Package 'gghotelling'

Automatic plotting of PCA objects

Description

Automatic plotting of PCA objects

Usage

## S3 method for class 'prcomp'
autoplot(object, dims = c(1, 2), biplot = FALSE, group = NULL, ...)

## S3 method for class 'prcomp'
autolayer(
  object,
  dims = c(1, 2),
  group = NULL,
  labels = NULL,
  type = c("t2data", "t2mean", "c2data"),
  outliers = TRUE,
  level = 0.95,
  ...
)

Arguments

object	An object of prcomp class
dims	Dimensions to plot
biplot	whether to show the loadings as well as the scores
group	Groups of the data to be shown on the plot
...	ignored
labels	optionally, a vector of labels for showing the outliers. If NULL, the outliers will be identified by row number.
type	The type of the coverage / confidence area shown by autolayer.prcomp(), can be one of t2data (T2 Hotelling coverage), c2data (chi-squared coverage) or t2mean (T-squared based confidence area for the group mean).
outliers	if TRUE, label the outliers.
level	Either coverage probability (for type = "t2data" and "c2data") or confidence level (for type = "t2mean").

Details

The functions autoplot.prcomp and autolayer.prcomp are for automatic plotting of prcomp objects, similar to ggfortify::autoplot.prcomp.

Note, however, that the group parameter is a vector of the same length as the number of rows in the PCA object, rather than a column name in the data frame.

Value

A ggplot2 object

Examples

pca <- prcomp(iris[,1:4], scale.=TRUE)

library(ggplot2)
autoplot(pca, group = iris$Species) +
  autolayer(pca, group = iris$Species)

# show the 90% confidence area for the group means
autoplot(pca, group = iris$Species) +
  autolayer(pca, group = iris$Species,
            type="t2mean", level = 0.90,
            outliers = FALSE)

---

Draw a convex hull around a group of points

Description

Draw a convex hull around a group of points

Usage

geom_hull(
  mapping = NULL,
  data = NULL,
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping	Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data	The data to be displayed in this layer. There are three options: If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot(). A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created. A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
...	Additional parameters passed to underlying ggplot2::geom_polygon() or to ggplot2::layer().
na.rm	Logical. Should missing values be removed? Default is FALSE.
show.legend	logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.
inherit.aes	If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

Value

A ggplot2 geom layer that can be added to a ggplot object.

Examples

# nothing
library(ggplot2)
ggplot(iris, aes(Sepal.Length, Sepal.Width, color=Species)) +
  geom_hull(mapping = aes(fill = Species), alpha=.1) +
  geom_point()

---

Hotelling ellipses for ggplot2

Description

Hotelling ellipses for ggplot2

Usage

geom_hotelling(
  mapping = NULL,
  data = NULL,
  position = "identity",
  ...,
  level = 0.95,
  type = "t2data",
  robust = FALSE,
  npoints = 100,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping	Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data	The data to be displayed in this layer. There are three options: If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot(). A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created. A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
...	Additional parameters passed to underlying ggplot2::geom_polygon() or to ggplot2::layer().
level	Either coverage probability (for type = "t2data" or "c2data") or confidence level (for type = "t2mean").
type	t2data - Hotelling T2 data ellipse; t2mean - Hotelling confidence interval for the mean; c2data - normal data ellipse (using chi squared distribution).
robust	If TRUE, then robust estimates of mean and covariance are used
npoints	Number of points to estimate
na.rm	Logical. Should missing values be removed? Default is FALSE.
show.legend	logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.
inherit.aes	If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

Details

This geom adds data or confidence ellipses to the plot. See hotelling_ellipse() documentation for more information.

Value

A ggplot2 geom layer that can be added to a ggplot object.

