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knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(mlspatial)
library(dplyr)
library(ggplot2)
library(tmap)
library(sf)
library(spdep)
library(randomForest)
library(xgboost)
library(e1071)
library(caret)
library(tidyr)
tm_shape(africa_shp) +
tm_polygons() +
tm_text("NAME", size = 0.5) + # Replace with correct column
tm_title ("Africa Countries")
ggplot(africa_shp) +
geom_sf(fill = "lightgray", color = "black") +
geom_sf_text(aes(label = NAME), size = 2) + # Replace as needed
ggtitle("Africa countries") +
theme_minimal()
# Join data
mapdata <- join_data(africa_shp, panc_incidence, by = "NAME")
## OR Joining/ merging my data and shapefiles
mapdata <- inner_join(africa_shp, panc_incidence, by = "NAME")
## OR mapdata <- left_join(nat, codata, by = "DISTRICT_N")
str(mapdata)
#> Classes 'sf' and 'data.frame': 53 obs. of 26 variables:
#> $ OBJECTID : int 2 3 5 6 7 8 9 10 11 12 ...
#> $ FIPS_CNTRY: chr "UV" "CV" "GA" "GH" ...
#> $ ISO_2DIGIT: chr "BF" "CV" "GM" "GH" ...
#> $ ISO_3DIGIT: chr "BFA" "CPV" "GMB" "GHA" ...
#> $ NAME : chr "Burkina Faso" "Cabo Verde" "Gambia" "Ghana" ...
#> $ COUNTRYAFF: chr "Burkina Faso" "Cabo Verde" "Gambia" "Ghana" ...
#> $ CONTINENT : chr "Africa" "Africa" "Africa" "Africa" ...
#> $ TOTPOP : int 20107509 560899 2051363 27499924 12413867 1792338 4689021 17885245 3758571 33986655 ...
#> $ incidence : num 330.4 53.4 31.4 856.3 163.1 ...
#> $ female : num 1683 362 140 4566 375 ...
#> $ male : num 1869 211 197 4640 1378 ...
#> $ ageb : num 669.7 93.7 68.7 2047 336.7 ...
#> $ agec : num 2878 480 268 7147 1414 ...
#> $ agea : num 4.597 0.265 0.718 11.888 2.13 ...
#> $ fageb : num 250.3 40.2 23.1 782 59.1 ...
#> $ fagec : num 1429 322 116 3775 315 ...
#> $ fagea : num 3.413 0.146 0.548 8.816 1.228 ...
#> $ mageb : num 419.5 53.5 45.6 1265 277.6 ...
#> $ magec : num 1448 158 152 3372 1100 ...
#> $ magea : num 1.184 0.12 0.17 3.073 0.902 ...
#> $ yra : num 182.4 30.2 16.6 524.7 73.1 ...
#> $ yrb : num 187.2 34.1 17.1 552.6 74.9 ...
#> $ yrc : num 193.1 35 18 578.5 76.9 ...
#> $ yrd : num 198.5 35.9 18.3 602.7 78.6 ...
#> $ yre : num 204.3 36.5 18.7 621.5 79.4 ...
#> $ geometry :sfc_MULTIPOLYGON of length 53; first list element: List of 1
#> ..$ :List of 1
#> .. ..$ : num [1:317, 1:2] 102188 90385 80645 74151 70224 ...
#> ..- attr(*, "class")= chr [1:3] "XY" "MULTIPOLYGON" "sfg"
#> - attr(*, "sf_column")= chr "geometry"
#> - attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..: NA NA NA NA NA NA NA NA NA NA ...
#> ..- attr(*, "names")= chr [1:25] "OBJECTID" "FIPS_CNTRY" "ISO_2DIGIT" "ISO_3DIGIT" ...#Visualize Pancreatic cancer Incidence by countries
#Basic map with labels
# quantile map
p1 <- tm_shape(mapdata) +
tm_fill("incidence", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Incidence")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p2 <- tm_shape(mapdata) +
tm_fill("female", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Female")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p3 <- tm_shape(mapdata) +
tm_fill("male", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Male")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p4 <- tm_shape(mapdata) +
tm_fill("ageb", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Age:20-54yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p5 <- tm_shape(mapdata) +
tm_fill("agec", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Age:55+yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p6 <- tm_shape(mapdata) +
tm_fill("agea", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Age:<20yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p7 <- tm_shape(mapdata) +
tm_fill("fageb", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Female:20-54yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p8 <- tm_shape(mapdata) +
tm_fill("fagec", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Female:55+yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p9 <- tm_shape(mapdata) +
tm_fill("fagea", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Female:<20yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p10 <- tm_shape(mapdata) +
tm_fill("mageb", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Male:20-54yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p11 <- tm_shape(mapdata) +
