Package 'dubicube'

Add effect classifications to a dataframe by comparing the confidence intervals with a reference and thresholds

Description

This function adds classified effects to a dataframe as ordered factor variables by comparing the confidence intervals with a reference and thresholds.

Usage

add_effect_classification(
  df,
  cl_columns,
  threshold,
  reference = 0,
  coarse = TRUE
)

Arguments

df	A dataframe containing summary data of confidence limits. Two columns are required containing lower and upper limits indicated by the cl_columns argument. Any other columns are optional.
cl_columns	A vector of 2 column names in df indicating respectively the lower and upper confidence limits (e.g. c("lcl", "ucl")).
threshold	A vector of either 1 or 2 thresholds. A single threshold will be transformed into reference + c(-abs(threshold), abs(threshold)).
reference	The null hypothesis value to compare confidence intervals against. Defaults to 0.
coarse	Logical, defaults to TRUE. If TRUE, add a coarse classification to the dataframe.

Details

This function is a wrapper around effectclass::classify() and effectclass::coarse_classification() from the effectclass package (Onkelinx, 2023). They classify effects in a stable and transparent manner.

Symbol	Fine effect / trend	Coarse effect / trend	Rule
⁠++⁠	strong positive effect / strong increase	positive effect / increase	confidence interval above the upper threshold
+	positive effect / increase	positive effect / increase	confidence interval above reference and contains the upper threshold
⁠+~⁠	moderate positive effect / moderate increase	positive effect / increase	confidence interval between reference and the upper threshold
~	no effect / stable	no effect / stable	confidence interval between thresholds and contains reference
⁠-~⁠	moderate negative effect / moderate decrease	negative effect / decrease	confidence interval between reference and the lower threshold
-	negative effect / decrease	negative effect / decrease	confidence interval below reference and contains the lower threshold
⁠--⁠	strong negative effect / strong decrease	negative effect / decrease	confidence interval below the lower threshold
⁠?+⁠	potential positive effect / potential increase	unknown effect / unknown	confidence interval contains reference and the upper threshold
⁠?-⁠	potential negative effect / potential decrease	unknown effect / unknown	confidence interval contains reference and the lower threshold
⁠?⁠	unknown effect / unknown	unknown effect / unknown	confidence interval contains the lower and upper threshold

Value

The returned value is a modified version of the original input dataframe df with additional columns effect_code and effect containing respectively the effect symbols and descriptions as ordered factor variables. In case of coarse = TRUE (by default) also effect_code_coarse and effect_coarse containing the coarse classification effects.

References

Onkelinx, T. (2023). effectclass: Classification and visualisation of effects [Computer software]. https://inbo.github.io/effectclass/

See Also

Other uncertainty: bootstrap_cube(), calculate_bootstrap_ci()

Examples

# Example dataset
ds <- data.frame(
  mean = c(0, 0.5, -0.5, 1, -1, 1.5, -1.5, 0.5, -0.5, 0),
  sd = c(1, 0.5, 0.5, 0.5, 0.5, 0.25, 0.25, 0.25, 0.25, 0.5)
)
ds$lcl <- qnorm(0.05, ds$mean, ds$sd)
ds$ucl <- qnorm(0.95, ds$mean, ds$sd)

add_effect_classification(
 df = ds,
 cl_columns = c("lcl", "ucl"),
 threshold = 1,
 reference = 0,
 coarse = TRUE)

---

Perform bootstrapping over a data cube for a calculated statistic

Description

This function generate samples bootstrap replicates of a statistic applied to a data cube. It resamples the data cube and computes a statistic fun for each bootstrap replicate, optionally comparing the results to a reference group (ref_group).

Usage

bootstrap_cube(
  data_cube,
  fun,
  ...,
  grouping_var,
  samples = 1000,
  ref_group = NA,
  seed = NA,
  progress = FALSE
)

Arguments

data_cube	A data cube object (class 'processed_cube' or 'sim_cube', see b3gbi::process_cube()) or a dataframe (from ⁠$data⁠ slot of 'processed_cube' or 'sim_cube'). To limit runtime, we recommend using a dataframe with custom function as fun.
fun	A function which, when applied to data_cube returns the statistic(s) of interest. This function must return a dataframe with a column diversity_val containing the statistic of interest.
...	Additional arguments passed on to fun.
grouping_var	A string specifying the grouping variable(s) for the bootstrap analysis. The output of fun(data_cube) returns a row per group.
samples	The number of bootstrap replicates. A single positive integer. Default is 1000.
ref_group	A string indicating the reference group to compare the statistic with. Default is NA, meaning no reference group is used.
seed	A positive numeric value setting the seed for random number generation to ensure reproducibility. If NA (default), then set.seed() is not called at all. If not NA, then the random number generator state is reset (to the state before calling this function) upon exiting this function.
progress	Logical. Whether to show a progress bar. Set to TRUE to display a progress bar, FALSE (default) to suppress it.