Examples

pca <- prcomp(iris[, 1:4], scale.=TRUE)
df <- cbind(iris, pca$x)
library(ggplot2)

  ggplot(df, aes(PC1, PC2)) +
    geom_hotelling(level=.99) +
    geom_point()

  ggplot(df, aes(PC1, PC2, color=Species)) +
    geom_hotelling() +
    geom_point()

  ggplot(df, aes(PC1, PC2, color=Species)) +
    geom_hotelling(alpha=0.1, aes(fill = Species)) +
    geom_point()

# compare the robust and regular approaches:
  ggplot(df, aes(PC1, PC2, color=Species)) +
    geom_hotelling() +
    geom_hotelling(robust = TRUE, linetype = "dashed") +
    geom_point()

---

Calculate Hotelling or data ellipse around some points

Description

Calculate Hotelling or data ellipse around some points

Usage

hotelling_ellipse(
  x,
  level = 0.95,
  npoints = 100,
  type = c("t2data", "t2mean", "c2data"),
  robust = FALSE
)

Arguments

x	A two-column matrix or data frame like object
level	Either coverage probability (for type = "t2data" or "c2data") or confidence level (for type = "t2mean").
npoints	Number of points to estimate
type	t2data - Hotelling T2 data ellipse; t2mean - Hotelling confidence interval for the mean; c2data - normal data ellipse (using chi squared distribution).
robust	If TRUE, then robust estimates of mean and covariance are used

Details

Calculate the T2 Hotelling ellipse or a data ellipse for the given coverage probability. There are three types of ellipses which can be plotted:

• T2 Hotelling data ellipses, showing data coverage (like the type="t" version of stat_ellipse)

• normal multivariate distribution ellipses (like the type="norm" version of the stat_ellipse) which use Mahalanobis distance and chi-squared statistic

• T2 Hotelling confidence ellipses of the group means.

The latter (for group means) correspond to the confidence interval for the mean in the univariate world, so the ellipses are very small (depending on the number of points).

The function can also use a robust estimator of location and scatter using the covMcd function, which uses the Maximum Covariance Determinant (MCD) estimator. Note that while this results in ellipses which are more resistent to outliers, the interpretation slightly changes, as the T2 statistic used is only an approximation in this case. In other words, use it for visualisation and QC, but not for statistical testing.

Value

A two-column matrix or data frame with npoints rows, containing the coordinates of the ellipse. The columns are named "x" and "y".

See Also

outliers() for calculating per-point based statistic and geom_hotelling() for plotting of the ellipse with ggplot

Examples

df <- iris[ iris$Species == "setosa", 1:2 ]
eli <- hotelling_ellipse(df)
plot(df[,1], df[,2])
lines(eli)

---

Calculate the T2/D2 statistic for individual points

Description

Calculate the T2/D2 statistic or Mahalanobis distance for individual points. For each point, it calculates the squared Mahalanobis distance from the center of the data, and compares it to the critical T2 or chi-squared value for the given coverage probability.

Usage

outliers(
  x,
  level = 0.95,
  robust = FALSE,
  type = c("t2data", "t2mean", "c2data")
)

plot_outliers(
  x,
  level = 0.95,
  robust = FALSE,
  type = c("t2data", "t2mean", "c2data"),
  labels = NULL
)

Arguments

x	A matrix or data frame with two columns
level	Either coverage probability (for type = "t2data" or "c2data") or confidence level (for type = "t2mean").
robust	If TRUE, then robust estimates of mean and covariance are used
type	what type of statistic should be calculated; can be t2data (for data coverage), t2mean (for difference from a mean) or "c2data" (for coverage calculated with the chi squared statistic)
labels	Optional labels to use on the plot instead of rownames

Details

The function can use a robust estimator of location and scatter using the covMcd function, which uses the Maximum Covariance Determinant (MCD) estimator. Note that while this results in ellipses which are more resistant to outliers, the interpretation slightly changes, as the T2 statistic used is only an approximation in this case. In other words, use it for visualisation and QC, but not for statistical testing.