tm_fill("magec", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Male:55+yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
p12 <- tm_shape(mapdata) +
tm_fill("magea", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Male:<20yrs")) + tm_borders(fill_alpha = .3) + tm_compass() +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"), frame = TRUE, component.autoscale = FALSE)
current.mode <- tmap_mode("plot")
tmap_arrange(p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12,
widths = c(.75, .75))
## Machine Learning Model building
# 1. Random Forest Regression
# Train Random Forest
set.seed(123)
rf_model <- randomForest(incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec +
magea + mageb + magec + yrb + yrc + yrd + yre, data = mapdata, ntree = 500,
importance = TRUE)
# View model results
print(rf_model)
#>
#> Call:
#> randomForest(formula = incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec + magea + mageb + magec + yrb + yrc + yrd + yre, data = mapdata, ntree = 500, importance = TRUE)
#> Type of random forest: regression
#> Number of trees: 500
#> No. of variables tried at each split: 5
#>
#> Mean of squared residuals: 76299.33
#> % Var explained: 91.35
varImpPlot(rf_model)
#Plot Variable Importance
library(ggplot2)
importance_df <- data.frame(
Variable = rownames(importance(rf_model)),
Importance = importance(rf_model)[, "IncNodePurity"])
ggplot(importance_df, aes(x = reorder(Variable, Importance), y = Importance)) +
geom_bar(stat = "identity", fill = "steelblue") +
coord_flip() +
labs(title = "Variable Importance (IncNodePurity)", x = "Variable", y = "Importance")
# 2. Gradient Boosting Machine (XGBoost)
# Prepare the data
x_vars <- model.matrix(incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec +
magea + mageb + magec + yrb + yrc + yrd + yre, data = mapdata)[,-1]
y <- mapdata$incidence
# Convert to DMatrix
dtrain <- xgb.DMatrix(data = x_vars, label = y)
# Train model
xgb_model <- xgboost(data = dtrain,
objective = "reg:squarederror",
nrounds = 100,
max_depth = 4,
eta = 0.1,
verbose = 0)
# Feature importance
xgb.importance(model = xgb_model)
#> Feature Gain Cover Frequency
#> <char> <num> <num> <num>
#> 1: female 9.762372e-01 0.41045424 0.471518987
#> 2: ageb 1.425639e-02 0.21332584 0.151898734
#> 3: agec 6.055607e-03 0.13157222 0.145569620
#> 4: male 3.411915e-03 0.12804660 0.136075949
#> 5: mageb 2.492252e-05 0.01400031 0.011075949
#> 6: magea 7.191460e-06 0.01808799 0.012658228
#> 7: fagec 6.206994e-06 0.03454090 0.030063291
#> 8: fageb 2.428280e-07 0.01108783 0.007911392
#> 9: magec 1.919227e-07 0.01829237 0.015822785
#> 10: agea 1.379456e-07 0.02059169 0.017405063
# 3. Support Vector Regression (SVR)
# Train SVR model
svr_model <- svm(incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec +
magea + mageb + magec + yrb + yrc + yrd + yre, data = mapdata,
type = "eps-regression",
kernel = "radial")
# Summary and predictions
summary(svr_model)
#>
#> Call:
#> svm(formula = incidence ~ female + male + agea + ageb + agec + fagea +
#> fageb + fagec + magea + mageb + magec + yrb + yrc + yrd + yre,
#> data = mapdata, type = "eps-regression", kernel = "radial")
#>
#>
#> Parameters:
#> SVM-Type: eps-regression
#> SVM-Kernel: radial
#> cost: 1
#> gamma: 0.06666667
#> epsilon: 0.1
#>
#>
#> Number of Support Vectors: 7
#mapdata$pred_svr <- predict(svr_model)# Model Evaluation (predictions):
# evaluate each model step-by-step:
# 1. Random Forest Evaluation
rf_preds <- predict(rf_model, newdata = mapdata)
rf_metrics <- postResample(pred = rf_preds, obs = mapdata$incidence)
print(rf_metrics)
#> RMSE Rsquared MAE
#> 98.2197100 0.9976235 30.2558297
# 2. XGBoost Evaluation
xgb_preds <- predict(xgb_model, newdata = x_vars)
xgb_metrics <- postResample(pred = xgb_preds, obs = mapdata$incidence)
print(xgb_metrics)
#> RMSE Rsquared MAE
#> 2.2921957 0.9999979 0.8058498
# 3. SVR Evaluation
svr_preds <- predict(svr_model, newdata = mapdata)
svr_metrics <- postResample(pred = svr_preds, obs = mapdata$incidence)
print(svr_metrics)
#> RMSE Rsquared MAE
#> 445.9372342 0.9178101 127.7105534
# Compare All Models
model_eval <- data.frame(
Model = c("Random Forest", "XGBoost", "SVR"),
