# Classification case: Assessing the performance of remote sensing models

#### Luciana Nieto & Adrian Correndo

#### 2024-06-30

## 1. Introduction

The `metrica` package was developed to visualize and compute the level of agreement between observed ground-truth values and model-derived (e.g., mechanistic or empirical) predicted.

This package is intended to fit into the following workflow:

1. a data set containing the observed values is used to train a model
2. the trained model is used to generate predicted
3. a data frame containing at least the observed and model-predicted values is created
4. `metrica` package is used to compute and evaluate the classification model based on observed and predicted values
5. `metrica` package is used to visualize model fit and selected fit metrics

This vignette introduces the functionality of the `metrica` package applied to observed and model-predicted values of a binary land cover classification scenario, where the two classes are vegetation (1) and non-vegetation (0)).

Let’s begin by loading the packages needed.
## Libraries

    library(metrica)
    library(dplyr)
    library(purrr)
    library(tidyr)

## 2. Example datasets

### 2.1. Kansas Land Cover data

Figure 1. This binary classification dataset corresponds to a Random Forest model using a 70:30 training:testing split to predict vegetation vs. other land coverage. This exercise focused on pixel level classification. The image is showing the classification map where yellow areas are associated to non-vegetation pixels (other), and the green areas to those classified as vegetation.

Now we load the binary `land_cover` data set already included with the `metrica` package. This data set contains two columns:

- `predicted`: model-predicted (random forest) land cover, being vegetation = 1 and other = 0,

- `actual`: ground-truth observed land cover, being 0 = vegetation and 1 = other

    # Load
    binary_landCover <- metrica::land_cover

    # Printing first observations
    head(binary_landCover)
    #>   actual predicted
    #> 1      0         0
    #> 2      1         1
    #> 3      1         1
    #> 4      0         0
    #> 5      0         0
    #> 6      1         1

### 2.2. Maize Phenology

Figure 2. This multiclass classification dataset corresponds to a Random Forest model using a 70:30 training:testing split to predict maize vegetation vs. other land coverage. This exercise focused on field level classification. The image is showing, in dark grey shapes, the fields used as the ground-truth locations to develop the model.

Now we load the multinomial `maize_phenology` data set, which is also already included with the `metrica` package. This multiclass data set presents 16 different classes corresponding to phenological stages of the maize (Zea Mays (L.)) crop.

    # Load
    multi_maize_phen <- metrica::maize_phenology

    # Printing first observations
    head(multi_maize_phen)
    #>   actual predicted
    #> 1     R1       V18
    #> 2     R2        R1
    #> 3     R2        R1
    #> 4     R2        R2
    #> 5     R2        R2
    #> 6     R2        R2

## 3 Visual assessment of agreement

### 3.1 Confusion matrix

The simplest way to visually assess agreement between observed and predicted classes is with a confusion matrix.

We can use the function `confusion_matrix()` from the metrica package.

The function requires specifying:

- the data frame object name (`data` argument)

- the name of the column containing observed values (`obs` argument)

- the name of the column containing predicted values (`pred` argument)

The output of the `confusion_matrix()` function is either a table (`plot = FALSE`) or a `ggplot2` object (`plot = TRUE`) that can be further customized:

### 3.1. Binary

    # a. Print
    binary_landCover %>% confusion_matrix(obs = actual, pred = predicted,
                                          plot = FALSE,
                                          unit = "count")
    #>          OBSERVED
    #> PREDICTED   0   1
    #>         0 181   6
    #>         1   6  92

    # b. Plot
    binary_landCover %>% confusion_matrix(obs = actual, pred = predicted,
                                          plot = TRUE,
                                          colors = c(low="#ffe8d6" , high="#892b64"),
                                          unit = "count")
    #> Warning: Using linewidth for a discrete variable is not advised.

    # c. Unit = proportion
    binary_landCover %>% confusion_matrix(obs = actual, pred = predicted,
                                          plot = TRUE,
                                          colors = c(low="#f9dbbd" , high="#892b64"),
                                          unit = "proportion")
    #> Warning: Using linewidth for a discrete variable is not advised.

