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:

- Random Forest (
`"rf"`

) - Cubist (
`"cubist"`

) - MARS (
`"earth"`

) - Linear Model (
`"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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