Details

Bootstrapping is a statistical technique used to estimate the distribution of a statistic by resampling with replacement from the original data (Davison & Hinkley, 1997; Efron & Tibshirani, 1994). In the case of data cubes, each row is sampled with replacement. Below are the common notations used in bootstrapping:

1. Original Sample Data: $\mathbf{X} = \{X_1, X_2, \ldots, X_n\}$

   • The initial set of observed data points. Here, $n$ is the sample size. This corresponds to the number of cells in a data cube or the number of rows in tabular format.

2. Statistic of Interest: $\theta$

   • The parameter or statistic being estimated, such as the mean $\bar{X}$, variance $\sigma^2$, or a biodiversity indicator. Let $\hat{\theta}$ denote the estimated value of $\theta$ calculated from the complete dataset $\mathbf{X}$.

3. Bootstrap Sample: $\mathbf{X}^* = \{X_1^*, X_2^*, \ldots, X_n^*\}$

   • A sample of size $n$ drawn with replacement from the original sample $\mathbf{X}$. Each $X_i^*$ is drawn independently from $\mathbf{X}$.

   • A total of $B$ bootstrap samples are drawn from the original data. Common choices for $B$ are 1000 or 10,000 to ensure a good approximation of the distribution of the bootstrap replications (see further).

4. Bootstrap Replication: $\hat{\theta}^*_b$

   • The value of the statistic of interest calculated from the $b$-th bootstrap sample $\mathbf{X}^*_b$. For example, if $\theta$ is the sample mean, $\hat{\theta}^*_b = \bar{X}^*_b$.

5. Bootstrap Statistics:

• Bootstrap Estimate of the Statistic: $\hat{\theta}_{\text{boot}}$

  • The average of the bootstrap replications:

$\hat{\theta}_{\text{boot}} = \frac{1}{B} \sum_{b=1}^B \hat{\theta}^*_b$

• Bootstrap Bias: $\text{Bias}_{\text{boot}}$

  • This bias indicates how much the bootstrap estimate deviates from the original sample estimate. It is calculated as the difference between the average bootstrap estimate and the original estimate:

$\text{Bias}_{\text{boot}} = \frac{1}{B} \sum_{b=1}^B (\hat{\theta}^*_b - \hat{\theta}) = \hat{\theta}_{\text{boot}} - \hat{\theta}$

• Bootstrap Standard Error: $\text{SE}_{\text{boot}}$

  • The standard deviation of the bootstrap replications, which estimates the variability of the statistic.

Value

A dataframe containing the bootstrap results with the following columns:

• sample: Sample ID of the bootstrap replicate

• est_original: The statistic based on the full dataset per group

• rep_boot: The statistic based on a bootstrapped dataset (bootstrap replicate)

• est_boot: The bootstrap estimate (mean of bootstrap replicates per group)

• se_boot: The standard error of the bootstrap estimate (standard deviation of the bootstrap replicates per group)

• bias_boot: The bias of the bootstrap estimate per group

References

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap Methods and their Application (1st ed.). Cambridge University Press. doi:10.1017/CBO9780511802843

Efron, B., & Tibshirani, R. J. (1994). An Introduction to the Bootstrap (1st ed.). Chapman and Hall/CRC. doi:10.1201/9780429246593

See Also

Other uncertainty: add_effect_classification(), calculate_bootstrap_ci()

Examples

# Get example data
# install.packages("remotes")
# remotes::install_github("b-cubed-eu/b3gbi")
library(b3gbi)
cube_path <- system.file(
  "extdata", "denmark_mammals_cube_eqdgc.csv",
  package = "b3gbi")
denmark_cube <- process_cube(
  cube_path,
  first_year = 2014,
  last_year = 2020)