### 3.2. Multiclass

    # a. Print
    multi_maize_phen %>% confusion_matrix(obs = actual, pred = predicted,
                                          plot = FALSE,
                                          unit = "count")
    #>          OBSERVED
    #> PREDICTED R1 R2 R3 R4 R5 R6 V10 V12 V13 V14 V15 V16 V18 V19 V9 VT
    #>       R1   0  2  0  0  0  0   0   0   0   0   0   0   0   0  0  0
    #>       R2   0  4  0  0  0  0   0   0   0   1   0   0   0   0  0  0
    #>       R3   0  1  2  0  0  0   0   0   0   0   0   0   0   0  0  0
    #>       R4   0  0  0  6  0  0   0   0   0   0   0   0   0   0  0  0
    #>       R5   0  0  0  0 12  1   0   0   0   0   0   0   0   0  0  0
    #>       R6   0  0  0  0  3 32   0   0   0   0   0   0   0   0  0  0
    #>       V10  0  0  0  0  0  0   6   0   0   1   0   0   0   0  0  0
    #>       V12  0  0  0  0  0  0   0   7   1   0   0   0   0   0  0  0
    #>       V13  0  0  0  0  0  0   0   0   6   0   0   0   0   0  0  0
    #>       V14  0  0  0  0  0  0   0   0   0   2   0   0   0   0  0  0
    #>       V15  0  0  0  0  0  0   0   0   0   0   1   0   0   0  0  1
    #>       V16  0  0  0  0  0  0   0   0   0   0   0   2   0   0  0  0
    #>       V18  1  0  0  0  0  0   0   0   0   0   0   0   4   0  0  0
    #>       V19  0  0  0  0  0  0   0   0   0   0   0   0   0   2  0  0
    #>       V9   0  0  0  0  0  0   0   0   0   0   0   0   0   0  2  0
    #>       VT   0  0  0  0  0  0   0   0   0   0   0   0   0   0  0  3

    # b. Plot
    multi_maize_phen %>% confusion_matrix(obs = actual, pred = predicted,
                                          plot = TRUE,
                                          colors = c(low="grey85" , high="steelblue"),
                                          unit = "count")
    #> Warning: Using linewidth for a discrete variable is not advised.

## 4. Numerical assessment of agreement

The metrica package contains functions for 26 scoring rules to assess the agreement between observed and predicted values for classification data.

A list with all the the classification metrics including their name, definition, details, formula, and function name, please check here.

All of the metric functions take at least three arguments:

- the data frame object name (`data` argument, optional)

- the name of the column containing observed values (`obs` argument)

- the name of the column containing predicted values (`pred` argument)

- an integer (1 or 2) indicating the alphanumerical order of the positive event (`pos_level` argument, Default = 2)

- a TRUE/FALSE indicating to estimate metrics for each single class (`atom` argument, Default = FALSE). This argument is only functional for multiclass datasets.

- a TRUE/FALSE indicating to store the numeric result as a list (`tidy` argument, Default = FALSE), or as a data frame (tidy = TRUE).

### 4.1. Single metrics

The user can choose to calculate a single metric, or to calculate all metrics at once.

To calculate a single metric, the metric function can be called. For example, to calculate \(accuracy\), we can use the `accuracy()` function:

    # Binary
    binary_landCover %>% accuracy(data = ., obs = actual, pred = predicted, tidy = TRUE)
    #>    accuracy
    #> 1 0.9578947

    # Multiclass
    maize_phenology %>% accuracy(data = ., obs = actual, pred = predicted, tidy = TRUE)
    #>    accuracy
    #> 1 0.8834951

Or considering imbalanced observations across classes we can call the `balacc()` function for balanced accuracy:

    # Binary
    binary_landCover %>% balacc(data = ., obs = actual, pred = predicted, tidy = TRUE)
    #>     balacc
    #> 1 0.953345

    # Multiclass
    maize_phenology %>% balacc(data = ., obs = actual, pred = predicted, tidy = TRUE)
    #>      balacc
    #> 1 0.9160466

Similarly, to calculate precision, we can use the `precision()` function:

    # Binary
    binary_landCover %>% precision(data = ., obs = actual, pred = predicted, tidy = TRUE)
    #>   precision
    #> 1 0.9387755

    # Multiclass
    maize_phenology %>% precision(data = ., obs = actual, pred = predicted, tidy = TRUE)
    #>   precision
    #> 1 0.8335108

