Explainers presented in this section are designed to better understand which variables are important.

Some models, such as linear regression or random forest, have a build-in *model specific* methods to calculate and visualize variable importance. They will be presented in Section 3.2.2.

Section 3.2.1 presents a model agnostic approach on the basis of permutations. The advantage of this approach is that different models can be compared within a single setup.

Model agnostic variable importance is calculated by means of permutations.
We simply substract the loss function calculated for validation dataset with permuted values for a single variable from the loss function calculated for validation dataset. This concept and some extensions are described in (Fisher, Rudin, and Dominici 2018Fisher, Aaron, Cynthia Rudin, and Francesca Dominici. 2018. “Model Class Reliance: Variable Importance Measures for Any Machine Learning Model Class, from the ’Rashomon’ Perspective.” *Journal of Computational and Graphical Statistics*. http://arxiv.org/abs/1801.01489.).

This method is implemented in the `variable_importance()`

function. The loss function is calculated for:

- the original validation
`data`

. It is an estimate of a model performance and will be denoted as`_full_model_`

, - validation data with resampled
`y`

labels. It is a kind of*worst case*loss when model are compared against random labels. It will be denoted as`_baseline_`

, - validation data with single variable being resampled. It tells us how much is gone from the model performance after the selected variable is blinded.

Let’s see how this function works for a random forest model.

```
## variable dropout_loss label
## 1 _full_model_ 285.1355 randomForest
## 2 no.rooms 391.0710 randomForest
## 3 construction.year 410.5866 randomForest
## 4 floor 445.2164 randomForest
## 5 surface 480.1431 randomForest
## 6 district 843.6519 randomForest
## 7 _baseline_ 1081.3710 randomForest
```

Here the `loss_root_mean_square()`

function is defined as square root from averaged squared differences between labels and model predictions.
The same method may be applied to a linear model. Since we are using the same loss function and the same method for variable permutations, the losses calculated with both methods can be directly compared.

```
## variable dropout_loss label
## 1 _full_model_ 284.2788 lm
## 2 construction.year 284.2638 lm
## 3 no.rooms 295.5020 lm
## 4 floor 495.7685 lm
## 5 surface 600.4308 lm
## 6 district 1025.7208 lm
## 7 _baseline_ 1232.6798 lm
```

It is much easier to compare both models when these values are plotted close to each other.
The generic `plot()`

function may handle both models.

What we can read out of this plot?

- left edges of intervals start in
`_full_model_`

for a given model. As we can see. the performances are similar for both models, - length of the interval corresponds to variable importance. In both models the most important variables are
`district`

and`surface`

, - in the random forest model the
`construction_year`

variable has some importance, while its importance for linear model is almost equal to zero, - the variable
`no.rooms`

(which is correlated with`surface`

) has some importance in the random forest model but not in the linear model.

We may be interested in variables that behave differently between models (like `construction_year`

) or variables that are important in both models (like `district`

or `surface`

). In the next section we introduce explainers for further investigation of these variables.

*NOTE:* If you want variable importance hooked at 0, just add `type = "difference"`

parameter to `variable_importance()`

.

```
vi_lm <- variable_importance(explainer_lm, loss_function = loss_root_mean_square, type = "difference")
vi_rf <- variable_importance(explainer_rf, loss_function = loss_root_mean_square, type = "difference")
plot(vi_lm, vi_rf)
```

Some models have build-in tools for calculation of variable importance.
Random forest uses two different measures - one based on out-of-bag data and second one based on gains in nodes. Read more about this approach in (Liaw and Wiener 2002Liaw, Andy, and Matthew Wiener. 2002. “Classification and Regression by randomForest.” *R News* 2 (3):18–22. http://CRAN.R-project.org/doc/Rnews/.).

Below we show an example of a dot plot that summarizes default importance measure for a random forest. The `varImpPlot()`

function is available in the `randomForest`

package.

It is easy to assess variable importance for linear models and generalized models, since model coefficients have direct interpretation.

Forest plots were initially used in the meta analysis to visualize effects in different studies. . At present, however, they are frequently used to present summary characteristics for models with linear structure / created with `lm`

or `glm`

functions.

There are various implementations of forest plots in R. In the package `forestmodel`

(see (Kennedy 2017Kennedy, Nick. 2017. *Forestmodel: Forest Plots from Regression Models*. https://CRAN.R-project.org/package=forestmodel.)) one can use `forest_model()`

function to draw a forest plot. This package is based on the `broom`

package (see (Robinson 2017Robinson, David. 2017. *Broom: Convert Statistical Analysis Objects into Tidy Data Frames*. https://CRAN.R-project.org/package=broom.)) and this is why it handles a large variety of different regression models.

In the package `sjPlot`

(see (Lüdecke 2017Lüdecke, Daniel. 2017. *SjPlot: Data Visualization for Statistics in Social Science*. https://CRAN.R-project.org/package=sjPlot.)) one can find `sjp.xyz()`

function to visualize coefficients of a `xyz`

model (like `sjp.glm()`

for `glm`

models) or a generic wrapper `plot_model()`

.

**Note!**

The `forestmodel`

package handles factor variables in a better way while the plots from `sjPlot`

are easier to read.