# Function to calculate statistic of interest
# Mean observations per year
mean_obs <- function(data) {
  out_df <- aggregate(obs ~ year, data, mean) # Calculate mean obs per year
  names(out_df) <- c("year", "diversity_val") # Rename columns
  return(out_df)
}
mean_obs(denmark_cube$data)

# Perform bootstrapping

bootstrap_mean_obs <- bootstrap_cube(
  data_cube = denmark_cube$data,
  fun = mean_obs,
  grouping_var = "year",
  samples = 1000,
  seed = 123,
  progress = FALSE)
head(bootstrap_mean_obs)

---

Calculate confidence intervals for a dataframe with bootstrap replicates

Description

This function calculates confidence intervals for a dataframe containing bootstrap replicates based on different methods, including percentile (perc), bias-corrected and accelerated (bca), normal (norm), and basic (basic).

Usage

calculate_bootstrap_ci(
  bootstrap_samples_df,
  grouping_var,
  type = c("perc", "bca", "norm", "basic"),
  conf = 0.95,
  aggregate = TRUE,
  data_cube = NA,
  fun = NA,
  ...,
  ref_group = NA,
  jackknife = ifelse(is.element("bca", type), "usual", NA),
  progress = FALSE
)

Arguments

bootstrap_samples_df	A dataframe containing the bootstrap replicates, where each row represents a bootstrap sample. As returned by bootstrap_cube(). Apart from the grouping_var column, the following columns should be present: est_original: The statistic based on the full dataset per group rep_boot: The statistic based on a bootstrapped dataset (bootstrap replicate)
grouping_var	A string specifying the grouping variable(s) used for the bootstrap analysis. This variable is used to split the dataset into groups for separate confidence interval calculations.
type	A character vector specifying the type(s) of confidence intervals to compute. Options include: "perc": Percentile interval "bca": Bias-corrected and accelerated interval "norm": Normal interval "basic": Basic interval "all": Compute all available interval types (default)
conf	A numeric value specifying the confidence level of the intervals. Default is 0.95 (95 % confidence level).
aggregate	Logical. If TRUE (default), the function returns distinct confidence limits per group. If FALSE, the confidence limits are added to the original bootstrap dataframe bootstrap_samples_df.
data_cube	Only used when type = "bca". A data cube object (class 'processed_cube' or 'sim_cube', see b3gbi::process_cube()) or a dataframe (from ⁠$data⁠ slot of 'processed_cube' or 'sim_cube'). As used by bootstrap_cube(). To limit runtime, we recommend using a dataframe with custom function as fun.
fun	Only used when type = "bca". A function which, when applied to data_cube returns the statistic(s) of interest. This function must return a dataframe with a column diversity_val containing the statistic of interest. As used by bootstrap_cube().
...	Additional arguments passed on to fun.
ref_group	Only used when type = "bca". A string indicating the reference group to compare the statistic with. Default is NA, meaning no reference group is used. As used by bootstrap_cube().
jackknife	Only used when type = "bca". A string specifying the jackknife resampling method for BCa intervals. "usual": Negative jackknife (default if BCa is selected). "pos": Positive jackknife
progress	Logical. Whether to show a progress bar for jackknifing. Set to TRUE to display a progress bar, FALSE (default) to suppress it.

Details

We consider four different types of intervals (with confidence level $\alpha$). The choice for confidence interval types and their calculation is in line with the boot package in R (Canty & Ripley, 1999) to ensure ease of implementation. They are based on the definitions provided by Davison & Hinkley (1997, Chapter 5) (see also DiCiccio & Efron, 1996; Efron, 1987).

1. Percentile: Uses the percentiles of the bootstrap distribution.

   $CI_{perc} = \left[ \hat{\theta}^*_{(\alpha/2)}, \hat{\theta}^*_{(1-\alpha/2)} \right]$

   where $\hat{\theta}^*_{(\alpha/2)}$ and $\hat{\theta}^*_{(1-\alpha/2)}$ are the $\alpha/2$ and $1-\alpha/2$ percentiles of the bootstrap distribution, respectively.

2. Bias-Corrected and Accelerated (BCa): Adjusts for bias and acceleration

   Bias refers to the systematic difference between the observed statistic from the original dataset and the center of the bootstrap distribution of the statistic. The bias correction term is calculated as follows:

   $\hat{z}_0 = \Phi^{-1}\left(\frac{\#(\hat{\theta}^*_b < \hat{\theta})}{B}\right)$

   where $\#$ is the counting operator and $\Phi^{-1}$ the inverse cumulative density function of the standard normal distribution.

