Construct limited rules offset from the origin

Source: R/stat-rule.r

Determine axis limits and offset vectors from reference data.

stat_rule(
  mapping = NULL,
  data = NULL,
  geom = "rule",
  position = "identity",
  fun.lower = "minpp",
  fun.upper = "maxpp",
  fun.offset = "minabspp",
  fun.args = list(),
  referent = NULL,
  show.legend = NA,
  inherit.aes = TRUE,
  ...
)

minpp(x, p = 0.1)

maxpp(x, p = 0.1)

minabspp(x, p = 0.1)

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.

fun.lower, fun.upper, fun.offset

Functions used to determine the limits of the rules and the translations of the axes from the projections of referent onto the axes and onto their normal vectors.

fun.args

Arguments passed to the fun.*.

referent

The reference data set; see Details.

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.

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. borders().

...

Additional arguments passed to ggplot2::layer().

x

A numeric vector.

p

A numeric value; the proportion of a range used as a buffer.

Value

A ggproto layer.

Details

Biplots with several axes can become cluttered and illegible. When this happens, Gower, Gardner–Lubbe, & le Roux (2011) recommend to translate the axes to a new point of intersection away from the origin, adjusting the axis markers accordingly. Then the axes converge in a region of the plot offset from most position markers or other elements. An alternative solution, implemented in the bipl5 package, is to translate each axis orthogonally away from the origin, which preserves the axis markers. This is the technique implemented here.

Separately, axes that fill the plotting window are uninformative when they exceed the range of the plotted position markers projected onto them. They may even be misinformative, suggesting that linear relationships extrapolate outside the data range. In these cases, Gower and Harding (1988) recommend using finite ranges determined by the data projection onto each axis.

Three functions control these operations: fun.offset computes the orthogonal distance of each axis from the origin, and fun.lower and fun.upper compute the distance along each axis of the endpoints to the (offset) origin. Both functions depend on what position data is to be offset from or limited to, which must be passed manually to the referent parameter.

Referential stats

This statistical transformation is done with respect to reference data passed to referent (ignored if NULL, the default, possibly resulting in empty output). See stat_referent() for more details. This relies on a sleight of hand through a new undocumented LayerRef class and associated ggplot2::ggplot_add() method. As a result, only layers constructed using this stat_*() shortcut will pass the necessary positional aesthetics to the $setup_params() step, making them available to pre-process referent data.

The biplot shortcuts automatically substitute the complementary matrix factor for referent = NULL and will use an integer vector to select a subset from this factor. These uses do not require the mapping passage.

Biplot layers

ggbiplot() uses ggplot2::fortify() internally to produce a single data frame with a .matrix column distinguishing the subjects ("rows") and variables ("cols"). The stat layers stat_rows() and stat_cols() simply filter the data frame to one of these two.

The geom layers geom_rows_*() and geom_cols_*() call the corresponding stat in order to render plot elements for the corresponding factor matrix. geom_dims_*() selects a default matrix based on common practice, e.g. points for rows and arrows for columns.

Computed variables

These are calculated during the statistical transformation and can be accessed with delayed evaluation.

axis

unique axis identifier (integer)

lower,upper

distances to endpoints from origin (before offset)

yintercept,xintercept

intercepts (possibly Inf) of offset axis

References

Gower JC, Gardner–Lubbe S, & le Roux NJ (2011) Understanding Biplots. Wiley, ISBN: 978-0-470-01255-0. https://www.wiley.com/go/biplots

Gower JC & Harding SA (1988) "Nonlinear biplots". Biometrika 75(3): 445–455. doi:10.1093/biomet/75.3.445

See also

Other stat layers: stat_center(), stat_chull(), stat_cone(), stat_projection(), stat_scale(), stat_spantree()

Examples

# Freestone primary glass measurements
print(glass)
#> # A tibble: 68 × 16
#>    Site      Anal  Context Form   SiO2  TiO2 Al2O3   FeO   MnO   MgO   CaO  Na2O
#>    <chr>     <chr> <chr>   <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#>  1 Bet Eli'… 1     L14.B1… Chunk  76.0 NA     3.29  0.45   0.1  0.57  5.96  12.1
#>  2 Bet Eli'… 2     L14.B1… Chunk  73.6  0.16  3.7   0.85  NA    0.68  6.65  13.0
#>  3 Bet Eli'… 3     L14.B1… Chunk  75.0  0.13  3.36  0.53  NA    0.58  7.27  11.4
#>  4 Bet Eli'… 4     L14.B1… Chunk  76.0 NA     3.06  0.35   0.1  0.61  7.63  11.3
#>  5 Bet Eli'… 5     L14.B1… Chunk  75.9 NA     3.13  0.33  NA    0.65  7.49  11.4
#>  6 Bet Eli'… 6     L14.B1… Chunk  74.4  0.14  3.33  0.45  NA    0.62  7.2   12.6
#>  7 Bet Eli'… 29    L31.B3… Chunk  75.8  0.09  3.27  0.52  NA    0.64  6.52  11.8
#>  8 Bet Eli'… 30    L31.B3… Chunk  73.4  0.11  3.5   0.68  NA    0.58  7.73  12.8
#>  9 Bet Eli'… 31    L31.B3… Chunk  75.2  0.11  3.39  0.49  NA    0.53  7.28  11.7
#> 10 Bet Eli'… 32    L31.B3… Chunk  73.7  0.16  3.42  0.53  NA    0.6   7.7   12.4
#> # ℹ 58 more rows
#> # ℹ 4 more variables: K2O <dbl>, P2O5 <dbl>, Cl <dbl>, SO3 <dbl>

