Package 'deaviz' reference manual

Title:	Visualization of Data Envelopment Analysis Problems
Description:	High-dimensional visualization methods for data envelopment analysis (DEA), gathering in one place techniques that have appeared in the literature but remained scattered and largely unimplemented: cross-efficiency matrix unfolding, the Porembski network with lambda edges, principal component analysis biplots, multidimensional-scaling colour-plots, self-organizing maps, the Costa bi-dimensional efficient frontier, parallel coordinates, radar charts, panel-data trajectory biplots, peer and reference networks, and a set of descriptive plots. The package is built around a single validated dea_data() object and uses the 'Benchmarking' package as its DEA engine. The implemented methods draw on a body of literature; representative references include Doyle and Green (1994) <doi:10.1057/jors.1994.84>, Porembski, Breitenstein and Alpar (2005) <doi:10.1007/s11123-005-1328-5> and Bana e Costa, Soares de Mello and Angulo Meza (2016) <doi:10.1016/j.ejor.2016.05.012>.
Authors:	Shahin Ashkiani [aut, cre]
Maintainer:	Shahin Ashkiani <[email protected]>
License:	AGPL (>= 3)
Version:	0.1.0
Built:	2026-07-03 07:51:16 UTC
Source:	https://github.com/pomelo64/deaviz

Coerce to a dea_data object

Description

Coerce to a dea_data object

Usage

as_dea_data(x, ...)
as_dea_data(x, ...)

Arguments

x

A dea_data object, or a data frame passed on to dea_data.

...

Passed to dea_data when x is not already a dea_data object.

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

Arguments

x

A dea_data object, or a data frame coerced by as_dea_data using the default i_/o_ prefix detection. For non-default column selection (explicit inputs/ outputs/id), build the object first with dea_data and pass it in.

rts

Returns to scale, one of "crs", "vrs", "drs", "irs", "irs2", "fdh" or "add".

orientation

Measurement orientation, forwarded to dea (e.g. "in", "out" or "graph").

dual

Logical; if TRUE the multiplier (dual) solution is also returned. Set FALSE to skip it when only the scores are needed.

slack

Logical; if TRUE slacks are computed as well.

...

Further arguments forwarded to dea.

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.

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

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)
compute_multiplier_weights(x, epsilon = 1e-06)

Arguments

x

A dea_data object, or a data frame coerced by as_dea_data.

epsilon

Non-Archimedean lower bound on every multiplier weight; must be a single non-negative number. Defaults to 1e-6.

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.

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

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

Arguments

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns to scale, passed to compute_efficiency: "crs" or "vrs".

xdim, ydim

Grid dimensions (positive integers; default 8 each).

rlen

Number of training iterations (default 1000).

seed

Optional single number; if supplied, SOM training is made reproducible without permanently changing the session's random state.

...

Further arguments passed to som.

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.

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

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)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

approach

Secondary goal: "benevolent" (maximise others' weighted output) or "aggressive" (minimise it).

epsilon

Lower bound applied to every multiplier weight. The default 0 reproduces the plain model (weights may be zero); set a small positive value (e.g. 1e-6) to enforce strictly positive, non-Archimedean weights.

normalize

Logical; if TRUE (default) inputs and outputs are max-normalised column-wise before solving, so the returned weights are on a comparable scale (useful for plotting).

weights

A list with input_weights and output_weights matrices, such as the result of compute_cross_efficiency_weights.

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

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

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

Arguments

data

A data frame (or object coercible to one) with named columns: at least one input column and one output column.

inputs, outputs

Optional column selectors (character names or integer positions). When supplied they take precedence over the i_/o_ prefixes. A column may not be assigned to both.

id

Optional single column (name or position) holding DMU labels. If NULL, the first unclassified non-numeric column is used, falling back to the row names. Numeric id columns (e.g. integer DMU codes) are not auto-detected, because they cannot be told apart from an input or output that lacks an i_/o_ prefix; name such a column here explicitly.

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.

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")

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

Arguments

x

A cross-efficiency matrix from compute_cross_efficiency, or a dea_data object / data frame from which one is computed.

labels

DMU tick labels: "all" (default) shows them, "none" hides them, and the name/id of a single DMU highlights that DMU's label(s) in colour.