   Acceleration quantifies how sensitive the variability of the statistic is to changes in the data.

   • $a=0$: The statistic's variability does not depend on the data (e.g., symmetric distribution)

   • $a>0$: Small changes in the data have a large effect on the statistic's variability (e.g., positive skew)

   • $a<0$: Small changes in the data have a smaller effect on the statistic's variability (e.g., negative skew).

   The acceleration term is calculated as follows:

   $\hat{a} = \frac{1}{6} \frac{\sum_{i = 1}^{n}(I_i^3)}{\left( \sum_{i = 1}^{n}(I_i^2) \right)^{3/2}}$

   where $I_i$ denotes the influence of data point $x_i$ on the estimation of $\theta$. $I_i$ can be estimated using jackknifing. Examples are (1) the negative jackknife: $I_i = (n-1)(\hat{\theta} - \hat{\theta}_{-i})$, and (2) the positive jackknife $I_i = (n+1)(\hat{\theta}_{-i} - \hat{\theta})$ (Frangos & Schucany, 1990). Here, $\hat{\theta}_{-i}$ is the estimated value leaving out the $i$’th data point $x_i$. The boot package also offers infinitesimal jackknife and regression estimation. Implementation of these jackknife algorithms can be explored in the future.

   The bias and acceleration estimates are then used to calculate adjusted percentiles.

   $\alpha_1 = \Phi\left( \hat{z}_0 + \frac{\hat{z}_0 + z_{\alpha/2}}{1 - \hat{a}(\hat{z}_0 + z_{\alpha/2})} \right)$, $\alpha_2 = \Phi\left( \hat{z}_0 + \frac{\hat{z}_0 + z_{1 - \alpha/2}}{1 - \hat{a}(\hat{z}_0 + z_{1 - \alpha/2})} \right)$

   So, we get

   $CI_{bca} = \left[ \hat{\theta}^*_{(\alpha_1)}, \hat{\theta}^*_{(\alpha_2)} \right]$

3. Normal: Assumes the bootstrap distribution of the statistic is approximately normal

   $CI_{norm} = \left[\hat{\theta} - \text{Bias}_{\text{boot}} - \text{SE}_{\text{boot}} \times z_{1-\alpha/2}, \hat{\theta} - \text{Bias}_{\text{boot}} + \text{SE}_{\text{boot}} \times z_{1-\alpha/2} \right]$

   where $z_{1-\alpha/2}$ is the $1-\alpha/2$ quantile of the standard normal distribution.

4. Basic: Centers the interval using percentiles

   $CI_{basic} = \left[ 2\hat{\theta} - \hat{\theta}^*_{(1-\alpha/2)}, 2\hat{\theta} - \hat{\theta}^*_{(\alpha/2)} \right]$

   where $\hat{\theta}^*_{(\alpha/2)}$ and $\hat{\theta}^*_{(1-\alpha/2)}$ are the $\alpha/2$ and $1-\alpha/2$ percentiles of the bootstrap distribution, respectively.

Value

A dataframe containing the bootstrap results with the following columns:

• est_original: The statistic based on the full dataset per group

• rep_boo

• est_boot: The bootstrap estimate (mean of bootstrap replicates per group)

• se_boot: The standard error of the bootstrap estimate (standard deviation of the bootstrap replicates per group)

• bias_boot: The bias of the bootstrap estimate per group

• int_type: The interval type

• ll: The lower limit of the confidence interval

• ul: The upper limit of the confidence interval

• conf: The confidence level of the interval When aggregate = FALSE, the dataframe contains the columns from bootstrap_samples_df with one row per bootstrap replicate.