RMSE = c(rf_metrics["RMSE"], xgb_metrics["RMSE"], svr_metrics["RMSE"]),
MAE = c(rf_metrics["MAE"], xgb_metrics["MAE"], svr_metrics["MAE"]),
Rsquared = c(rf_metrics["Rsquared"], xgb_metrics["Rsquared"], svr_metrics["Rsquared"]))
print(model_eval)
#> Model RMSE MAE Rsquared
#> 1 Random Forest 98.219710 30.2558297 0.9976235
#> 2 XGBoost 2.292196 0.8058498 0.9999979
#> 3 SVR 445.937234 127.7105534 0.9178101
#Choosing the Best Model
#Lowest RMSE and MAE = most accurate predictions
#Highest R² = best variance explanation
#Sort and interpret:
model_eval[order(model_eval$RMSE), ] # Best = Top row
#> Model RMSE MAE Rsquared
#> 2 XGBoost 2.292196 0.8058498 0.9999979
#> 1 Random Forest 98.219710 30.2558297 0.9976235
#> 3 SVR 445.937234 127.7105534 0.9178101#### Models Predicted plots
# Create a data frame from your table
model_preds <- data.frame(rf_preds, xgb_preds, svr_preds)
# Add observation ID
model_preds$ID <- 1:nrow(model_preds)
# Reshape for plotting
model_long <- model_preds %>%
tidyr::pivot_longer(cols = c("rf_preds", "xgb_preds", "svr_preds"), names_to = "Model", values_to = "Predicted")
# Plot
ggplot(model_long, aes(x = ID, y = Predicted, color = Model)) +
geom_line(linewidth = 0.5) +
labs(title = "Model Predictions Over Observations",
x = "Observation", y = "Predicted Incidence") +
theme_minimal()
## plot actual vs predicted
oldpar <- par(mfrow = c(1, 3)) # 3 plots side-by-side
# Random Forest
plot(mapdata$incidence, mapdata$rf_pred,
xlab = "Observed", ylab = "Predicted",
main = "Random Forest", pch = 19, col = "steelblue")
abline(0, 1, col = "red", lwd = 2)
# XGBoost
plot(mapdata$incidence, mapdata$xgb_pred,
xlab = "Observed", ylab = "Predicted",
main = "XGBoost", pch = 19, col = "darkgreen")
abline(0, 1, col = "red", lwd = 2)
# SVR
plot(mapdata$incidence, mapdata$svr_pred,
xlab = "Observed", ylab = "Predicted",
main = "SVR", pch = 19, col = "purple")
abline(0, 1, col = "red", lwd = 2)
par(oldpar)
## Actual vs predicted plot with correlations
library(ggplot2)
library(ggpubr) # For stat_cor
mapdata$rf_pred <- predict(rf_model)
mapdata$xgb_pred <- predict(xgb_model, newdata = x_vars)
mapdata$svr_pred <- predict(svr_model, newdata = mapdata)
# Random Forest Plot
p1 <- ggplot(mapdata, aes(x = incidence, y = rf_pred)) +
geom_point(color = "steelblue", alpha = 0.6) +
geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
stat_cor(method = "pearson", aes(label = paste0("R² = ")), label.x = 0) +
labs(title = "Random Forest", x = "Observed Incidence", y = "Predicted Incidence") +
theme_minimal()
# XGBoost Plot
p2 <- ggplot(mapdata, aes(x = incidence, y = xgb_pred)) +
geom_point(color = "darkgreen", alpha = 0.6) +
geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
stat_cor(method = "pearson", aes(label = paste0("R² = ")), label.x = 0) +
labs(title = "XGBoost", x = "Observed Incidence", y = "Predicted Incidence") +
theme_minimal()
# SVR Plot
p3 <- ggplot(mapdata, aes(x = incidence, y = svr_pred)) +
geom_point(color = "purple", alpha = 0.6) +
geom_abline(slope = 1, intercept = 0, color = "red", linetype = "dashed") +
stat_cor(method = "pearson", aes(label = paste0("R² = ")), label.x = 0) +
labs(title = "SVR", x = "Observed Incidence", y = "Predicted Incidence") +
theme_minimal()
combined_plot <- ggarrange(p1, p2, p3, ncol = 3, nrow = 1, common.legend = FALSE)## CROSS-VALIDATION
#Step 1: Prepare common setup
# Set seed for reproducibility
set.seed(123)
# Define 5-fold cross-validation
cv_control <- trainControl(method = "cv", number = 5)
# 1. Random Forest
library(randomForest)
rf_cv <- train(
incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec +
magea + mageb + magec + yrb + yrc + yrd + yre,
data = mapdata,
method = "rf",
trControl = cv_control,
tuneLength = 3,
importance = TRUE
)
print(rf_cv)
#> Random Forest
#>
#> 53 samples
#> 16 predictors
#>
#> No pre-processing
#> Resampling: Cross-Validated (5 fold)
#> Summary of sample sizes: 41, 45, 42, 42, 42
#> Resampling results across tuning parameters:
#>
#> mtry RMSE Rsquared MAE
#> 2 214.1022 0.9875411 82.55215
#> 8 231.4409 0.9836142 86.88933
#> 15 239.2705 0.9825693 90.05875
#>
#> RMSE was used to select the optimal model using the smallest value.
#> The final value used for the model was mtry = 2.