### 4.2. Metrics summary

The user can also calculate all metrics at once using the function `metrics_summary()`:

    # Get all at once with metrics_summary()
    # Binary
    binary_landCover %>% metrics_summary(data = ., obs = actual, pred = predicted, type = "classification")
    #>         Metric        Score
    #> 1     accuracy   0.95789474
    #> 2   error_rate   0.04210526
    #> 3    precision   0.93877551
    #> 4       recall   0.93877551
    #> 5  specificity   0.96791444
    #> 6       balacc   0.95334497
    #> 7       fscore   0.93877551
    #> 8          agf   0.95323364
    #> 9        gmean   0.95323364
    #> 10        khat   0.90668995
    #> 11         mcc   0.90668995
    #> 12         fmi   0.93877551
    #> 13         bmi   0.90668995
    #> 14         csi   0.32974910
    #> 15      deltap   0.90668995
    #> 16       posLr  29.25850340
    #> 17       negLr   0.06325403
    #> 18         dor 462.55555556
    #> 19         npv   0.96791444
    #> 20         FPR   0.03208556
    #> 21         FNR   0.06122449
    #> 22         FDR   0.06122449
    #> 23         FOR   0.03208556
    #> 24      preval   0.34385965
    #> 25    preval_t   0.50382084
    #> 26     AUC_roc   0.41849817
    #> 27          p4   0.95312232

    # Multiclass
    multi_maize_phen %>% metrics_summary(data = ., obs = actual, pred = predicted, type = "classification")
    #> Warning in metrica::fscore(data = ~., obs = ~actual, pred = ~predicted, : For
    #> multiclass cases, the fscore should be estimated at a class level. Please,
    #> consider using `atom = TRUE`
    #> Warning in metrica::agf(data = ~., obs = ~actual, pred = ~predicted, pos_level
    #> = pos_level): For multiclass cases, the agf should be estimated at a class
    #> level. Please, consider using `atom = TRUE`
    #> Warning in metrica::fmi(data = ~., obs = ~actual, pred = ~predicted, pos_level
    #> = pos_level): The Fowlkes-Mallows Index is not available for multiclass cases.
    #> The result has been recorded as NaN.
    #> Warning in metrica::preval(data = ~., obs = ~actual, pred = ~predicted, : For
    #> multiclass cases, prevalence should be estimated at a class level. A NaN has
    #> been recorded as the result. Please, use `atom = TRUE`
    #> Warning in metrica::preval_t(data = ~., obs = ~actual, pred = ~predicted, : For multiclass cases, prevalence threshold should be estimated at a class level.
    #>       A NaN has been recorded as the result. Please, use `atom = TRUE`.
    #> Warning in metrica::p4(data = ~., obs = ~actual, pred = ~predicted, pos_level =
    #> pos_level): Sorry, the p4 metric has not been generalized for multinomial
    #> cases. A NaN has been recorded as the result
    #>         Metric        Score
    #> 1     accuracy 8.834951e-01
    #> 2   error_rate 1.165049e-01
    #> 3    precision 8.335108e-01
    #> 4       recall 8.405168e-01
    #> 5  specificity 9.915764e-01
    #> 6       balacc 9.160466e-01
    #> 7       fscore 8.369991e-01
    #> 8          agf 9.123017e-01
    #> 9        gmean 9.129275e-01
    #> 10        khat 8.624527e-01
    #> 11         mcc 8.636129e-01
    #> 12         fmi          NaN
    #> 13         bmi 8.320932e-01
    #> 14         csi 5.577765e-02
    #> 15      deltap 8.254693e-01
    #> 16       posLr 9.978151e+01
    #> 17       negLr 1.608381e-01
    #> 18         dor 6.203850e+02
    #> 19         npv 9.919585e-01
    #> 20         FPR 8.423572e-03
    #> 21         FNR 1.594832e-01
    #> 22         FDR 1.664892e-01
    #> 23         FOR 8.041482e-03
    #> 24      preval          NaN
    #> 25    preval_t          NaN
    #> 26     AUC_roc 9.160466e-01
    #> 27          p4          NaN

Alternatively, if the user is only looking for specific metrics, within the same function `metrics_summary()`, the user can pass a list of desired metrics using the argument “metrics_list” as follows:

    # Get a selected list at once with metrics_summary()
    selected_class_metrics <- c("accuracy", "precision", "recall", "fscore")

    # Binary
    bin_sum <- binary_landCover %>%
      metrics_summary(data = .,
                      obs = actual, pred = predicted,
                      type = "classification",
                      metrics_list = selected_class_metrics, pos_level = 1)

    # Multiclass
    multi_maize_phen %>%
      metrics_summary(data = .,
                      obs = actual, pred = predicted,
                      type = "classification",
                      metrics_list = selected_class_metrics)
    #> Warning in metrica::fscore(data = ~., obs = ~actual, pred = ~predicted, : For
    #> multiclass cases, the fscore should be estimated at a class level. Please,
    #> consider using `atom = TRUE`
    #> Warning in metrica::agf(data = ~., obs = ~actual, pred = ~predicted, pos_level
    #> = pos_level): For multiclass cases, the agf should be estimated at a class
    #> level. Please, consider using `atom = TRUE`
    #> Warning in metrica::fmi(data = ~., obs = ~actual, pred = ~predicted, pos_level
    #> = pos_level): The Fowlkes-Mallows Index is not available for multiclass cases.
    #> The result has been recorded as NaN.
    #> Warning in metrica::preval(data = ~., obs = ~actual, pred = ~predicted, : For
    #> multiclass cases, prevalence should be estimated at a class level. A NaN has
    #> been recorded as the result. Please, use `atom = TRUE`
    #> Warning in metrica::preval_t(data = ~., obs = ~actual, pred = ~predicted, : For multiclass cases, prevalence threshold should be estimated at a class level.
    #>       A NaN has been recorded as the result. Please, use `atom = TRUE`.
    #> Warning in metrica::p4(data = ~., obs = ~actual, pred = ~predicted, pos_level =
    #> pos_level): Sorry, the p4 metric has not been generalized for multinomial
    #> cases. A NaN has been recorded as the result
    #>      Metric     Score
    #> 1  accuracy 0.8834951
    #> 2 precision 0.8335108
    #> 3    recall 0.8405168
    #> 4    fscore 0.8369991

### 4.3. Class wise metrics (`atom` = TRUE)

For multiclass cases, most of the classification metrics can (and should) be estimated at the class level and not simply as an overall average across classes. With the exceptions of kappa (khat), mcc, fmi, and AUC_roc, all classification metrics can be estimated at the class level using the argument `atom = TRUE`, as follows:

    # Precision
    maize_phenology %>% metrica::precision(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    #>     precision
    #> R1  0.0000000
    #> R2  0.8000000
    #> R3  0.6666667
    #> R4  1.0000000
    #> R5  0.9230769
    #> R6  0.9142857
    #> V10 0.8571429
    #> V12 0.8750000
    #> V13 1.0000000
    #> V14 1.0000000
    #> V15 0.5000000
    #> V16 1.0000000
    #> V18 0.8000000
    #> V19 1.0000000
    #> V9  1.0000000
    #> VT  1.0000000
    # Recall
    maize_phenology %>% metrica::recall(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    #>        recall
    #> R1  0.0000000
    #> R2  0.5714286
    #> R3  1.0000000
    #> R4  1.0000000
    #> R5  0.8000000
    #> R6  0.9696970
    #> V10 1.0000000
    #> V12 1.0000000
    #> V13 0.8571429
    #> V14 0.5000000
    #> V15 1.0000000
    #> V16 1.0000000
    #> V18 1.0000000
    #> V19 1.0000000
    #> V9  1.0000000
    #> VT  0.7500000
    # Specificity
    maize_phenology %>% metrica::specificity(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    #>          spec
    #> R1  0.9803922
    #> R2  0.9895833
    #> R3  0.9900990
    #> R4  1.0000000
    #> R5  0.9886364
    #> R6  0.9571429
    #> V10 0.9896907
    #> V12 0.9895833
    #> V13 1.0000000
    #> V14 1.0000000
    #> V15 0.9901961
    #> V16 1.0000000
    #> V18 0.9898990
    #> V19 1.0000000
    #> V9  1.0000000
    #> VT  1.0000000

