## Intro

In the previous articles you have learned the core functions of SDMtune for training, evaluating and display the output of a model. In this article you will learn how to perform data-driven variable selection.

## Explore variable correlation

We extract 10000 background locations using the function randomPoints included in the dismo package (we set the seed to have reproducible results). After we create an SWD() object using the prepareSWD() function:

set.seed(25)
bg <- dismo::randomPoints(predictors, 10000)
#> Warning in dismo::randomPoints(predictors, 10000): generated random points =
#> 0.9775 times requested number
bg <- prepareSWD(species = "Bgs", a = bg, env = predictors, categorical = "biome")
#> Extracting predictor information for absence/background locations...
#> Info: 9 absence/background locations are NA for some environmental variables, they are discarded!

The environmental variables we downloaded have a coarse resolution and the function can extract a bit less than 10000 random locations (see the warning message).

With the function plotCor() you can create an heat map showing the degree of autocorrelation:

plotCor(bg, method = "spearman", cor_th = 0.7)

You can select a different correlation method or set a different correlation threshold. Another useful function is corVar() that instead of creating a heat map prints the pairs of correlated variables according to the given method and correlation threshold:

corVar(bg, method = "spearman", cor_th = 0.7)
#>    Var1  Var2      value
#> 1  bio1  bio6  0.9513541
#> 2 bio12 bio16  0.9447559
#> 3  bio6  bio7 -0.8734498
#> 4  bio1  bio8  0.8459649
#> 5 bio16  bio6  0.7471269
#> 6  bio6  bio8  0.7286723
#> 7  bio1  bio7 -0.7119135
#> 8 bio16  bio7 -0.7027568
#> 9  bio1 bio16  0.7023585

As you can see there are few variables that have a correlation coefficient greater than 0.7 in absolute value.

## Remove highly correlated variables

SDMtune implements an algorithm that removes highly correlated variables repeating the following steps:

1. ranks the variables according to the permutation importance or the percent contribution (the second method is available only for Maxent models).
2. checks if the variable ranked as most important is highly correlated with other variables, according to the given method and correlation threshold. If the algorithm finds correlated variables it moves to the next step, otherwise checks the other variables in the rank;
3. performs a leave one out Jackknife test among the correlated variables;
4. remove the variable that decreases the less the model performance when removed, according to the given metric on the training dataset.

The process is repeated until the remaining variables have a correlation coefficient lower than the provided correlation threshold. In the next example we remove the variables that have a Spearman correlation coefficient $$|r_s|\leq0.7$$ and checking the AUC on the training dataset (we use only one permutation to save time but you are free to increase this value). If you use RStudio, the function creates an interactive real-time chart in the viewer pane. Run the following code and hover over the chart during the execution of the function to get extra information:

selected_variables_model <- varSel(maxnet_model, metric = "auc", test = test, bg4cor = bg, method = "spearman", cor_th = 0.7, permut = 1)
#> Removed variables: bio16, bio6, bio7, bio8

As you can see some variables have been removed. The output of the function is the model trained with the selected variables:

selected_variables_model
#> Object of class SDMmodel
#> Method: Maxnet
#>
#> Species: Virtual species
#> Presence locations: 320
#> Absence locations: 5000
#>
#> Model configurations:
#> --------------------
#> fc: lqph
#> reg: 1
#>
#> Variables:
#> ---------
#> Continuous: bio1 bio12 bio17 bio5
#> Categorical: biome

### Try yourself

Remove highly correlated variables using the default_model, ranking the variables with the percent contribution and using the AICc as evaluation metric. Check the help of the function varSel() and highlight the next cell to see the solution:

# You need to pass the env argument for the AICc and the use_pc argument to use the percent contribution
selected_variables_model <- varSel(default_model, metric = "aicc", bg4cor = bg, method = "spearman", cor_th = 0.7, env = predictors, use_pc = TRUE)

## Remove variables with low importance

There are cases in which a model has some environmental variables ranked with very low contribution and you may want to remove some of them to reduce the model complexity. SDMtune offers two different strategies implemented in the function reduceVar(). We will use the maxnet_model trained with all the variables. Let’s first check the permutation importance (we use only one permutation to save time):

varImp(maxnet_model, permut = 1)
#>   Variable Permutation_importance
#> 1     bio1                   56.1
#> 2     bio8                   19.5
#> 3    bio17                    6.3
#> 4    biome                    4.7
#> 5    bio12                    3.5
#> 6     bio5                    3.5
#> 7     bio7                    3.2
#> 8     bio6                    1.6
#> 9    bio16                    1.5

We will use the function reduceVar() only for demonstration purpose. In the first example we want to remove all the environmental variables that have a permutation importance lower than 6%, no matter if the model performance decreases. The function removes the last ranked environmental variable, trains a new model and computes a new rank. The process is repeated until all the remaining environmental variables have an importance greater than 6%:

cat("Testing AUC before: ", auc(maxnet_model, test = test))
#> Testing AUC before:  0.8505888
reduced_variables_model <- reduceVar(maxnet_model, th = 6, metric = "auc", test = test, permut = 1)
#> Removed variables: bio16, bio6, bio7, bio5, bio17, biome
cat("Testing AUC after: ", auc(reduced_variables_model, test = test))
#> Testing AUC after:  0.8520787

In the second example we want to remove the environmental variables that have a permutation importance lower than 15% only if removing the variables the model performance does not decrease, according to the given metric. In this case the function performs a leave one out Jackknife test and remove the environmental variables in a step-wise fashion as described in the previous example, but only if the model performance doesn’t drop:

cat("Testing AUC before: ", auc(maxnet_model, test = test))
#> Testing AUC before:  0.8505888
reduced_variables_model <- reduceVar(maxnet_model, th = 15, metric = "auc", test = test, permut = 1, use_jk = TRUE)
#> Removed variables: bio16, bio6, bio5, bio12, biome, bio8
cat("Testing AUC after: ", auc(reduced_variables_model, test = test))
#> Testing AUC after:  0.8533188

As you can see in this case several variables have been removed and the AUC in the testing dataset didn’t decrease.

### Try yourself

Reduce the number of variables using the model trained with the cross validation and using as metric the TSS. Highlight the following cell for the solution:

# You need to pass TRUE to the test argument
selected_variables_model <- reduceVar(cv_model, th = 6, metric = "tss", test = TRUE, permut = 1)