# 2. XGBoost
library(xgboost)
xgb_cv <- train(
incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec +
magea + mageb + magec + yrb + yrc + yrd + yre,
data = mapdata,
method = "xgbTree",
trControl = cv_control,
tuneLength = 3
)
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#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
#> [09:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
print(xgb_cv)
#> eXtreme Gradient Boosting
#>
#> 53 samples
#> 16 predictors
#>
#> No pre-processing
#> Resampling: Cross-Validated (5 fold)
#> Summary of sample sizes: 43, 43, 42, 43, 41
#> Resampling results across tuning parameters:
#>
#> eta max_depth colsample_bytree subsample nrounds RMSE Rsquared
#> 0.3 1 0.6 0.50 50 77.51211 0.9825285
#> 0.3 1 0.6 0.50 100 74.53665 0.9848370
#> 0.3 1 0.6 0.50 150 74.12358 0.9856897
#> 0.3 1 0.6 0.75 50 87.75916 0.9804207
#> 0.3 1 0.6 0.75 100 85.75756 0.9801767
#> 0.3 1 0.6 0.75 150 85.03767 0.9810229
#> 0.3 1 0.6 1.00 50 108.10833 0.9623482
#> 0.3 1 0.6 1.00 100 110.16070 0.9535319
#> 0.3 1 0.6 1.00 150 111.31761 0.9516319
#> 0.3 1 0.8 0.50 50 72.75480 0.9726405
#> 0.3 1 0.8 0.50 100 66.34459 0.9740674
#> 0.3 1 0.8 0.50 150 65.37974 0.9750195
#> 0.3 1 0.8 0.75 50 103.75480 0.9728968
#> 0.3 1 0.8 0.75 100 104.71482 0.9697262
#> 0.3 1 0.8 0.75 150 106.92944 0.9666806
#> 0.3 1 0.8 1.00 50 85.97447 0.9655598
#> 0.3 1 0.8 1.00 100 86.83885 0.9575015
#> 0.3 1 0.8 1.00 150 86.85652 0.9557451
#> 0.3 2 0.6 0.50 50 94.00716 0.9842634
#> 0.3 2 0.6 0.50 100 92.24585 0.9854197
#> 0.3 2 0.6 0.50 150 92.44745 0.9854256
#> 0.3 2 0.6 0.75 50 68.03277 0.9812312
#> 0.3 2 0.6 0.75 100 67.78304 0.9814041
#> 0.3 2 0.6 0.75 150 67.81383 0.9813999
#> 0.3 2 0.6 1.00 50 99.36000 0.9709040
#> 0.3 2 0.6 1.00 100 98.55775 0.9714097
#> 0.3 2 0.6 1.00 150 98.53653 0.9714456
#> 0.3 2 0.8 0.50 50 87.25126 0.9782998
#> 0.3 2 0.8 0.50 100 85.04951 0.9777886
#> 0.3 2 0.8 0.50 150 84.72495 0.9778720
#> 0.3 2 0.8 0.75 50 79.05042 0.9853749
#> 0.3 2 0.8 0.75 100 78.56149 0.9857103
#> 0.3 2 0.8 0.75 150 78.48532 0.9857411
#> 0.3 2 0.8 1.00 50 103.38290 0.9827400
#> 0.3 2 0.8 1.00 100 102.86457 0.9832881
#> 0.3 2 0.8 1.00 150 102.77863 0.9833378
#> 0.3 3 0.6 0.50 50 79.92382 0.9871462
#> 0.3 3 0.6 0.50 100 70.76064 0.9873868
#> 0.3 3 0.6 0.50 150 70.44796 0.9875159
#> 0.3 3 0.6 0.75 50 77.02424 0.9820164
#> 0.3 3 0.6 0.75 100 76.72561 0.9823722
#> 0.3 3 0.6 0.75 150 76.69185 0.9823914
#> 0.3 3 0.6 1.00 50 116.69622 0.9864377
#> 0.3 3 0.6 1.00 100 116.53618 0.9864894
#> 0.3 3 0.6 1.00 150 116.52377 0.9864951
#> 0.3 3 0.8 0.50 50 61.89082 0.9885897
#> 0.3 3 0.8 0.50 100 58.47174 0.9895862
#> 0.3 3 0.8 0.50 150 58.42756 0.9897027
#> 0.3 3 0.8 0.75 50 58.14062 0.9783710
#> 0.3 3 0.8 0.75 100 57.26210 0.9785542
#> 0.3 3 0.8 0.75 150 57.26729 0.9785667
#> 0.3 3 0.8 1.00 50 89.04480 0.9754549
#> 0.3 3 0.8 1.00 100 88.94853 0.9756043
#> 0.3 3 0.8 1.00 150 88.95190 0.9756110
#> 0.4 1 0.6 0.50 50 140.70223 0.9663413
#> 0.4 1 0.6 0.50 100 133.59046 0.9713471
#> 0.4 1 0.6 0.50 150 132.51984 0.9706645
#> 0.4 1 0.6 0.75 50 121.39408 0.9703187
#> 0.4 1 0.6 0.75 100 120.30878 0.9691842
#> 0.4 1 0.6 0.75 150 120.08749 0.9683910
#> 0.4 1 0.6 1.00 50 118.90278 0.9496329
#> 0.4 1 0.6 1.00 100 113.22443 0.9513211
#> 0.4 1 0.6 1.00 150 113.67348 0.9494586
#> 0.4 1 0.8 0.50 50 105.04239 0.9694201
#> 0.4 1 0.8 0.50 100 107.82358 0.9698624
#> 0.4 1 0.8 0.50 150 108.38966 0.9703541
