```
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
```

```
## # A tibble: 4 x 4
## # Groups: model [?]
## model dataType rsq rmse
## <fctr> <fctr> <dbl> <dbl>
## 1 cubist Training 0.259 5.44
## 2 gamSpline Training 0.398 4.33
## 3 lm Training 0.398 4.36
## 4 rf Training 0.939 1.58
```

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
```

```
## Cubist GAM Linear.Model Random.Forest
## Cubist 1.0000000 0.6854560 0.6435265 0.6997470
## GAM 0.6854560 1.0000000 0.9392300 0.8466576
## Linear.Model 0.6435265 0.9392300 1.0000000 0.8228443
## Random.Forest 0.6997470 0.8466576 0.8228443 1.0000000
```

Here is the resulting map:

```
# Plot result
plot(ens, col = viridis(100), main = "CCC Weighted Average")
```