Package {deaviz}

deaviz: Visualization of Data Envelopment Analysis Problems

Description

deaviz collects high-dimensional visualization methods for data envelopment analysis (DEA) in a single package. It is built around one validated data object, dea_data, which every function accepts (data frames are coerced automatically). Analysis functions are named compute_* and return values; visualization functions are named plot_*.

Workflow

Build a dea_data object (or pass a data frame, recognised by i_/o_ column prefixes or explicit inputs/outputs), then call any compute_* or plot_* function on it. The dea solver in the Benchmarking package is the computational engine; plotting uses plotly and ggplot2. These and the other modelling packages are listed in Suggests: each function checks for the ones it needs and gives an informative error if they are missing.

Author(s)

Maintainer: Shahin Ashkiani Contact@Shahin-Ashkiani.com

Authors:

• Shahin Ashkiani Contact@Shahin-Ashkiani.com

References

Ashkiani, S. (2019). Four Essays on Data Visualization and Anomaly Detection of Data Envelopment Analysis Problems [PhD thesis, Universitat Autonoma de Barcelona]. https://ddd.uab.cat/record/240333

Adler, N., & Raveh, A. (2008). Presenting DEA graphically. Omega, 36(5), 715–729.

Bana e Costa, C. A., Soares de Mello, J. C. C. B., & Angulo Meza, L. (2016). A new approach to the bi-dimensional representation of the DEA efficient frontier with multiple inputs and outputs. European Journal of Operational Research, 255(1), 175–186. doi:10.1016/j.ejor.2016.05.012

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. doi:10.1057/jors.1994.84

Porembski, M., Breitenstein, K., & Alpar, P. (2005). Visualizing efficiency and reference relations in data envelopment analysis with an application to the branches of a German bank. Journal of Productivity Analysis, 23(2), 203–221. doi:10.1007/s11123-005-1328-5

Ashkiani, S., & Mar-Molinero, C. (2017). Visualization of cross-efficiency matrices using multidimensional unfolding. In Recent Applications of Data Envelopment Analysis.

See Also

Useful links:

• https://github.com/Pomelo64/deaviz

• Report bugs at https://github.com/Pomelo64/deaviz/issues

Coerce to a dea_data object

Description

Coerce to a dea_data object

Usage

as_dea_data(x, ...)

Arguments

Value

A dea_data object.

Examples

df <- data.frame(city = c("A", "B"), i_x = c(4, 7), o_y = c(5, 8))
d <- as_dea_data(df)   # coerces a data frame to dea_data
as_dea_data(d)         # already a dea_data: returned unchanged

Inputs and outputs of 35 major Chinese cities

Description

A benchmark data envelopment analysis (DEA) dataset describing 35 major Chinese cities by three inputs and three outputs. Originally introduced by Sueyoshi (1992), it is the example dataset used to illustrate the DEA-Viz methods in Ashkiani (2019) and has appeared in several DEA studies.

Usage

chinese_cities

Format

A data frame with 35 rows and 7 variables:

DMU

City name (the decision-making unit label).

industrial_labour_force

Input 1: industrial labour force.

working_funds

Input 2: working funds.

investments

Input 3: investment.

gross_industrial_output

Output 1: gross industrial output.

profit_and_tax

Output 2: profit and tax.

retail_sales

Output 3: retail sales.

Details

Columns 2–4 are inputs and columns 5–7 are outputs; column 1 holds the DMU labels. Because the columns are not i_/o_ prefixed, pass them explicitly to dea_data (see Examples).

Source

Sueyoshi, T. (1992). Measuring the industrial performance of Chinese cities by data envelopment analysis. Socio-Economic Planning Sciences, 26(2), 75-88. doi:10.1016/0038-0121(92)90015-W

Reproduced as the worked example in Ashkiani, S. (2019), Four Essays on Data Visualization and Anomaly Detection of Data Envelopment Analysis Problems (PhD thesis), Universitat Autonoma de Barcelona.