References

Canty, A., & Ripley, B. (1999). boot: Bootstrap Functions (Originally by Angelo Canty for S) [Computer software]. https://CRAN.R-project.org/package=boot

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap Methods and their Application (1st ed.). Cambridge University Press. doi:10.1017/CBO9780511802843

DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical Science, 11(3). doi:10.1214/ss/1032280214

Efron, B. (1987). Better Bootstrap Confidence Intervals. Journal of the American Statistical Association, 82(397), 171–185. doi:10.1080/01621459.1987.10478410

Efron, B., & Tibshirani, R. J. (1994). An Introduction to the Bootstrap (1st ed.). Chapman and Hall/CRC. doi:10.1201/9780429246593

Frangos, C. C., & Schucany, W. R. (1990). Jackknife estimation of the bootstrap acceleration constant. Computational Statistics & Data Analysis, 9(3), 271–281. doi:10.1016/0167-9473(90)90109-U

See Also

Other uncertainty: add_effect_classification(), bootstrap_cube()

Examples

# Get example data
# install.packages("remotes")
# remotes::install_github("b-cubed-eu/b3gbi")
library(b3gbi)
cube_path <- system.file(
  "extdata", "denmark_mammals_cube_eqdgc.csv",
  package = "b3gbi")
denmark_cube <- process_cube(
  cube_path,
  first_year = 2014,
  last_year = 2020)

# Function to calculate statistic of interest
# Mean observations per year
mean_obs <- function(data) {
  out_df <- aggregate(obs ~ year, data, mean) # Calculate mean obs per year
  names(out_df) <- c("year", "diversity_val") # Rename columns
  return(out_df)
}
mean_obs(denmark_cube$data)

# Perform bootstrapping

bootstrap_mean_obs <- bootstrap_cube(
  data_cube = denmark_cube$data,
  fun = mean_obs,
  grouping_var = "year",
  samples = 1000,
  seed = 123,
  progress = FALSE)
head(bootstrap_mean_obs)

# Calculate confidence limits
# Percentile interval
ci_mean_obs1 <- calculate_bootstrap_ci(
  bootstrap_samples_df = bootstrap_mean_obs,
  grouping_var = "year",
  type = "perc",
  conf = 0.95,
  aggregate = TRUE)
ci_mean_obs1

# All intervals
ci_mean_obs2 <- calculate_bootstrap_ci(
  bootstrap_samples_df = bootstrap_mean_obs,
  grouping_var = "year",
  type = c("perc", "bca", "norm", "basic"),
  conf = 0.95,
  aggregate = TRUE,
  data_cube = denmark_cube$data, # Required for BCa
  fun = mean_obs,                # Required for BCa
  progress = FALSE)
ci_mean_obs2

---

Leave-one-out cross-validation for data cubes

Description

This function performs leave-one-out (LOO) or k-fold (experimental) cross-validation (CV) on a biodiversity data cube to assess the performance of a specified indicator function. It partitions the data by a specified variable, calculates the specified indicator on training data, and compares it with the true values to evaluate the influence of one or more categories on the final result.

Usage

cross_validate_cube(
  data_cube,
  fun,
  ...,
  grouping_var,
  out_var = "taxonKey",
  crossv_method = c("loo", "kfold"),
  k = ifelse(crossv_method == "kfold", 5, NA),
  max_out_cats = 1000,
  progress = FALSE
)

Arguments

data_cube	A data cube object (class 'processed_cube' or 'sim_cube', see b3gbi::process_cube()) or a dataframe (from ⁠$data⁠ slot of 'processed_cube' or 'sim_cube'). To limit runtime, we recommend using a dataframe with custom function as fun.
fun	A function which, when applied to data_cube returns the statistic(s) of interest. This function must return a dataframe with a column diversity_val containing the statistic of interest.
...	Additional arguments passed on to fun.
grouping_var	A string specifying the grouping variable(s) for fun. The output of fun(data_cube) returns a row per group.
out_var	A string specifying the column by which the data should be left out iteratively. Default is "taxonKey" which can be used for leave-one-species-out CV.
crossv_method	Method of data partitioning. If crossv_method = "loo" (default), ⁠S = number of unique values in out_var⁠ training partitions are created containing S - 1 rows each. If crossv_method = "kfold", the aggregated data is split the data into k exclusive partitions containing S / k rows each. K-fold CV is experimental and results should be interpreted with caution.
k	Number of folds (an integer). Used only if crossv_method = "kfold". Default 5.
max_out_cats	An integer specifying the maximum number of unique categories in out_var to leave out iteratively. Default is 1000. This can be increased if needed, but keep in mind that a high number of categories in out_var may significantly increase runtime.
progress	Logical. Whether to show a progress bar. Set to TRUE to display a progress bar, FALSE (default) to suppress it.