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 1).

fade

Controls the single-DMU focus view. When one DMU is given to labels, all other marks (and, for the network plots, everything outside that DMU's sub-network; for the panel biplot, the other trajectories) are faded so the chosen DMU stands out. TRUE (default) uses a sensible fade level; FALSE disables it; a single number in [0, 1] sets the alpha of the faded marks directly, where larger values fade them less (e.g. 0.4 leaves them more visible).

x_angle

Angle in degrees for the x-axis tick labels, useful when the input/output (or DMU) names on the x-axis are long and overlap. NULL (default) keeps the plot's standard orientation; for example x_angle = 45 tilts the labels to make them readable.

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

When x is data rather than a matrix, further arguments (e.g. approach, epsilon) passed to compute_cross_efficiency.

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

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))

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

Arguments

x

A cross-efficiency matrix from compute_cross_efficiency, or a dea_data object / data frame from which one is computed.

labels

Which DMUs to label: "none" (default), "all" (label every DMU; ggrepel with max.overlaps = Inf), "max.overlaps" (ggrepel using max.overlaps.value), or the name/id of a single DMU to highlight just that one. Use "id" to print each DMU's row number inside its own marker.

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

fade

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

When x is data rather than a matrix, further arguments (e.g. approach, epsilon) passed to compute_cross_efficiency.

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.

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)

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,
  ...
)
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

x

A weights list from compute_cross_efficiency_weights, or a dea_data object / data frame from which the weights are computed.

approach

Secondary goal used when the weights are computed from data: "benevolent" (default) or "aggressive". Ignored when x is an already-computed weights list.

standardize

Logical; if TRUE (default) the weights are row-standardised with standardize_weights before plotting.

labels

DMU tick labels: "all" (default) shows them, "none" hides them, and the name/id of a single DMU highlights that DMU's label(s) in colour.

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 1).

fade

x_angle

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

When x is data, further arguments passed to compute_cross_efficiency_weights.

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns-to-scale model(s) passed to compute_efficiency; a character vector with any of "crs" (default), "vrs", "drs", "irs", "fdh", "add". Supplying more than one compares models.

orientation

Measurement orientation passed to compute_efficiency.

type

"histogram" (default), "box", or "bar" (one bar per DMU).

bins

Number of histogram bins (used when type = "histogram").

labels

Which DMUs to mark: "none" (default), "all" (rug on histograms, jittered points on boxplots), or the name/id of a single DMU to mark with a dashed line (histogram), a point (boxplot), or a highlighted axis label (bar).

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to the underlying geom.

Value

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

dim_x, dim_y, dim_z

Names of the quantities to map to the three axes. Each is either an input/output variable name or an efficiency model ("crs", "vrs", "drs", "irs", "fdh", "add"; a trailing "_efficiency" is also accepted).

color

Quantity mapping to point colour (same options as the axes; default "crs").

orientation

Measurement orientation for efficiency scores, passed to compute_efficiency (default "in").

labels

Which DMUs to label: "none" (default), "all" / "max.overlaps" (label every point), or the name/id of a single DMU to label only that one.

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

...

Additional arguments passed to plotly::plot_ly.

Value

A plotly object.

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

orientation

Measurement orientation, "in" or "out".

point_size

Point size (default 2).

transparency

Point alpha in [0, 1] (default 0.7).

fade

labels

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_point.

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

type

"histogram" (default) or "box".

bins

Number of histogram bins (used when type = "histogram").

scale

Logical; if TRUE (default) variables are standardised (z-scored) before plotting.

labels

Which DMUs to mark: "none" (default), "all" (a rug of every DMU on histograms, jittered points on boxplots), or the name/id of a single DMU to mark it with a dashed vertical line (histogram) or a point (boxplot).

max.overlaps.value

Accepted for API consistency with the other plots; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

x_angle

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; if FALSE (default) returns a static ggplot2 object, if TRUE an interactive plotly object.

...

Additional arguments passed to the underlying geom (geom_histogram or geom_boxplot).

Value

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns to scale passed to compute_efficiency.

orientation

Measurement orientation passed to compute_efficiency.

tol

Tolerance for treating a score as efficient (default 1e-6).

labels

Logical; if TRUE (default) the count and percentage are printed on each bar.

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_col.

