library(dissever) library(raster) library(viridis) library(dplyr) library(magrittr)
Here is the coarse model to dissever:
plot(edgeroi$carbon, col = viridis(100))
and here are the covariates that will be used for the disseveration:
plot(edgeroi$predictors, col = viridis(100))
In this section, we will dissever the sample dataset with the available environmental covariates, using 4 different regression methods:
"rf"
)"cubist"
)"earth"
)"lm"
)It is simple to switch between regression methods using the method
option of dissever
.
But first let's setup some parameters:
min_iter <- 5 # Minimum number of iterations max_iter <- 10 # Maximum number of iterations p_train <- 0.025 # Subsampling of the initial data
We can then launch the 4 different disseveration procedures:
# Random Forest res_rf <- dissever( coarse = edgeroi$carbon, # stack of fine resolution covariates fine = edgeroi$predictors, # coarse resolution raster method = "rf", # regression method used for disseveration p = p_train, # proportion of pixels sampled for training regression model min_iter = min_iter, # minimum iterations max_iter = max_iter # maximum iterations ) # Cubist res_cubist <- dissever( coarse = edgeroi$carbon, fine = edgeroi$predictors, method = "cubist", p = p_train, min_iter = min_iter, max_iter = max_iter ) # GAM res_gam <- dissever( coarse = edgeroi$carbon, fine = edgeroi$predictors, method = "gamSpline", p = p_train, min_iter = min_iter, max_iter = max_iter ) # Linear model res_lm <- dissever( coarse = edgeroi$carbon, fine = edgeroi$predictors, method = "lm", p = p_train, min_iter = min_iter, max_iter = max_iter )
The object returned by dissever
is an object of class dissever
. It's basically a list
with 3 elements:
fit
: a train
object storing the regression model used in the final disseveration
map
: a RasterLayer
object storing the dissevered map
* perf
: a data.frame
object storing the evolution of the RMSE (and confidence intervals) with the disseveration iterations.
The dissever
result has a plot
function that can plot either the map or the performance results, depending on the type
option.
Below are the dissevered maps for all 4 regression methods:
# Plotting maps par(mfrow = c(2, 2)) plot(res_rf, type = 'map', main = "Random Forest") plot(res_cubist, type = 'map', main = "Cubist") plot(res_gam, type = 'map', main = "GAM") plot(res_lm, type = 'map', main = "Linear Model")
We can also analyse and plot the optimisation of the dissevering model:
# Plot performance par(mfrow = c(2, 2)) plot(res_rf, type = 'perf', main = "Random Forest") plot(res_cubist, type = 'perf', main = "Cubist") plot(res_gam, type = 'perf', main = "GAM") plot(res_lm, type = 'perf', main = "Linear Model")
The tools provided by the caret
package can also be leveraged, e.g. to plot the observed vs. predicted values:
# Plot preds vs obs preds <- extractPrediction(list(res_rf$fit, res_cubist$fit, res_gam$fit, res_lm$fit)) plotObsVsPred(preds)
The models can be compared using the preds
object that we just derived using the extractPrediction
function. In this case I'm computing the R^2^, the RMSE and the CCC for each model:
# Compare models perf <- preds %>% group_by(model, dataType) %>% summarise( rsq = cor(obs, pred)^2, rmse = sqrt(mean((pred - obs)^2)) ) perf
We can either take the best option (in this case Random Forest -- but the results probably show that we should add some kind of validation process), or use a simple ensemble-type approach. For the latter, I am computing weights for each of the maps based on the CCC of the 4 different regression models:
# We can weight results with Rsquared w <- perf$rsq / sum(perf$rsq) # Make stack of weighted predictions and compute sum l_maps <- list(res_cubist$map, res_gam$map, res_lm$map, res_rf$map) ens <- lapply(1:4, function(x) l_maps[[x]] * w[x]) %>% stack %>% sum
Ensemble modelling seem to work better when the models are not too correlated -- i.e. when they capture different facets of the data:
s_res <- stack(l_maps) names(s_res) <- c('Cubist', 'GAM', 'Linear Model', 'Random Forest') s_res %>% as.data.frame %>% na.exclude %>% cor
Here is the resulting map:
# Plot result plot(ens, col = viridis(100), main = "CCC Weighted Average")
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