Examples

d <- dea_data(
  chinese_cities,
  inputs  = c("industrial_labour_force", "working_funds", "investments"),
  outputs = c("gross_industrial_output", "profit_and_tax", "retail_sales"),
  id      = "DMU"
)
d

Compute DEA efficiency scores

Description

Computes data envelopment analysis (DEA) efficiency scores for a set of decision-making units, under any of the returns-to-scale assumptions supported by dea. The numerical work is done by the Benchmarking package; this function wraps it so the input/output data follow the dea_data contract and the call sits inside one consistent entry point.

Usage

compute_efficiency(
  x,
  rts = c("crs", "vrs", "drs", "irs", "irs2", "fdh", "add"),
  orientation = "in",
  dual = TRUE,
  slack = FALSE,
  ...
)

Arguments

Details

The returns-to-scale assumption is selected with rts: in particular "crs" (constant) and "vrs" (variable) are the two most common models, but "drs", "irs", "irs2", "fdh" and "add" are available as well.

Value

The Farrell object returned by dea, whose $eff component holds the efficiency scores.

See Also

dea, which performs the computation; dea_data for the data contract.

Examples

df <- data.frame(i_x = c(2, 3, 4), o_y = c(1, 2, 2))
compute_efficiency(df, rts = "crs")$eff
compute_efficiency(df, rts = "vrs")$eff

Compute DEA multiplier (weight) solutions

Description

Solves the input-oriented, constant-returns-to-scale (CCR) multiplier DEA model for every decision-making unit and returns the optimal efficiency scores together with the input and output weights. A non-Archimedean lower bound epsilon keeps all weights strictly positive.

Usage

compute_multiplier_weights(x, epsilon = 1e-06)

Arguments

Details

For unit o the model maximises the weighted output u^\top y_o subject to the normalisation v^\top x_o = 1 and u^\top y_j - v^\top x_j \le 0 for every unit j, with u, v \ge \epsilon. The optimal value is the unit's efficiency score.

DEA multiplier solutions are generally not unique: efficient units and degenerate vertices admit alternative optimal weight vectors. This function returns one optimal solution (the vertex the solver settles on), not a canonical one. Treat the returned weights accordingly when they feed downstream calculations such as cross-efficiency.

Value

A list with components

eff

named numeric vector of efficiency scores.

input_weights

matrix of input multipliers (one row per DMU, one column per input).

output_weights

matrix of output multipliers (one row per DMU, one column per output).

All rows are labelled with the DMU labels carried by x.

See Also

compute_efficiency for scores via dea; dea_data for the data contract.

Examples

df <- data.frame(i_x = c(2, 3, 4), o_y = c(1, 2, 2))
w <- compute_multiplier_weights(df)
w$eff
w$input_weights

Fit a self-organizing map to a DEA problem

Description

Trains a hexagonal self-organizing map (SOM) on the standardised input/output data and records, for every node, the mean DEA efficiency of the DMUs mapped to it. The result feeds plot_io_som (and other SOM views), so the map is trained once and reused.

Usage

compute_som(
  x,
  rts = c("crs", "vrs"),
  xdim = 8,
  ydim = 8,
  rlen = 1000,
  seed = NULL,
  ...
)

Arguments

Value

An object of class dea_som: a list with the fitted som (a kohonen object), the DMU labels, per-DMU efficiency, per-node mean node_efficiency (NA for empty nodes), and the grid dimensions.

See Also

plot_io_som, som

Examples

df <- data.frame(
  dmu  = paste0("D", 1:12),
  i_x1 = runif(12, 2, 9), i_x2 = runif(12, 1, 5),
  o_y1 = runif(12, 3, 9), o_y2 = runif(12, 1, 4)
)
som <- compute_som(df, xdim = 4, ydim = 4, seed = 1)
som

Cross-efficiency and benevolent weights

Description

Functions for the cross-efficiency analysis of a DEA problem: the cross-efficiency matrix itself (compute_cross_efficiency), the benevolent multiplier weights used to build it (compute_cross_efficiency_weights), and a helper to put those weights on a common scale (standardize_weights).