Value

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

scale

Logical; if TRUE (default) each variable is standardised (z-scored) before plotting.

labels

DMU tick labels: "all" (default) shows them, "none" hides them, and the name/id of a single DMU highlights that DMU's label(s) in colour.

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 1).

fade

x_angle

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_tile.

Value

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

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)

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns to scale, passed to compute_efficiency: "crs" or "vrs".

edge_threshold

Minimum envelopment weight for an edge to be drawn (single non-negative number, default 0.1).

labels

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

transparency

Node alpha in [0, 1] (default 0.7); lower values reveal overlapping nodes.

fade

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Further arguments passed to sammon (e.g. niter).

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

transform

What to compute distances on: "none" (the original inputs and outputs) or "ratio" (all output/input ratios).

dist_method

Distance measure, passed to dist.

mds_type

Scaling level, passed to smacofSym.

encode

What to colour by: an efficiency model ("crs", "vrs", "drs", "irs", "fdh", "add") or the name of one of the distance-space columns.

point_size

Point size (default 2).

transparency

Point alpha in [0, 1] (default 0.7).

fade

labels

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title. If NULL (default) one is generated.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_point.

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

efficiency

Efficiency model used to colour the lines by efficient/inefficient status: "crs" (default), "vrs" or "none".

orientation

Measurement orientation for the efficiency scores, passed to compute_efficiency (default "in").

labels

Which DMUs to label at the right-hand axis: "none" (default), "all", "max.overlaps", or the name/id of a single DMU (also highlights that DMU's line).

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

fade

x_angle

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_line.

Value

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns to scale, passed to compute_efficiency: "crs" or "vrs".

vector_size

Positive multiplier scaling the length of the variable vectors relative to the point cloud (default 1).

text_size

Size of the variable labels (default 3).

labels

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

transparency

Point alpha in [0, 1] (default 0.7).

fade

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

seed

Optional seed for geom_text_repel label placement (static mode only). Default NA.

...

Additional arguments passed to geom_point.

Value

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

rts

Returns to scale, passed to compute_efficiency: "crs" or "vrs".

layout

Node layout: "pca" (default, first two principal components of the standardised inputs/outputs), "mds" (classical multidimensional scaling), "circle", "fr" (Fruchterman-Reingold force-directed) or "stress" (stress majorization). The last two require the igraph package (and graphlayouts for true stress majorization; otherwise a Kamada-Kawai layout is used).

size_by_peers

Logical; if TRUE, efficient nodes are sized by the number of inefficient units that target them. If FALSE (default) all nodes have the same size.

tol

Tolerance for a positive envelopment weight (default 1e-6).

labels

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

transparency

Node alpha in [0, 1] (default 0.7); lower values reveal overlapping nodes.

fade

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_point.

Value

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

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)

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

efficiency

Efficiency model used to colour the DMUs by efficient/inefficient status: "crs" (default), "vrs" or "none".

orientation

Measurement orientation for the efficiency scores.

labels

DMU emphasis: "none" (default) or "all" draw every DMU normally; the name/id of a single DMU outlines that DMU's polygon in bold so it stands out. (Variable axis labels are always shown.)

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

fade

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; if FALSE (default) a static ggplot2 radar; if TRUE an interactive plotly scatterpolar.

...

Additional arguments passed to geom_polygon (static mode).

Value

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

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")

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,
  ...
)
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

x

A dea_data object, or a data frame coerced by as_dea_data.

vars

Character vector of input/output column names to include. Defaults to all inputs and outputs.

efficiency

Optional character vector of efficiency models to compute and include as columns, any of "crs", "vrs", "drs", "irs", "fdh", "add".

color

Efficiency model used to colour points by efficient/inefficient status: one of "crs" (default), "vrs", "drs", "irs", "fdh", "add", or "none".

correlation

Logical; if TRUE (default) the Pearson correlation is printed in the top-left corner of each panel.

orientation

Measurement orientation used when computing efficiency scores.

labels

Which DMUs to label: "none" (default), "all", "max.overlaps", or the name/id of a single DMU to highlight it. (Uses geom_text with overlap-thinning rather than ggrepel, since repel is unsafe inside facets.)

max.overlaps.value

Accepted for API consistency; unused here (default 10).

transparency

Point alpha in [0, 1] (default 0.7).

fade

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_point.