    # atom = TRUE available for more functions available (remove #)
    # F-score
    # maize_phenology %>% metrica::fscore(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Adjusted F-score
    # maize_phenology %>% metrica::agf(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # G-mean
    # maize_phenology %>% metrica::gmean(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Negative predictive value
    # maize_phenology %>% metrica::npv(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Prevalence
    # maize_phenology %>% metrica::preval(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Prevalence threshold
    # maize_phenology %>% metrica::preval_t(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # False omission rate
    # maize_phenology %>% metrica::FOR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # False detection rate
    # maize_phenology %>% metrica::FDR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # False positive rate
    # maize_phenology %>% metrica::FPR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Falase negative rate
    # maize_phenology %>% metrica::FNR(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Delta-p
    # maize_phenology %>% metrica::deltap(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Critical Success Index
    # maize_phenology %>% metrica::csi(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Bookmaker Informedness
    # maize_phenology %>% metrica::bmi(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Positive likelihood ratio
    # maize_phenology %>% metrica::posLr(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Negative likelihood ratio
    # maize_phenology %>% metrica::negLr(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)
    # # Diagnostic odds ratio
    # maize_phenology %>% metrica::dor(obs = actual, pred = predicted, atom = TRUE, tidy = TRUE)

### 4.4. Multiple models

In some cases, multiple runs of a model are available to compare vs. observed values (e.g. cross-validation folds). Thus, we can also fit the agreement analysis for several datasets as follows:

    set.seed(15)
    # Let's simulated two extra runs of the same model for Land Cover
    fold_2 <- data.frame(actual = sample(c(0,1), 285, replace = TRUE),
                         predicted = sample(c(0,1), 285, replace = TRUE))
    fold_3 <- data.frame(actual = sample(c(0,1), 285, replace = TRUE),
                         predicted = sample(c(0,1), 285, replace = TRUE))

    # a. Create nested df with the folds
    binary_nested_folds <- bind_rows(list(fold_1 = binary_landCover,
                                          fold_2 = fold_2,
                                          fold_3 = fold_3),
                                 .id = "id") %>%
      dplyr::group_by(id) %>% tidyr::nest()

    head(binary_nested_folds %>% group_by(id) %>% dplyr::slice_head(n=2))
    #> # A tibble: 3 × 2
    #> # Groups:   id [3]
    #>   id     data
    #>   <chr>  <list>
    #> 1 fold_1 <tibble [285 × 2]>
    #> 2 fold_2 <tibble [285 × 2]>
    #> 3 fold_3 <tibble [285 × 2]>

    # b. Run
    binary_folds_summary <- binary_nested_folds %>%
      # Store metrics in new.column "performance"
      dplyr::mutate(performance =
                      purrr::map(data,
                                 ~metrica::metrics_summary(data = .,
                                                           obs = actual, pred = predicted,
                                                           type = "classification"))) %>%
      dplyr::select(-data) %>%
      tidyr::unnest(cols = performance) %>%
      dplyr::arrange(Metric)

    head(binary_folds_summary)
    #> # A tibble: 6 × 3
    #> # Groups:   id [3]
    #>   id     Metric   Score
    #>   <chr>  <chr>    <dbl>
    #> 1 fold_1 AUC_roc 0.418
    #> 2 fold_2 AUC_roc 0.446
    #> 3 fold_3 AUC_roc 0.513
    #> 4 fold_1 FDR     0.0612
    #> 5 fold_2 FDR     0.620
    #> 6 fold_3 FDR     0.471

#### 4.4.1. Non-nested data

#### 4.4.1.1. Using `group_map()`

    non_nested_folds <- binary_nested_folds %>% unnest(cols = "data")

    # Using group_map()
    binary_folds_summary_2 <- non_nested_folds %>%
      dplyr::group_by(id) %>%
      dplyr::group_map(~metrics_summary(data = ., obs = actual, pred = predicted, type = "classification"))