Details

This function assesses the influence of each category in out_var on the indicator value by iteratively leaving out one category at a time, similar to leave-one-out cross-validation. K-fold CV works in a similar fashion but is experimental and will not be covered here.

1. Original Sample Data: $\mathbf{X} = \{X_{11}, X_{12}, X_{13}, \ldots, X_{sn}\}$

   • The initial set of observed data points, where there are $s$ different categories in out_var and $n$ total samples across all categories (= the sample size). $n$ corresponds to the number of cells in a data cube or the number of rows in tabular format.

2. Statistic of Interest: $\theta$

   • The parameter or statistic being estimated, such as the mean $\bar{X}$, variance $\sigma^2$, or a biodiversity indicator. Let $\hat{\theta}$ denote the estimated value of $\theta$ calculated from the complete dataset $\mathbf{X}$.

3. Cross-Validation (CV) Sample: $\mathbf{X}_{-s_j}$

   • The full dataset $\mathbf{X}$ excluding all samples belonging to category $j$. This subset is used to investigate the influence of category $j$ on the estimated statistic $\hat{\theta}$.

4. CV Estimate for Category $\mathbf{j}$: $\hat{\theta}_{-s_j}$

   • The value of the statistic of interest calculated from $\mathbf{X}_{-s_j}$, which excludes category $j$. For example, if $\theta$ is the sample mean, $\hat{\theta}_{-s_j} = \bar{X}_{-s_j}$.

5. Error Measures:

   • The Error is the difference between the statistic estimated without category $j$ ($\hat{\theta}_{-s_j}$) and the statistic calculated on the complete dataset ($\hat{\theta}$).

   $\text{Error}_{s_j} = \hat{\theta}_{-s_j} - \hat{\theta}$

   • The Relative Error is the absolute error, normalised by the true estimate $\hat{\theta}$ and a small error term $\epsilon = 10^{-8}$ to avoid division by zero.

   $\text{Rel. Error}_{s_j} = \frac{|\hat{\theta}_{-s_j} - \hat{\theta}|}{\hat{\theta} +\epsilon}$

   • The Percent Error is the relative error expressed as a percentage.

   $\text{Perc. Error}_{s_j} = \text{Rel. Error}_{s_j} \times 100 \%$

6. Summary Measures:

   • The Mean Relative Error (MRE) is the average of the relative errors over all categories.

   $\text{MRE} = \frac{1}{s} \sum_{j=1}^s \text{Rel. Error}_{s_j}$

   • The Mean Squared Error (MSE) is the average of the squared errors.

   $\text{MSE} = \frac{1}{s} \sum_{j=1}^s (\text{Error}_{s_j})^2$

   • The Root Mean Squared Error (RMSE) is the square root of the MSE.

   $\text{RMSE} = \sqrt{\text{MSE}}$

Value

A dataframe containing the cross-validation results with the following columns:

• Cross-Validation id (id_cv)

• The grouping variable grouping_var (e.g., year)

• The category left out during each cross-validation iteration (specified out_var with suffix '_out' in lower case)

• The computed statistic values for both training (rep_cv) and true datasets (est_original)

• Error metrics: error (error), squared error (sq_error), absolute difference (abs_error), relative difference (rel_error), and percent difference (perc_error)

• Error metrics summarised by grouping_var: mean relative difference (mre), mean squared error (mse) and root mean squared error (rmse)

See Details section on how these error metrics are calculated.

Examples

# Get example data
# install.packages("remotes")
# remotes::install_github("b-cubed-eu/b3gbi")
library(b3gbi)
cube_path <- system.file(
  "extdata", "denmark_mammals_cube_eqdgc.csv",
  package = "b3gbi")
denmark_cube <- process_cube(
  cube_path,
  first_year = 2014,
  last_year = 2020)

# Function to calculate statistic of interest
# Mean observations per year
mean_obs <- function(data) {
  out_df <- aggregate(obs ~ year, data, mean) # Calculate mean obs per year
  names(out_df) <- c("year", "diversity_val") # Rename columns
  return(out_df)
}
mean_obs(denmark_cube$data)

# Perform leave-one-species-out CV

cv_mean_obs <- cross_validate_cube(
  data_cube = denmark_cube$data,
  fun = mean_obs,
  grouping_var = "year",
  out_var = "taxonKey",
  crossv_method = "loo",
  progress = FALSE)
head(cv_mean_obs)

---