Value

A data frame with one row per point including the columns d2 (squared mahalanobis distance or robust squared distance), t2crit (critical T squared value for the given level), c2crit (critical X squared value for the given level) and is_outlier (logical, whether d2 > t2crit or d2 > c2crit, depending on type).

See Also

hotelling_ellipse for more information on the differences between t2data, t2mean and c2data modes.

Examples

library(ggplot2)

pca <- prcomp(iris[, 1:4], scale.=TRUE)
pca_df <- cbind(iris, pca$x)
outlier_stats <- outliers(pca_df[ , c("PC1", "PC2")], level = 0.95)

# use plot_outliers() to directly plot them
plot_outliers(pca_df[ , c("PC1", "PC2")], level = 0.95)

---

Bag plots

Description

Bag plots for ggplot2

Usage

geom_bag(
  mapping = NULL,
  data = NULL,
  position = "identity",
  ...,
  what = c("bag", "loop"),
  type = c("hdepth", "projdepth", "sprojdepth", "dprojdepth"),
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping	Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data	The data to be displayed in this layer. There are three options: If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot(). A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created. A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
...	Additional parameters passed to underlying ggplot2::geom_polygon() or to ggplot2::layer().
what	What to plot. Either "bag" (the inner bag region) or "loop" (the outer loop).
type	Determines the depth function used to construct the bagplot: "hdepth" for halfspace depth, "projdepth" for projection depth, "sprojdepth" for skewness-adjusted projection depth and "dprojdepth" for directional projection depth. Defaults to "hdepth".
na.rm	Logical. Should missing values be removed? Default is FALSE.
show.legend	logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.
inherit.aes	If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

Details

Bag plots are 2-dimensional generalizations of box plots. This geom adds a bag region (which contains 50% of the data points, just like the "box" in "box plots") to the plot, plus the "loop" which can be used to identify potential outliers.

geom_bag() is just a wrapper around the mrfDepth::compBagplot() function which actually does the calculations, and the arguments are passed on to that function.

The geom either plots the inner "bag" or the outer "loop", but not both. If you need both, you can add two geom_bag layers to your ggplot object.

Value

A ggplot2 geom layer that can be added to a ggplot object.

Examples

library(ggplot2)
ggplot(iris, aes(x = Sepal.Width, y = Sepal.Length, color = Species)) +
  geom_point() +
  geom_bag(aes(fill = Species), alpha = .1, what = "loop") +
  geom_bag(aes(fill = Species), alpha = .3)

---

KDE contours for ggplot2

Description

Kernel density estimate contours for ggplot2

Usage

geom_kde(
  mapping = NULL,
  data = NULL,
  position = "identity",
  ...,
  coverage = 0.95,
  n = 100,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping	Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data	The data to be displayed in this layer. There are three options: If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot(). A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created. A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
...	Additional parameters passed to underlying ggplot2::geom_polygon() or to ggplot2::layer().
coverage	What fraction of the points should be enclosed by the contour
n	Number of grid points in each direction (passed to kde2d)
show.legend	logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.
inherit.aes	If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

Details

This function uses the kde2d function to estimate density along a grid, and then plots a contour for a selected coverage.

Value

A ggplot2 geom layer that can be added to a ggplot object.

See Also

geom_hull() for simple convex contours and geom_hotelling() for Hotelling T2 ellipses.

Examples

library(ggplot2)

# following shows a comparison
# between a convex hull and KDE contour
df <- data.frame(x=rnorm(500) + 5)
df$y <- df$x^5 + rnorm(500)*500
ggplot(df, aes(x=x, y=y)) +
  geom_point()+
  geom_hull(color = "grey") +
  geom_kde(color="red", linewidth=1)
  