#> 0.4 1 0.8 0.75 50 153.50867 0.9427469
#> 0.4 1 0.8 0.75 100 148.30620 0.9487484
#> 0.4 1 0.8 0.75 150 149.49092 0.9492826
#> 0.4 1 0.8 1.00 50 97.42608 0.9576658
#> 0.4 1 0.8 1.00 100 91.74249 0.9596515
#> 0.4 1 0.8 1.00 150 90.99246 0.9592085
#> 0.4 2 0.6 0.50 50 93.35311 0.9708654
#> 0.4 2 0.6 0.50 100 95.07506 0.9707180
#> 0.4 2 0.6 0.50 150 94.89844 0.9707940
#> 0.4 2 0.6 0.75 50 71.25586 0.9781923
#> 0.4 2 0.6 0.75 100 71.37091 0.9784772
#> 0.4 2 0.6 0.75 150 71.30138 0.9784914
#> 0.4 2 0.6 1.00 50 106.94425 0.9783419
#> 0.4 2 0.6 1.00 100 106.57502 0.9786253
#> 0.4 2 0.6 1.00 150 106.53421 0.9786394
#> 0.4 2 0.8 0.50 50 69.66801 0.9876778
#> 0.4 2 0.8 0.50 100 68.00072 0.9880788
#> 0.4 2 0.8 0.50 150 68.19230 0.9879329
#> 0.4 2 0.8 0.75 50 70.73793 0.9700478
#> 0.4 2 0.8 0.75 100 70.12544 0.9706356
#> 0.4 2 0.8 0.75 150 70.11536 0.9706220
#> 0.4 2 0.8 1.00 50 79.88233 0.9844111
#> 0.4 2 0.8 1.00 100 79.76636 0.9844580
#> 0.4 2 0.8 1.00 150 79.72954 0.9844831
#> 0.4 3 0.6 0.50 50 59.00555 0.9937262
#> 0.4 3 0.6 0.50 100 59.19193 0.9938993
#> 0.4 3 0.6 0.50 150 59.22514 0.9938975
#> 0.4 3 0.6 0.75 50 100.17948 0.9764393
#> 0.4 3 0.6 0.75 100 100.03388 0.9766898
#> 0.4 3 0.6 0.75 150 100.02630 0.9766957
#> 0.4 3 0.6 1.00 50 106.97402 0.9792226
#> 0.4 3 0.6 1.00 100 106.88879 0.9792971
#> 0.4 3 0.6 1.00 150 106.88569 0.9792982
#> 0.4 3 0.8 0.50 50 120.04486 0.9765378
#> 0.4 3 0.8 0.50 100 120.12232 0.9765760
#> 0.4 3 0.8 0.50 150 120.10263 0.9765777
#> 0.4 3 0.8 0.75 50 86.76026 0.9681896
#> 0.4 3 0.8 0.75 100 86.62827 0.9687068
#> 0.4 3 0.8 0.75 150 86.62227 0.9687191
#> 0.4 3 0.8 1.00 50 70.25068 0.9843500
#> 0.4 3 0.8 1.00 100 70.28841 0.9843700
#> 0.4 3 0.8 1.00 150 70.28776 0.9843709
#> MAE
#> 54.65428
#> 52.06881
#> 50.60871
#> 60.06351
#> 56.05069
#> 54.11307
#> 65.59206
#> 64.50375
#> 64.40123
#> 46.90761
#> 41.90154
#> 41.52556
#> 62.63757
#> 61.17063
#> 61.29549
#> 53.13176
#> 51.18509
#> 50.40242
#> 49.96162
#> 48.67661
#> 48.47087
#> 41.44950
#> 41.17389
#> 41.23609
#> 55.43944
#> 54.77878
#> 54.79039
#> 47.32302
#> 45.59611
#> 45.62411
#> 44.50286
#> 44.19403
#> 44.08855
#> 54.21665
#> 53.49812
#> 53.40870
#> 43.92885
#> 40.14532
#> 40.07339
#> 42.48043
#> 42.33643
#> 42.31961
#> 54.61403
#> 54.60299
#> 54.59477
#> 37.92887
#> 36.13997
#> 36.09046
#> 34.22140
#> 33.83544
#> 33.82400
#> 49.67038
#> 49.60288
#> 49.60279
#> 83.12435
#> 77.55708
#> 76.74397
#> 67.75398
#> 65.06029
#> 64.83385
#> 72.54725
#> 67.23458
#> 67.18036
#> 67.66800
#> 65.94107
#> 65.24107
#> 91.32890
#> 83.03416
#> 82.64282
#> 61.12489
#> 56.48147
#> 55.81566
#> 59.70785
#> 61.30165
#> 61.03857
#> 45.36963
#> 45.13388
#> 45.10589
#> 58.85405
#> 58.47487
#> 58.46973
#> 43.66037
#> 42.89484
#> 43.34947
#> 42.51137
#> 42.45496
#> 42.47265
#> 45.44857
#> 45.41403
#> 45.43604
#> 36.85656
#> 36.79573
#> 36.83167
#> 56.73538
#> 56.51237
#> 56.50071
#> 53.35098
#> 53.32043
#> 53.31983
#> 61.47282
#> 61.62869
#> 61.62023
#> 54.06670
#> 53.93185
#> 53.91606
#> 43.49995
#> 43.58945
#> 43.58928
#>
#> Tuning parameter 'gamma' was held constant at a value of 0
#> Tuning
#> parameter 'min_child_weight' was held constant at a value of 1
#> RMSE was used to select the optimal model using the smallest value.
#> The final values used for the model were nrounds = 100, max_depth = 3, eta
#> = 0.3, gamma = 0, colsample_bytree = 0.8, min_child_weight = 1 and subsample
#> = 0.75.