Usage

compute_cross_efficiency(
  x,
  approach = c("benevolent", "aggressive"),
  epsilon = 0
)

compute_cross_efficiency_weights(
  x,
  approach = c("benevolent", "aggressive"),
  epsilon = 0,
  normalize = TRUE
)

standardize_weights(weights)

Arguments

Value

compute_cross_efficiency returns an n \times n numeric matrix whose entry [k, j] is the efficiency of DMU j evaluated with the weights of DMU k (rows are rating units, columns are rated units). Row and column names are the DMU labels.

compute_cross_efficiency_weights returns a list with matrices input_weights and output_weights (one row per DMU, labelled).

standardize_weights returns a list of the same shape as weights, row-standardised and rounded to 5 digits.

Functions

• compute_cross_efficiency(): Compute the cross-efficiency matrix.

• compute_cross_efficiency_weights(): Secondary-goal multiplier weights for every DMU.

• standardize_weights(): Row-standardise a set of weights so that, within each DMU, the input weights sum to one and the output weights sum to one.

Secondary-goal model

Multiplier (weight) solutions in DEA are not unique, so cross-efficiency requires a secondary goal to choose among a unit's optimal weights. For unit o the model fixes the unit's own efficiency at its CRS score \theta_o and then, among all weight vectors that keep it there, optimises the total weighted output of the other units – maximising it for the "benevolent" approach, minimising it for the "aggressive" one. The unit's own efficiencies \theta_o and the fall-back weights come from a single dea solve.

References

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. doi:10.1057/jors.1994.84

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. doi:10.1057/jors.1994.84

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. doi:10.1057/jors.1994.84

See Also

compute_efficiency, dea_data

Examples

df <- data.frame(
  dmu   = c("A", "B", "C", "D"),
  i_x1  = c(4, 7, 8, 4),
  i_x2  = c(3, 3, 1, 2),
  o_y   = c(1, 1, 1, 1)
)
ce <- compute_cross_efficiency(df, approach = "benevolent")
round(ce, 3)
colMeans(ce)   # each unit's average cross-efficiency

Create a DEA data object

Description

Builds a validated dea_data object from a data frame, classifying columns into inputs and outputs. By default columns are recognised by an i_ prefix (inputs) and an o_ prefix (outputs); the prefixes are stripped from the stored names for display. Columns can also be selected explicitly via inputs/outputs, which overrides the prefixes. Any remaining column is treated as metadata; a non-numeric one (or an explicit id) supplies the DMU labels.

Usage

dea_data(data, inputs = NULL, outputs = NULL, id = NULL)

Arguments

Value

An object of class dea_data: a list with components

X

numeric matrix of inputs (one row per DMU).

Y

numeric matrix of outputs (one row per DMU).

labels

character vector of DMU labels.

See Also

compute_efficiency, as_dea_data

Examples

df <- data.frame(
  city  = c("A", "B", "C"),
  i_lab = c(10, 12, 9),
  i_cap = c(5, 6, 4),
  o_gdp = c(100, 130, 90)
)
dea_data(df)

# explicit selection, no prefixes needed:
df2 <- setNames(df, c("city", "lab", "cap", "gdp"))
dea_data(df2, inputs = c("lab", "cap"), outputs = "gdp", id = "city")

# numeric DMU id codes must be named explicitly:
df3 <- data.frame(dmu = 1001:1003, i_x = c(2, 3, 4), o_y = c(1, 2, 2))
dea_data(df3, id = "dmu")

Heatmap of a cross-efficiency matrix

Description

Draws the cross-efficiency matrix (CEM) as a heatmap: each cell is the efficiency of the rated DMU (x-axis) evaluated with the weights of the rating DMU (y-axis). The diagonal holds the simple (self) efficiencies.

Usage

plot_cem_heatmap(
  x,
  labels = "all",
  max.overlaps.value = 10,
  transparency = 1,
  fade = TRUE,
  x_angle = NULL,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. doi:10.1057/jors.1994.84

See Also

compute_cross_efficiency, plot_cem_unfolding

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_cem_heatmap(compute_cross_efficiency(df))

Unfolding map of a cross-efficiency matrix

Description

Applies multidimensional unfolding (Ashkiani and Mar-Molinero, 2017) to a cross-efficiency matrix, placing each DMU twice – once as a "rating" unit (the weights it applies) and once as a "rated" unit – so that a rating unit sits close to the units it scores highly. Dissimilarities are taken as 1 - CEM.