    binary_folds_summary_2
    #> [[1]]
    #>         Metric        Score
    #> 1     accuracy   0.95789474
    #> 2   error_rate   0.04210526
    #> 3    precision   0.93877551
    #> 4       recall   0.93877551
    #> 5  specificity   0.96791444
    #> 6       balacc   0.95334497
    #> 7       fscore   0.93877551
    #> 8          agf   0.95323364
    #> 9        gmean   0.95323364
    #> 10        khat   0.90668995
    #> 11         mcc   0.90668995
    #> 12         fmi   0.93877551
    #> 13         bmi   0.90668995
    #> 14         csi   0.32974910
    #> 15      deltap   0.90668995
    #> 16       posLr  29.25850340
    #> 17       negLr   0.06325403
    #> 18         dor 462.55555556
    #> 19         npv   0.96791444
    #> 20         FPR   0.03208556
    #> 21         FNR   0.06122449
    #> 22         FDR   0.06122449
    #> 23         FOR   0.03208556
    #> 24      preval   0.34385965
    #> 25    preval_t   0.50382084
    #> 26     AUC_roc   0.41849817
    #> 27          p4   0.95312232
    #>
    #> [[2]]
    #>         Metric      Score
    #> 1     accuracy  0.4350877
    #> 2   error_rate  0.5649123
    #> 3    precision  0.3795620
    #> 4       recall  0.4062500
    #> 5  specificity  0.4585987
    #> 6       balacc  0.4324244
    #> 7       fscore  0.3924528
    #> 8          agf  0.4388081
    #> 9        gmean  0.4316315
    #> 10        khat -0.1342793
    #> 11         mcc -0.1345500
    #> 12         fmi  0.3926794
    #> 13         bmi -0.1351513
    #> 14         csi  0.2488038
    #> 15      deltap -0.1339515
    #> 16       posLr  0.7503676
    #> 17       negLr  1.2947049
    #> 18         dor  0.5795666
    #> 19         npv  0.4864865
    #> 20         FPR  0.5414013
    #> 21         FNR  0.5937500
    #> 22         FDR  0.6204380
    #> 23         FOR  0.5135135
    #> 24      preval  0.4491228
    #> 25    preval_t  0.5151462
    #> 26     AUC_roc  0.4457023
    #> 27          p4  0.4286205
    #>
    #> [[3]]
    #>         Metric      Score
    #> 1     accuracy 0.51578947
    #> 2   error_rate 0.48421053
    #> 3    precision 0.52857143
    #> 4       recall 0.50684932
    #> 5  specificity 0.52517986
    #> 6       balacc 0.51601459
    #> 7       fscore 0.51748252
    #> 8          agf 0.50934678
    #> 9        gmean 0.51593318
    #> 10        khat 0.03199606
    #> 11         mcc 0.03202444
    #> 12         fmi 0.51759643
    #> 13         bmi 0.03202917
    #> 14         csi 0.34741784
    #> 15      deltap 0.03201970
    #> 16       posLr 1.06745538
    #> 17       negLr 0.93901295
    #> 18         dor 1.13678451
    #> 19         npv 0.50344828
    #> 20         FPR 0.47482014
    #> 21         FNR 0.49315068
    #> 22         FDR 0.47142857
    #> 23         FOR 0.49655172
    #> 24      preval 0.51228070
    #> 25    preval_t 0.50444076
    #> 26     AUC_roc 0.51257025
    #> 27          p4 0.51577792

#### 4.4.1.2. Using `summarise()`

    # Using summarise()
    binary_folds_summary_3 <- non_nested_folds %>%
      dplyr::group_by(id) %>%
      dplyr::summarise(metrics_summary(obs = actual, pred = predicted, type = "classification")) %>%
      dplyr::arrange(Metric)
    #> Warning: Returning more (or less) than 1 row per `summarise()` group was deprecated in
    #> dplyr 1.1.0.
    #> ℹ Please use `reframe()` instead.
    #> ℹ When switching from `summarise()` to `reframe()`, remember that `reframe()`
    #>   always returns an ungrouped data frame and adjust accordingly.
    #> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
    #> generated.
    #> `summarise()` has grouped output by 'id'. You can override using the `.groups`
    #> argument.

    binary_folds_summary_3
    #> # A tibble: 81 × 3
    #> # Groups:   id [3]
    #>    id     Metric   Score
    #>    <chr>  <chr>    <dbl>
    #>  1 fold_1 AUC_roc 0.418
    #>  2 fold_2 AUC_roc 0.446
    #>  3 fold_3 AUC_roc 0.513
    #>  4 fold_1 FDR     0.0612
    #>  5 fold_2 FDR     0.620
    #>  6 fold_3 FDR     0.471
    #>  7 fold_1 FNR     0.0612
    #>  8 fold_2 FNR     0.594
    #>  9 fold_3 FNR     0.493
    #> 10 fold_1 FOR     0.0321
    #> # ℹ 71 more rows