# 3. Support Vector Regression (SVR)
library(e1071)
library(kernlab)
svr_cv <- train(
incidence ~ female + male + agea + ageb + agec + fagea + fageb + fagec +
magea + mageb + magec + yrb + yrc + yrd + yre,
data = mapdata,
method = "svmRadial",
trControl = cv_control,
preProcess = c("center", "scale"), # SVR often benefits from scaling
tuneLength = 3
)
print(svr_cv)
#> Support Vector Machines with Radial Basis Function Kernel
#>
#> 53 samples
#> 16 predictors
#>
#> Pre-processing: centered (15), scaled (15)
#> Resampling: Cross-Validated (5 fold)
#> Summary of sample sizes: 42, 42, 44, 42, 42
#> Resampling results across tuning parameters:
#>
#> C RMSE Rsquared MAE
#> 0.25 650.5027 0.6279956 301.1569
#> 0.50 631.0990 0.6401412 288.2435
#> 1.00 616.1446 0.6475419 276.9980
#>
#> Tuning parameter 'sigma' was held constant at a value of 5.615089
#> RMSE was used to select the optimal model using the smallest value.
#> The final values used for the model were sigma = 5.615089 and C = 1.
# Compare All Models (from CV)
results <- resamples(list(
RF = rf_cv,
XGB = xgb_cv,
SVR = svr_cv
))
# Summary of RMSE, MAE, Rsquared
summary(results)
#>
#> Call:
#> summary.resamples(object = results)
#>
#> Models: RF, XGB, SVR
#> Number of resamples: 5
#>
#> MAE
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> RF 20.31325 21.17305 41.25341 82.55215 147.75263 182.26841 0
#> XGB 14.50613 19.26326 26.05017 33.83544 53.93394 55.42368 0
#> SVR 78.46538 133.65823 165.17365 276.99798 478.34369 529.34896 0
#>
#> RMSE
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> RF 31.72226 36.05807 91.66574 214.1022 396.83212 514.2326 0
#> XGB 18.12370 29.80374 36.72109 57.2621 96.40236 105.2596 0
#> SVR 93.38999 187.69338 239.85619 616.1446 1264.83400 1294.9496 0
#>
#> Rsquared
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> RF 0.9632935 0.9818386 0.9957268 0.9875411 0.9976922 0.9991540 0
#> XGB 0.9414156 0.9547185 0.9972071 0.9785542 0.9995794 0.9998504 0
#> SVR 0.2589199 0.3684605 0.7853384 0.6475419 0.8635981 0.9613925 0
# Boxplot of performance
bwplot(results)
## Spatial maps of predicted values of each model
# 1. Random Forest Spatial Map
mapdata$pred_rf <- predict(rf_model, newdata = mapdata)
tm_shape(mapdata) +
tm_fill("pred_rf", fill.scale =tm_scale_intervals(values = "brewer.greens", style = "quantile"),
fill.legend = tm_legend(title = "Inci_pred_rf")) + tm_borders(fill_alpha = .2) +
tm_compass() + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE)
# 2. XGBoost Spatial Map
# Ensure matrix used in training
mapdata$pred_xgb <- predict(xgb_model, newdata = x_vars)
tm_shape(mapdata) +
tm_fill("pred_xgb", fill.scale =tm_scale_intervals(values = "brewer.purples", style = "quantile"),
fill.legend = tm_legend(title = "Inci_pred_xgb")) + tm_borders(fill_alpha = .2) +
tm_compass() + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE)
# 3. Support Vector Regression (SVR) Spatial Map
mapdata$pred_svr <- predict(svr_model, newdata = mapdata)
tm_shape(mapdata) +
tm_fill("pred_svr", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Inci_pred_svr")) + tm_borders(fill_alpha = .2) +
tm_compass() + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE)
# Compare Side by Side
tmap_arrange(
tm_shape(mapdata) +
tm_fill("pred_rf", fill.scale =tm_scale_intervals(values = "brewer.greens", style = "quantile"),
fill.legend = tm_legend(title = "Inci_pred_rf")) + tm_borders(fill_alpha = .2) +
tm_compass() + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE),
tm_shape(mapdata) +
tm_fill("pred_xgb", fill.scale =tm_scale_intervals(values = "brewer.purples", style = "quantile"),
fill.legend = tm_legend(title = "Inci_pred_xgb")) + tm_borders(fill_alpha = .2) +
tm_compass() + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE),
tm_shape(mapdata) +
tm_fill("pred_svr", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Inci_pred_svr")) + tm_borders(fill_alpha = .2) +
tm_compass() + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE),
nrow = 1
)
# Predicted Residuals
# we've already trained all 3 models and have `mapdata$incidence` as your actual values.
### Step 1: Generate predictions and residuals for each model
# Random Forest
rf_preds <- predict(rf_model, newdata = mapdata)
rf_resid <- mapdata$incidence - rf_preds
# XGBoost
xgb_preds <- predict(xgb_model, newdata = x_vars) # x_vars = model.matrix(...)