Usage

plot_cem_unfolding(
  x,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Ashkiani, S., & Mar-Molinero, C. (2017). Visualization of cross-efficiency matrices using multidimensional unfolding. In Recent Applications of Data Envelopment Analysis.

See Also

compute_cross_efficiency, unfolding

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
ce <- compute_cross_efficiency(df)
plot_cem_unfolding(ce)

Heatmap of secondary-goal multiplier weights

Description

Draws a heatmap of each DMU's secondary-goal (benevolent or aggressive) multiplier weights, one row per DMU and one column per input/output. By default the weights are row-standardised (input weights sum to one, output weights sum to one within each DMU) so the relative emphasis is comparable across units.

Usage

plot_cem_weights_heatmap(
  x,
  approach = c("benevolent", "aggressive"),
  standardize = TRUE,
  labels = "all",
  max.overlaps.value = 10,
  transparency = 1,
  fade = TRUE,
  x_angle = NULL,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567–578. doi:10.1057/jors.1994.84

See Also

compute_cross_efficiency_weights, standardize_weights

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_cem_weights_heatmap(df, approach = "benevolent")

Efficiency scores of the DMUs

Description

Summarises the DEA efficiency scores of the decision-making units as a histogram (default), a boxplot, or a per-DMU bar chart. More than one returns-to-scale model can be requested at once: histograms are then stacked vertically (one panel per model) and boxplots are drawn side by side, each model in its own colour.

Usage

plot_efficiency_distributions(
  x,
  rts = "crs",
  orientation = "in",
  type = c("histogram", "box", "bar"),
  bins = 30,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

compute_efficiency, plot_io_efficients

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_efficiency_distributions(df, rts = "crs")
plot_efficiency_distributions(df, rts = c("crs", "vrs"), type = "box")

Interactive 3-D scatter plot of a DEA problem

Description

Plots the DMUs in three dimensions, with each axis and the point colour set to any input/output variable or any DEA efficiency model (so a returns-to- scale efficiency such as "crs" or "vrs" can be used as a dimension). Efficiencies are computed only when referenced, each at most once. This plot is always interactive (plotly); it has no static form.

Usage

plot_io_3dscatter(
  x,
  dim_x,
  dim_y,
  dim_z,
  color = "crs",
  orientation = "in",
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  subtitle = NULL,
  title = NULL,
  ...
)

Arguments

Value

A plotly object.

See Also

compute_efficiency

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_3dscatter(df, dim_x = "x1", dim_y = "x2", dim_z = "y", color = "crs")

Costa bi-dimensional efficient frontier

Description

Draws the Costa et al. (2016) two-dimensional representation of a DEA problem. Each DMU's multiplier weights are standardised and used to collapse its inputs and outputs into a single weighted input I and weighted output O; efficient units fall on the O = I diagonal (the frontier) and inefficient units below it. Uses the constant-returns-to-scale model; weights come from compute_efficiency.

Usage

plot_io_costa_frontier(
  x,
  orientation = c("in", "out"),
  point_size = 2,
  transparency = 0.7,
  fade = TRUE,
  labels = "none",
  max.overlaps.value = 10,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Bana e Costa, C. A., Soares de Mello, J. C. C. B., & Angulo Meza, L. (2016). A new approach to the bi-dimensional representation of the DEA efficient frontier with multiple inputs and outputs. European Journal of Operational Research, 255(1), 175–186. doi:10.1016/j.ejor.2016.05.012

See Also

compute_efficiency

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_costa_frontier(df, orientation = "in")

Distributions of inputs and outputs

Description

Shows the distribution of every input and output, either as faceted histograms (default) or as boxplots. By default the variables are standardised so they share a common scale.

Usage

plot_io_distributions(
  x,
  type = c("histogram", "box"),
  bins = 30,
  scale = TRUE,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  x_angle = NULL,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

dea_data

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_distributions(df)
plot_io_distributions(df, type = "box")

Counts of efficient and inefficient DMUs

Description

Classifies the DMUs as efficient or inefficient (efficiency score equal to 1 within a tolerance) and draws a bar chart of the counts, annotated with the percentage of DMUs in each group.