## 5. Visual Assessment

### 5.1. Customizing the confusion matrix

To print the metrics on the `confusion_matrix()`, just use print.metrics = TRUE. Warning: do not forget to specify your ‘metrics.list’ and choice wisely:

    selected_metrics <- c("accuracy", "precision", "recall", "khat",
                       "mcc", "fscore", "agf", "npv", "FPR", "FNR")

    binary_matrix_metrics <-
      binary_landCover %>%
      confusion_matrix(obs = actual, pred = predicted,
                       plot = TRUE,
                       colors = c(low="#ffe8d6" , high="#892b64"),
                       unit = "count",
                       # Print metrics_summary
                       print_metrics = TRUE,
                       # List of performance metrics
                       metrics_list = selected_metrics,
                       # Position (bottom or top)
                       position_metrics = "bottom")

    binary_matrix_metrics
    #> Warning: Using linewidth for a discrete variable is not advised.

    multinomial_matrix_metrics <-
      maize_phenology %>%
      confusion_matrix(obs = actual, pred = predicted,
                       plot = TRUE,
                       colors = c(low="grey85" , high="steelblue"),
                       unit = "count",
                       # Print metrics_summary
                       print_metrics = TRUE,
                       # List of performance metrics
                       metrics_list = selected_metrics,
                       # Position (bottom or top)
                       position_metrics = "bottom")
    #> Warning in metrica::fscore(data = ~data, obs = ~actual, pred = ~predicted, :
    #> For multiclass cases, the fscore should be estimated at a class level. Please,
    #> consider using `atom = TRUE`
    #> Warning in metrica::agf(data = ~data, obs = ~actual, pred = ~predicted, : For
    #> multiclass cases, the agf should be estimated at a class level. Please,
    #> consider using `atom = TRUE`
    #> Warning in metrica::fmi(data = ~data, obs = ~actual, pred = ~predicted, : The
    #> Fowlkes-Mallows Index is not available for multiclass cases. The result has
    #> been recorded as NaN.
    #> Warning in metrica::preval(data = ~data, obs = ~actual, pred = ~predicted, :
    #> For multiclass cases, prevalence should be estimated at a class level. A NaN
    #> has been recorded as the result. Please, use `atom = TRUE`
    #> Warning in metrica::preval_t(data = ~data, obs = ~actual, pred = ~predicted, : For multiclass cases, prevalence threshold should be estimated at a class level.
    #>       A NaN has been recorded as the result. Please, use `atom = TRUE`.
    #> Warning in metrica::p4(data = ~data, obs = ~actual, pred = ~predicted,
    #> pos_level = pos_level): Sorry, the p4 metric has not been generalized for
    #> multinomial cases. A NaN has been recorded as the result

    multinomial_matrix_metrics
    #> Warning: Using linewidth for a discrete variable is not advised.

Also, as a ggplot element, outputs are flexible of further edition:

    binary_matrix_metrics +
      # Modify labels
      ggplot2::labs(x = "Observed Vegetation",
           y = "Predicted Vegetation",
           title = "Binary Confusion Matrix")
    #> Warning: Using linewidth for a discrete variable is not advised.

    multinomial_matrix_metrics +
      # Modify labels
      ggplot2::labs(x = "Observed Corn Phenology",
           y = "Predicted Corn Phenology",
           title = "Multinomial Confusion Matrix")+
      # Modify theme
      ggplot2::theme_light()
    #> Warning: Using linewidth for a discrete variable is not advised.

## 6. Exporting

To export the metrics summary table, the user can simply write it to file with the function `write.csv()`:

    metrics_summary(data = binary_landCover,
                    obs = obs,
                    pred = pred,
                    type = "classification") %>%
      write.csv("binary_landcover_metrics_summary.csv")

Similarly, to export a plot, the user can simply write it to file with the function `ggsave()`:

    ggsave(plot = multinomial_matrix_metrics,
           "multinomial_matrix_metrics.png",
           width = 8,
           height = 7)