xgb_resid <- mapdata$incidence - xgb_preds
# SVR
svr_preds <- predict(svr_model, newdata = mapdata)
svr_resid <- mapdata$incidence - svr_preds
### Step 2: Combine into a single data frame
residuals_df <- data.frame(
actual = mapdata$incidence,
rf_pred = rf_preds,
rf_resid = rf_resid,
xgb_pred = xgb_preds,
xgb_resid = xgb_resid,
svr_pred = svr_preds,
svr_resid = svr_resid
)
# export
library(writexl)
### Compare residual distributions
boxplot(residuals_df$rf_resid, residuals_df$xgb_resid, residuals_df$svr_resid,
names = c("RF", "XGB", "SVR"),
main = "Model Residuals",
ylab = "Prediction Error (Residual)")
## Spatial maps of residual values from each model
#Add residuals to mapdata
#You should already have these from the previous steps:
mapdata$rf_resid <- residuals_df$rf_resid
mapdata$xgb_resid <- residuals_df$xgb_resid
mapdata$svr_resid <- residuals_df$svr_resid
# Set tmap mode to plot (static map)
tmap_mode("plot")
# Create individual residual maps
map_rf <- tm_shape(mapdata) +
tm_fill("rf_resid", fill.scale =tm_scale_intervals(values = "brewer.greens", style = "quantile",
midpoint = 0), fill.legend = tm_legend(title = "Inci_rf_resid")) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE)
map_xgb <- tm_shape(mapdata) +
tm_fill("xgb_resid", fill.scale =tm_scale_intervals(values = "brewer.purples", style = "quantile",
midpoint = 0), fill.legend = tm_legend(title = "Inci_xgb_resid")) + tm_borders(fill_alpha = .2) +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE)
map_svr <- tm_shape(mapdata) +
tm_fill("svr_resid", fill.scale =tm_scale_intervals(values = "brewer.reds", style = "quantile"),
fill.legend = tm_legend(title = "Inci_svr_resid")) + tm_borders(fill_alpha = .2) +
tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"),
frame = TRUE, component.autoscale = FALSE)
#Step 3: Combine maps in a grid
# Combine maps in a grid layout
tmap_arrange(map_rf, map_xgb, map_svr, nrow = 1)
##Barplot and Spatial maps for RMSE and MAE
#Step 1: Calculate RMSE and MAE for each model
# Random Forest
rf_metrics <- postResample(pred = rf_preds, obs = mapdata$incidence)
# XGBoost
xgb_metrics <- postResample(pred = xgb_preds, obs = mapdata$incidence)
# SVR
svr_metrics <- postResample(pred = svr_preds, obs = mapdata$incidence)
#Step 2: Combine into a summary data frame
model_eval <- data.frame(
Model = c("Random Forest", "XGBoost", "SVR"),
RMSE = c(rf_metrics["RMSE"], xgb_metrics["RMSE"], svr_metrics["RMSE"]),
MAE = c(rf_metrics["MAE"], xgb_metrics["MAE"], svr_metrics["MAE"]),
Rsquared = c(rf_metrics["Rsquared"], xgb_metrics["Rsquared"], svr_metrics["Rsquared"])
)
print(model_eval)
#> Model RMSE MAE Rsquared
#> 1 Random Forest 98.219710 30.2558297 0.9976235
#> 2 XGBoost 2.292196 0.8058498 0.9999979
#> 3 SVR 445.937234 127.7105534 0.9178101
#Visualize MAE and RMSE
oldpar <- par(mfrow = c(1, 3))
#Barplot of RMSE
barplot(model_eval$RMSE, names.arg = model_eval$Model,
col = "skyblue", las = 1, main = "Model RMSE", ylab = "RMSE")
#Barplot of MAE
barplot(model_eval$MAE, names.arg = model_eval$Model,
col = "lightgreen", las = 1, main = "Model MAE", ylab = "MAE")
#Barplot of MAE
barplot(model_eval$Rsquared, names.arg = model_eval$Model,
col = "grey", las = 1, main = "Model Rsquared", ylab = "MAE")
par(oldpar)
#Add metrics to residual maps as captions
map_rf <- tm_shape(mapdata) +
tm_fill("rf_resid", fill.scale =tm_scale_intervals(values = "brewer.greens", midpoint = 0),
title = paste0("rf_resid\nRMSE: ", round(rf_metrics["RMSE"], 2),
"\nMAE: ", round(rf_metrics["MAE"], 2))) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"))
map_xgb <- tm_shape(mapdata) +
tm_fill("xgb_resid", fill.scale =tm_scale_intervals(values = "-RdBu", midpoint = 0),
title = paste0("xgb_resid\nRMSE: ", round(xgb_metrics["RMSE"], 2),
"\nMAE: ", round(xgb_metrics["MAE"], 2))) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"))
map_svr <- tm_shape(mapdata) +
tm_fill("svr_resid", fill.scale =tm_scale_intervals(values = "-RdBu", midpoint = 0),
title = paste0("svr_resid\nRMSE: ", round(svr_metrics["RMSE"], 2),
"\nMAE: ", round(svr_metrics["MAE"], 2))) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"))
tmap_arrange(map_rf, map_xgb, map_svr, nrow = 1)
#Global Moran’s I, Local Moran’s I (LISA), Cluster categories (e.g., High-High, Low-Low), Maps: Moran’s I map,
#LISA clusters, High-High clusters using the predicted values from the four machine learning models
#Assumptions: Your spatial data is in mapdata (an sf object).