Usage

plot_io_efficients(
  x,
  rts = c("crs", "vrs", "drs", "irs", "fdh", "add"),
  orientation = "in",
  tol = 1e-06,
  labels = TRUE,
  transparency = 0.7,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

plot_efficiency_distributions, compute_efficiency

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_efficients(df, rts = "crs")

Heatmap of standardised inputs and outputs

Description

Draws a DMU-by-variable heatmap of the input and output values, with DMUs on the y-axis and variables on the x-axis (inputs labelled I_, outputs O_). By default the values are standardised column-wise so they are comparable across variables.

Usage

plot_io_heatmap(
  x,
  scale = TRUE,
  labels = "all",
  max.overlaps.value = 10,
  transparency = 1,
  fade = TRUE,
  x_angle = NULL,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

dea_data

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_heatmap(df)

DEA reference (lambda) network

Description

Projects the DMUs into two dimensions with Sammon mapping and draws the DEA reference network on top: each DMU is a node coloured by efficiency status, and an edge joins unit r to a reference peer c whenever the envelopment weight \lambda_{rc} exceeds edge_threshold. Edge width is proportional to \lambda, shown in the legend.

Usage

plot_io_lambda_network(
  x,
  rts = c("crs", "vrs"),
  edge_threshold = 0.1,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Porembski, M., Breitenstein, K., & Alpar, P. (2005). Visualizing efficiency and reference relations in data envelopment analysis with an application to the branches of a German bank. Journal of Productivity Analysis, 23(2), 203–221. doi:10.1007/s11123-005-1328-5

Sammon, J. W. (1969). A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5), 401–409. doi:10.1109/T-C.1969.222678

See Also

compute_efficiency, plot_io_peer_network, sammon

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_lambda_network(df, rts = "crs")

MDS co-plot of a DEA problem

Description

Places the DMUs in two dimensions by multidimensional scaling (Adler and Raveh, 2008) and colours them by a chosen quantity: a DEA efficiency score, or one of the input/output variables (or their output-to-input ratios).

Usage

plot_io_mds(
  x,
  transform = c("none", "ratio"),
  dist_method = c("euclidean", "manhattan", "maximum", "canberra", "minkowski"),
  mds_type = c("ratio", "interval", "ordinal", "mspline"),
  encode = "crs",
  point_size = 2,
  transparency = 0.7,
  fade = TRUE,
  labels = "none",
  max.overlaps.value = 10,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

References

Adler, N., & Raveh, A. (2008). Presenting DEA graphically. Omega, 36(5), 715–729.

de Leeuw, J., & Mair, P. (2009). Multidimensional scaling using majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1–30. doi:10.18637/jss.v031.i03

See Also

compute_efficiency, smacofSym

Examples

df <- data.frame(
  dmu  = paste0("D", 1:8),
  i_x1 = c(4, 7, 8, 4, 2, 5, 6, 3),
  i_x2 = c(3, 3, 1, 2, 4, 2, 5, 1),
  o_y  = c(5, 8, 6, 7, 3, 9, 4, 6)
)
plot_io_mds(df, encode = "crs")

Parallel coordinates plot of a DEA problem

Description

Draws a parallel-coordinates plot with one axis per input and output, each axis min-max scaled to [0, 1] so they are comparable. Each DMU is one line; lines are coloured by efficient/inefficient status.

Usage

plot_io_parcoo(
  x,
  efficiency = c("crs", "vrs", "none"),
  orientation = "in",
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  x_angle = NULL,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

compute_efficiency, plot_io_radar

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_parcoo(df, efficiency = "crs")

PCA biplot of a DEA problem

Description

Runs a principal component analysis on the standardised input/output data and draws a biplot: DMUs as points coloured by efficiency status, and the variables as labelled vectors. Efficiency comes from compute_efficiency.

Usage

plot_io_pca_biplot(
  x,
  rts = c("crs", "vrs"),
  vector_size = 1,
  text_size = 3,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  seed = NA,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

compute_efficiency

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y1 = c(5, 8, 6, 7, 3, 9),
  o_y2 = c(2, 3, 1, 2, 1, 4)
)
plot_io_pca_biplot(df, rts = "crs")

DEA peer (target) network

Description

Draws a directed network of DMUs: each inefficient unit has arrows pointing to its efficient peers (the targets in its DEA reference set, i.e. the efficient units with a positive envelopment weight). Arrowheads stop short of the target node so the direction stays readable. Nodes are coloured by efficiency status and, optionally, efficient nodes are sized by how often they are a target.