# we can also achieve similar effects to geom_contour
pca <- prcomp(iris[, 1:4], scale.=TRUE)
df <- cbind(iris, pca$x)
  
# following is similar to geom_contour
pca <- prcomp(iris[, 1:4], scale.=TRUE)
df <- cbind(iris, pca$x)
p <- ggplot(df, aes(x = PC1, y = PC2, color=Species))
for(i in seq(.05, .95, length.out = 10)) {
  p <- p + geom_kde(aes(fill = Species), alpha =.05, coverage = i, n = 100)
}
p + geom_point()

---

Calculate per-point Hotelling statistic

Description

Calculate per-point Hotelling statistic for use in ggplot

Usage

stat_outliers(
  mapping = NULL,
  data = NULL,
  geom = "point",
  position = "identity",
  ...,
  type = c("t2data", "c2data"),
  level = 0.95,
  outlier_only = FALSE,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping	Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.
data	The data to be displayed in this layer. There are three options: If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot(). A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created. A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).
geom	The geometric object to use to display the data for this layer. When using a ⁠stat_*()⁠ function to construct a layer, the geom argument can be used to override the default coupling between stats and geoms. The geom argument accepts the following: A Geom ggproto subclass, for example GeomPoint. A string naming the geom. To give the geom as a string, strip the function name of the geom_ prefix. For example, to use geom_point(), give the geom as "point". For more information and other ways to specify the geom, see the layer geom documentation.
position	A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following: The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position. A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter". For more information and other ways to specify the position, see the layer position documentation.
...	Additional parameters passed to underlying ggplot2::geom_polygon() or to ggplot2::layer().
type	t2data - Hotelling T2 data ellipse; t2mean - Hotelling confidence interval for the mean; c2data - normal data ellipse (using chi squared distribution).
level	Either coverage probability (for type = "t2data" or "c2data") or confidence level (for type = "t2mean").
outlier_only	Only return the statistic for outliers
na.rm	Logical. Should missing values be removed? Default is FALSE.
show.legend	logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.
inherit.aes	If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

Details

This calculates the Hotelling statistic for each point in the plot, group-wise. This allows to use the statistics is_outlier, d2 (the squared Mahalanobis distance), c2crit (critical Chi-squared value for the specified level) and t2crit (critical Hotelling T2 value for the squared Mahalanobis distance) to be used as graphical parameters, e.g. for coloring the points (see Examples below) using the ggplot2::after_stat() function.

The is_outlier is simply either d2 > t2crit (if type="t2data" or type="t2mean") or d2 > c2crit (if type="c2data").

The type argument chooses between the regular Hotelling statistic (with type="t2data") or the Chi-squared statistic (with type="c2data"). The Hotelling statistic for the mean is not allowed as it makes no sense in the context of the outliers.

The function is a wrapper around the outliers() function, which does the actual calculations, and the parameters passed (level, type, robust) are passed on to that function. For example, to calculate robust statistic, use stat_outliers(robust=TRUE).

Value

A stat layer that can be added to a ggplot object.

Examples

pca <- prcomp(iris[, 1:4], scale.=TRUE)
df <- cbind(iris, pca$x)

library(ggplot2)
ggplot(df, aes(PC1, PC2, group=Species)) +
  geom_hotelling(alpha=0.1, aes(fill = Species)) +
  scale_color_manual(values=c("TRUE"="red", "FALSE"="grey")) +
  stat_outliers(aes(color = after_stat(is_outlier)))

ggplot(df, aes(PC1, PC2, group=Species)) +
  geom_hotelling(alpha=0.1, level = .75, aes(fill = Species)) +
  stat_outliers(level = .75,
                        size=2,
                        aes(shape = Species,
                        color = after_stat(d2)))

# label the outliers
# note that you need to add the label aesthetics for the label geom to
# work
ggplot(df, aes(PC1, PC2, group=Species, label=rownames(df))) +
  geom_hotelling(level = 0.75, alpha=0.1, aes(fill = Species)) +
  geom_point(aes(color = Species)) +
  stat_outliers(level = .75, geom="label",
                        outlier_only = TRUE)

---