Value

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

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")

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",
  ...
)
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

som

A dea_som object from compute_som, or a dea_data object / data frame, in which case the map is fitted first.

labels

Which DMUs to write on the map: "all" (default), "none", or the name/id of a single DMU to label only that one.

max.overlaps.value

Accepted for API consistency; unused here (default 10).

jitter_sd

Standard deviation of the random jitter applied to label positions so co-located labels do not overlap (default 0.1).

seed

Optional single number making the label jitter reproducible without changing the session's random state.

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

subtitle

Optional subtitle shown beneath the title.

title

Plot title.

...

When som is data rather than a dea_som, further arguments passed to compute_som.

Value

The dea_som object, invisibly.

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)

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

Arguments

som

A dea_som object from compute_som, or a dea_data object / data frame, in which case the map is fitted first.

variables

Optional character vector selecting which variables to draw (default: all). Names are matched against the input/output column names.

ncol

Number of panels per row (positive integer; default 3).

labels

Logical; if TRUE (default) each panel is titled with its variable name.

transparency

Opacity of the markers/areas, a single number in [0, 1] (default 0.7).

subtitle

Optional subtitle shown beneath the title.

title

Optional overall title drawn above the panel grid.

...

When som is data rather than a dea_som, further arguments passed to compute_som.

Value

The dea_som object, invisibly.

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)

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,
  ...
)
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

panel_data

A long-format data frame with one row per DMU-period, containing an identifier column and a period column (see id and period); the remaining columns are inputs/outputs.

inputs, outputs

Optional input/output column selectors, given either as character names or as integer column positions (e.g. inputs = 3:5). If NULL (default), columns are recognised by the i_ and o_ prefixes, as in dea_data.

id, period

The identifier and period columns, given as a name or an integer position (default "Label" and "Period").

color

Efficiency model for point colour, computed per period: "crs" (default) or "vrs".

orientation

Measurement orientation for the efficiency scores.

vector_size

Positive multiplier scaling the loading vectors.

transparency

Point opacity. Either a single number in [0, 1] (constant alpha, default 0.7) or the string "efficiency", in which case point alpha is mapped to the efficiency score (more efficient DMUs drawn more opaque).

fade

labels

Which DMU trajectories to label at their latest period. One of "none" (default, no labels), "all" (label every DMU, with ggrepel max.overlaps = Inf), "max.overlaps" (label with ggrepel using max.overlaps.value), or the name/id of a single DMU to highlight just that one. Use "id" to print each DMU's row number inside its own marker.

max.overlaps.value

Passed to ggrepel when labels = "max.overlaps" (default 10); larger values keep more crowded labels.

period_labels

Logical; if TRUE each point is labelled with its period. Default FALSE.

size_by_efficiency

Logical; if TRUE point size grows with the efficiency score. Default FALSE.

subtitle

Optional subtitle shown beneath the title.

title

Optional plot title.

interactive

Logical; static ggplot2 (default) or interactive plotly.

...

Additional arguments passed to geom_point.

Value

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

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

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

Arguments

x

A dea_data object, as returned by dea_data.

...

Ignored.

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

Arguments

x

A dea_som object, as returned by compute_som.

...

Ignored.

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
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"
)

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

Package 'deaviz'

Help Index

Coerce to a dea_data object

Description

Usage

Arguments

Value

Examples

Inputs and outputs of 35 major Chinese cities

Description

Usage

Format

Details

Source

Examples

Compute DEA efficiency scores

Description

Usage

Arguments

Details

Value

See Also

Examples

Compute DEA multiplier (weight) solutions

Description

Usage

Arguments

Details

Value

See Also

Examples

Fit a self-organizing map to a DEA problem

Description

Usage

Arguments

Value

See Also

Examples

Cross-efficiency and benevolent weights

Description

Usage

Arguments

Value

Functions

Secondary-goal model

References

See Also

Examples

Create a DEA data object

Description

Usage

Arguments

Value

See Also

Examples

Heatmap of a cross-efficiency matrix

Description

Usage

Arguments

Value

References

See Also

Examples

Unfolding map of a cross-efficiency matrix

Description

Usage

Arguments

Value

References

See Also

Examples

Heatmap of secondary-goal multiplier weights

Description

Usage

Arguments

Value

References

See Also

Examples

Efficiency scores of the DMUs