Usage

plot_io_peer_network(
  x,
  rts = c("crs", "vrs"),
  layout = c("pca", "mds", "circle", "fr", "stress"),
  size_by_peers = FALSE,
  tol = 1e-06,
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

compute_efficiency, plot_io_lambda_network

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_peer_network(df, rts = "crs", size_by_peers = TRUE)

Radar plot of inputs and outputs

Description

Draws a radar (spider) plot with one axis per input and output, each min-max scaled to [0, 1], and one closed polygon per DMU with straight edges. Polygons are coloured by efficient/inefficient status. A radial counterpart to plot_io_parcoo.

Usage

plot_io_radar(
  x,
  efficiency = c("crs", "vrs", "none"),
  orientation = "in",
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

plot_io_parcoo, compute_efficiency

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_radar(df, efficiency = "crs")

Pairwise scatter plots of inputs, outputs and efficiency scores

Description

Builds the pairwise scatter plots of a chosen set of columns: any subset of the inputs and outputs, plus optionally one or more efficiency scores. For k selected columns it draws all choose(k, 2) pairwise panels. For example, selecting one input, one output and the CRS score gives three panels.

Usage

plot_io_scatter(
  x,
  vars = NULL,
  efficiency = NULL,
  color = c("crs", "vrs", "drs", "irs", "fdh", "add", "none"),
  correlation = TRUE,
  orientation = "in",
  labels = "none",
  max.overlaps.value = 10,
  transparency = 0.7,
  fade = TRUE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

dea_data, compute_efficiency

Examples

df <- data.frame(
  dmu  = paste0("D", 1:6),
  i_x1 = c(4, 7, 8, 4, 2, 5),
  i_x2 = c(3, 3, 1, 2, 4, 2),
  o_y  = c(5, 8, 6, 7, 3, 9)
)
plot_io_scatter(df, vars = c("x1", "y"), efficiency = "crs")

Plot a self-organizing map of DEA efficiency

Description

Draws the hexagonal SOM as a property map, colouring each node by the mean efficiency of the DMUs assigned to it, and (optionally) labels the nodes with the DMU names. Uses base graphics, so the plot is produced as a side effect on the active device.

Usage

plot_io_som(
  som,
  labels = "all",
  max.overlaps.value = 10,
  jitter_sd = 0.1,
  seed = NULL,
  transparency = 0.7,
  subtitle = NULL,
  title = "SOM: mean efficiency per node",
  ...
)

Arguments

Value

The dea_som object, invisibly.

See Also

compute_som

Examples

df <- data.frame(
  dmu  = paste0("D", 1:12),
  i_x1 = runif(12, 2, 9), i_x2 = runif(12, 1, 5),
  o_y1 = runif(12, 3, 9), o_y2 = runif(12, 1, 4)
)
som <- compute_som(df, xdim = 4, ydim = 4, seed = 1)
plot_io_som(som)

Plot the component planes of a DEA self-organizing map

Description

Draws one SOM property map per input/output variable – the "component planes" – each node coloured by that variable's codebook weight. This shows how each input and output varies across the trained map. Uses base graphics, so the panels are produced as a side effect on the active device.

Usage

plot_io_som_components(
  som,
  variables = NULL,
  ncol = 3,
  labels = TRUE,
  transparency = 0.7,
  subtitle = NULL,
  title = NULL,
  ...
)

Arguments

Value

The dea_som object, invisibly.

See Also

compute_som, plot_io_som

Examples

df <- data.frame(
  dmu  = paste0("D", 1:12),
  i_x1 = runif(12, 2, 9), i_x2 = runif(12, 1, 5),
  o_y1 = runif(12, 3, 9), o_y2 = runif(12, 1, 4)
)
som <- compute_som(df, xdim = 4, ydim = 4, seed = 1)
plot_io_som_components(som)

Panel PCA biplot with DMU trajectories

Description

For panel (long-format) DEA data, computes a single principal-component embedding of the pooled, standardised inputs and outputs (so the axes and loading vectors are fixed), then draws each DMU's path through time as a connected trajectory. Points are coloured by a DEA efficiency score and the arrow on each trajectory points from the earliest to the latest period.

