred_test_rmse_rel <- (svm_tvi_pred_test_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_tvi_pred_test_rmse_rel[1] 81.64739
svm_tvi_pred_train_rmse/svm_tvi_pred_test_rmse[1] 0.5553904
svm_tvi_pred_test_rmse/svm_tvi_pred_train_rmse[1] 1.800535
svm_tvi_linearSupport Vector Machines with Linear Kernel
68 samples
1 predictor
Pre-processing: centered (1), scaled (1)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 62, 61, 61, 60, 60, 63, ...
Resampling results across tuning parameters:
C RMSE Rsquared MAE
0.0000000 NaN NaN NaN
0.1578947 1.950356 0.6349996 1.709669
0.3157895 1.960512 0.6349996 1.723443
0.4736842 1.959892 0.6349996 1.721897
0.6315789 1.964540 0.6349996 1.727960
0.7894737 1.967339 0.6349996 1.730148
0.9473684 1.967347 0.6349996 1.730150
1.1052632 1.967348 0.6349996 1.730178
1.2631579 1.968587 0.6349996 1.729028
1.4210526 1.968587 0.6349996 1.729028
1.5789474 1.968421 0.6349996 1.729307
1.7368421 1.968387 0.6349996 1.729135
1.8947368 1.968422 0.6349996 1.729201
2.0526316 1.968389 0.6349996 1.729128
2.2105263 1.968405 0.6349996 1.729136
2.3684211 1.968306 0.6349996 1.729026
2.5263158 1.965546 0.6349996 1.725820
2.6842105 1.965546 0.6349996 1.725820
2.8421053 1.965572 0.6349996 1.725866
3.0000000 1.965551 0.6349996 1.725843
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was C = 0.1578947.
plot(svm_tvi_linear)
densityplot(svm_tvi_linear)
svm_tvi_linear$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 0.157894736842105
Linear (vanilla) kernel function.
Number of Support Vectors : 62
Objective Function Value : -5.4886
Training error : 0.462526
plot(svm_tvi_linear)
# model 7 - TVI-SW results
summary(lm(predict(svm_tvi_sw_linear) ~ train.data$CBI_total_2))Call:
lm(formula = predict(svm_tvi_sw_linear) ~ train.data$CBI_total_2)
Residuals:
Min 1Q Median 3Q Max
-3.8173 -1.0741 0.1161 1.1070 2.3619
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.82547 0.30408 9.292 1.32e-13 ***
train.data$CBI_total_2 0.32438 0.06088 5.328 1.29e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.4 on 66 degrees of freedom
Multiple R-squared: 0.3008, Adjusted R-squared: 0.2902
F-statistic: 28.39 on 1 and 66 DF, p-value: 1.29e-06
svm_tvi_sw_pred_train <- predict(svm_tvi_sw_linear, data = train.data)
svm_tvi_sw_pred_train_mae <- mae(svm_tvi_sw_pred_train, train.data$CBI_total_2)
svm_tvi_sw_pred_train_mae[1] 1.806979
svm_tvi_sw_pred_train_mae_rel <- (svm_tvi_sw_pred_train_mae/mean(train.data$CBI_total_2)) *
100
svm_tvi_sw_pred_train_mae_rel[1] 43.60762
svm_tvi_sw_pred_train_rmse <- rmse(svm_tvi_sw_pred_train, train.data$CBI_total_2)
svm_tvi_sw_pred_train_rmse[1] 2.334681
svm_tvi_sw_pred_train_rmse_rel <- (svm_tvi_sw_pred_train_rmse/mean(train.data$CBI_total_2)) *
100
svm_tvi_sw_pred_train_rmse_rel[1] 56.34259
svm_tvi_sw_pred_train_R2 <- R2(svm_tvi_sw_pred_train, train.data$CBI_total_2)
svm_tvi_sw_pred_train_R2[1] 0.3007533
TheilU(train.data$CBI_total_2, svm_tvi_sw_pred_train, type = 2)[1] 0.4674601
svm_tvi_sw_train_Ubias <- ((svm_tvi_sw_pred_train_mae) * 68)/((svm_tvi_sw_pred_train_mae)^2)
svm_tvi_sw_train_Ubias[1] 37.63186
svm_tvi_sw_pred_test <- predict(svm_tvi_sw_linear, data = darkwoods_fire_plots_data)
svm_tvi_sw_pred_test_rmse <- rmse(svm_tvi_sw_pred_test, darkwoods_fire_plots_data$CBI_total_2)
svm_tvi_sw_pred_test_rmse[1] 3.242471
svm_tvi_sw_pred_test_rmse_rel <- (svm_tvi_sw_pred_test_rmse/mean(darkwoods_fire_plots_data$CBI_total_2)) *
100
svm_tvi_sw_pred_test_rmse_rel[1] 76.97004
svm_tvi_sw_pred_train_rmse/svm_tvi_sw_pred_test_rmse[1] 0.7200314
svm_tvi_sw_pred_test_rmse/svm_tvi_sw_pred_train_rmse[1] 1.388828
svm_tvi_sw_linearSupport Vector Machines with Linear Kernel
68 samples
1 predictor
Pre-processing: centered (1), scaled (1)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 60, 60, 60, 61, 61, 62, ...
Resampling results across tuning parameters:
C RMSE Rsquared MAE
0.0000000 NaN NaN NaN
0.1578947 2.297153 0.396146 1.849692
0.3157895 2.298457 0.396146 1.851282
0.4736842 2.304871 0.396146 1.847169
0.6315789 2.305587 0.396146 1.849281
0.7894737 2.304099 0.396146 1.847315
0.9473684 2.313694 0.396146 1.860001
1.1052632 2.313672 0.396146 1.859977
1.2631579 2.312657 0.396146 1.859622
1.4210526 2.312658 0.396146 1.859631
1.5789474 2.314405 0.396146 1.853914
1.7368421 2.314410 0.396146 1.853921
1.8947368 2.314410 0.396146 1.853921
2.0526316 2.314410 0.396146 1.853921
2.2105263 2.314410 0.396146 1.853921
2.3684211 2.314414 0.396146 1.853927
2.5263158 2.314471 0.396146 1.853917
2.6842105 2.314410 0.396146 1.853921
2.8421053 2.314410 0.396146 1.853921
3.0000000 2.314686 0.396146 1.853845
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was C = 0.1578947.
plot(svm_tvi_sw_linear)
densityplot(svm_tvi_sw_linear)
svm_tvi_sw_linear$finalModelSupport Vector Machine object of class "ksvm"
SV type: eps-svr (regression)
parameter : epsilon = 0.1 cost C = 0.157894736842105
Linear (vanilla) kernel function.
Number of Support Vectors : 62
Objective Function Value : -6.0505
Training error : 0.690878
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