# Dissever Tutorial In dissever: Spatial Downscaling using the Dissever Algorithm

```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))
```

## Example

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
)
```

# Analysing the results

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.

## Maps

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")
```

## Convergence

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")
```

## Performance of the regression

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
```

# Ensemble approach

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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dissever documentation built on May 1, 2019, 8:42 p.m.