Usage

plot_panel_io_biplot(
  panel_data,
  inputs = NULL,
  outputs = NULL,
  id = "Label",
  period = "Period",
  color = c("crs", "vrs"),
  orientation = "in",
  vector_size = 1,
  transparency = 0.7,
  fade = TRUE,
  labels = "none",
  max.overlaps.value = 10,
  period_labels = FALSE,
  size_by_efficiency = FALSE,
  subtitle = NULL,
  title = NULL,
  interactive = FALSE,
  ...
)

Arguments

Value

A ggplot2 object, or a plotly object when interactive = TRUE.

See Also

plot_io_pca_biplot, compute_efficiency

Examples

# Real multi-period example: 22 Taiwanese banks over 2009-2011.
# Columns can be given by position (inputs are columns 3-5, outputs 6-8) ...
plot_panel_io_biplot(
  taiwanese_banks, id = "DMU", period = "Year",
  inputs = 3:5, outputs = 6:8, labels = "Cathay"
)

# ... or by name, with the loading vectors and a single bank's trajectory.
plot_panel_io_biplot(
  taiwanese_banks, id = "DMU", period = "Year",
  inputs  = c("labour", "physical_capital", "purchased_funds"),
  outputs = c("demand_deposits", "short_term_loans", "long_term_loans"),
  transparency = "efficiency", labels = "all"
)

# A toy long-format frame using the i_/o_ prefix convention also works.
panel <- data.frame(
  Label  = rep(paste0("D", 1:4), each = 3),
  Period = rep(2019:2021, times = 4),
  i_x1   = c(4,5,5, 7,6,6, 8,8,7, 4,3,4),
  i_x2   = c(3,3,2, 3,4,3, 1,2,2, 2,2,1),
  o_y    = c(5,6,7, 8,8,9, 6,6,7, 7,8,8)
)
plot_panel_io_biplot(panel, labels = "D2")   # highlight a single DMU

Print a DEA data object

Description

Print a DEA data object

Usage

## S3 method for class 'dea_data'
print(x, ...)

Arguments

Value

x, invisibly.

Print a fitted DEA self-organizing map

Description

Print a fitted DEA self-organizing map

Usage

## S3 method for class 'dea_som'
print(x, ...)

Arguments

Value

x, invisibly.

Inputs and outputs of 22 Taiwanese commercial banks, 2009-2011

Description

A balanced panel (long-format) data envelopment analysis (DEA) dataset describing 22 Taiwanese commercial banks over three years (2009-2011) by three inputs and three outputs. It is the worked example of Kao and Liu (2014) on multi-period efficiency measurement, and is the example dataset for plot_panel_io_biplot.

Usage

taiwanese_banks

Format

A data frame with 66 rows (22 banks \times 3 years) and 8 variables:

DMU

Bank name (the decision-making unit label).

Year

Period: 2009, 2010 or 2011.

labour

Input 1 (I1): labour.

physical_capital

Input 2 (I2): physical capital.

purchased_funds

Input 3 (I3): purchased funds.

demand_deposits

Output 1 (O1): demand deposits.

short_term_loans

Output 2 (O2): short-term loans.

long_term_loans

Output 3 (O3): medium- and long-term loans.

Details

Columns 3-5 are inputs (I1-I3) and columns 6-8 are outputs (O1-O3); DMU and Year identify each observation. The input/output columns are not i_/o_ prefixed, so pass them by position (e.g. inputs = 3:5, outputs = 6:8) or by name to plot_panel_io_biplot (see Examples).

Source

Kao, C. and Liu, S.-T. (2014). Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese commercial banks. Omega, 47, 90-98. doi:10.1016/j.omega.2013.09.001

Examples

plot_panel_io_biplot(
  taiwanese_banks, id = "DMU", period = "Year",
  inputs = 3:5, outputs = 6:8, labels = "Cathay"
)