#Predicted values for each model are already stored in: rf_preds, xgb_preds, svr_preds, mlp_preds
#STEP 1: Create Spatial Weights (if not done yet)
neighbors <- poly2nb(mapdata) #if this gives warning, use the below codes
mapdata <- st_as_sf(mapdata) # If it's not already sf
mapdata <- st_make_valid(mapdata) # Fix any invalid geometries
neighbors <- poly2nb(mapdata, snap = 1e-15) ## Try 1e-6, 1e-5, or higher if needed. You can adjust snap upward incrementally until the warnings disappear or are reduced
listw <- nb2listw(neighbors, style = "W", zero.policy = TRUE)
#STEP 2: Define a function to compute Moran’s I and cluster categories
analyze_spatial_autocorrelation <- function(mapdata, values, listw, model_name, signif_level = 0.05) {
# Standardize predicted values
mapdata$val_st <- scale(values)[, 1]
# Compute lag
mapdata$lag_val <- lag.listw(listw, mapdata$val_st, zero.policy = TRUE)
# Global Moran's I
global_moran <- moran.test(values, listw, zero.policy = TRUE)
# Local Moran's I (LISA)
lisa <- localmoran(values, listw, zero.policy = TRUE)
lisa_df <- as.data.frame(lisa)
#rename p-value column
colnames(lisa_df)[5] <- "Pr_z"
# Add to mapdata
mapdata$Ii <- lisa_df$Ii
mapdata$Z_Ii <- lisa_df$Z.I
mapdata$Pr_z <- lisa_df$Pr_z
#mapdata$Pr_z <- lisa_df[, "Pr(z > 0)"]
# Classify clusters
mapdata <- mapdata %>%
mutate(
cluster = case_when(
val_st > 0 & lag_val > 0 & Pr_z <= signif_level ~ "High-High",
val_st < 0 & lag_val < 0 & Pr_z <= signif_level ~ "Low-Low",
val_st < 0 & lag_val > 0 & Pr_z <= signif_level ~ "Low-High",
val_st > 0 & lag_val < 0 & Pr_z <= signif_level ~ "High-Low",
TRUE ~ "Not Significant"
)
)
return(list(
map = mapdata,
global_moran = global_moran
))
}
#STEP 3: Run the function for each model
rf_result <- analyze_spatial_autocorrelation(mapdata, rf_preds, listw, "Random Forest")
xgb_result <- analyze_spatial_autocorrelation(mapdata, xgb_preds, listw, "XGBoost")
svr_result <- analyze_spatial_autocorrelation(mapdata, svr_preds, listw, "SVR")
#STEP 4: Mapping LISA Clusters and High-High Areas for Random Forest
tmap_mode("plot")
# LISA Cluster Map. fill.scale =tm_scale_intervals(values = "-RdBu")
tm_rf <- tm_shape(rf_result$map) +
tm_fill(
"cluster",
fill.scale = tm_scale(values = c(
"High-High" = "red",
"Low-Low" = "blue",
"Low-High" = "lightblue",
"High-Low" = "pink",
"Not Significant" = "gray90")),
fill.legend = tm_legend(title = "LISA Clusters - RF")) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"))
# Mapping LISA Clusters and High-High Areas for XGBoost
tmap_mode("plot")
# LISA Cluster Map
tm_xgb <- tm_shape(xgb_result$map) +
tm_fill("cluster",
fill.scale = tm_scale(values = c(
"High-High" = "red",
"Low-Low" = "blue",
"Low-High" = "lightblue",
"High-Low" = "pink",
"Not Significant" = "gray90")),
fill.legend = tm_legend(title = "LISA Clusters - XGBoost")) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"))
#Mapping LISA Clusters and High-High Areas for SVR
tmap_mode("plot")
# LISA Cluster Map
tm_svr <- tm_shape(svr_result$map) +
tm_fill("cluster",
fill.scale = tm_scale(values = c(
"High-High" = "red",
"Low-Low" = "blue",
"Low-High" = "lightblue",
"High-Low" = "pink",
"Not Significant" = "gray90")),
fill.legend = tm_legend(title = "LISA Clusters - SVR")) +
tm_borders(fill_alpha = .2) + tm_layout(legend.text.size = 0.5, legend.position = c("left", "bottom"))
tmap_arrange(tm_rf, tm_xgb, tm_svr, nrow = 1)
#You can also arrange maps side-by-side using tmap_arrange().
#View Global Moran’s I Results
#These print the test statistic and p-values for global spatial autocorrelation of predictions.
rf_result$global_moran
#>
#> Moran I test under randomisation
#>
#> data: values
#> weights: listw
#> n reduced by no-neighbour observations
#>
#> Moran I statistic standard deviate = -0.24595, p-value = 0.5971
#> alternative hypothesis: greater
#> sample estimates:
#> Moran I statistic Expectation Variance
#> -0.044681255 -0.022727273 0.007967958
xgb_result$global_moran
#>
#> Moran I test under randomisation
#>
#> data: values
#> weights: listw
#> n reduced by no-neighbour observations
#>
#> Moran I statistic standard deviate = -0.32541, p-value = 0.6276
#> alternative hypothesis: greater
#> sample estimates:
#> Moran I statistic Expectation Variance
#> -0.051276885 -0.022727273 0.007697266
svr_result$global_moran
#>
#> Moran I test under randomisation
#>
#> data: values
#> weights: listw
#> n reduced by no-neighbour observations
#>
#> Moran I statistic standard deviate = -0.28034, p-value = 0.6104
#> alternative hypothesis: greater
#> sample estimates:
#> Moran I statistic Expectation Variance
#> -0.05111299 -0.02272727 0.01025262These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.