# default (standardized) linear discriminant analysis of sites on measurements
glass_lda <- MASS::lda(Site ~ SiO2 + Al2O3 + FeO + MgO + CaO, glass)
# bestow 'tbl_ord' class & augment observation, centroid, and variable fields
as_tbl_ord(glass_lda) %>%
  augment_ord() %>%
  print() -> glass_lda
#> # A tbl_ord of class 'lda': (72 x 3) x (5 x 3)'
#> # 3 coordinates: LD1, LD2, LD3
#> # 
#> # Rows (principal): [ 72 x 3 | 5 ]
#>     LD1    LD2      LD3 |   name         prior counts grouping
#>                         |   <chr>        <dbl>  <int> <chr>   
#> 1  1.82  1.21   0.672   | 1 Apollonia    0.132      9 Apollon…
#> 2 -5.62 -0.364  0.00398 | 2 Banias       0.265     18 Banias  
#> 3  2.47 -1.63  -0.0833  | 3 Bet Eli'ez…  0.397     27 Bet Eli…
#> 4  1.31  2.84  -0.277   | 4 Dor          0.206     14 Dor     
#> 5  2.99 -2.03   1.22    | 5 1           NA         NA Bet Eli…
#> # ℹ 67 more rows
#> # ℹ 1 more variable: .element <chr>
#> # 
#> # Columns (standard): [ 5 x 3 | 2 ]
#>        LD1     LD2    LD3 |   name  .element
#>                           |   <chr> <chr>   
#> 1  0.00681 -0.618  -0.468 | 1 SiO2  active  
#> 2  2.05    -1.04    0.660 | 2 Al2O3 active  
#> 3 -1.93    -0.165  -2.44  | 3 FeO   active  
#> 4 -1.76    -1.82    0.599 | 4 MgO   active  
#> 5 -0.275   -0.0942 -1.42  | 5 CaO   active  
# row-standard biplot
glass_lda %>%
  confer_inertia(1) %>%
  ggbiplot(aes(shape = grouping)) +
  theme_bw() + theme_biplot() +
  geom_rows_point(size = 4) +
  geom_rows_point(elements = "score") +
  stat_cols_rule(
    aes(label = name), color = "#888888", num = 8L,
    ref_elements = "score", fun.offset = \(x) minabspp(x, p = .1),
    text_size = 2.5, label_dodge = .02
  ) +
  scale_shape_manual(values = c(2L, 3L, 0L, 5L)) +
  ggtitle(
    "LDA of Freestone glass measurements",
    "Row-standard biplot of standardized LDA"
  )


# contribution LDA of sites on measurements
glass_lda <-
  lda_ord(Site ~ SiO2 + Al2O3 + FeO + MgO + CaO, glass,
          axes.scale = "contribution")
# bestow 'tbl_ord' class & augment observation, centroid, and variable fields
as_tbl_ord(glass_lda) %>%
  augment_ord() %>%
  print() -> glass_lda
#> # A tbl_ord of class 'lda_ord': (72 x 3) x (5 x 3)'
#> # 3 coordinates: LD1, LD2, LD3
#> # 
#> # Rows (principal): [ 72 x 3 | 5 ]
#>     LD1    LD2      LD3 |   name         prior counts grouping
#>                         |   <chr>        <dbl>  <int> <chr>   
#> 1  1.82  1.21   0.672   | 1 Apollonia    0.132      9 Apollon…
#> 2 -5.62 -0.364  0.00398 | 2 Banias       0.265     18 Banias  
#> 3  2.47 -1.63  -0.0833  | 3 Bet Eli'ez…  0.397     27 Bet Eli…
#> 4  1.31  2.84  -0.277   | 4 Dor          0.206     14 Dor     
#> 5  2.99 -2.03   1.22    | 5 1           NA         NA Bet Eli…
#> # ℹ 67 more rows
#> # ℹ 1 more variable: .element <chr>
#> # 
#> # Columns (standard): [ 5 x 3 | 2 ]
#>       LD1    LD2     LD3 |   name  .element
#>                          |   <chr> <chr>   
#> 1  0.166  -0.871 -0.160  | 1 SiO2  active  
#> 2  0.663  -0.164 -0.0442 | 2 Al2O3 active  
#> 3 -0.142  -0.112 -0.192  | 3 FeO   active  
#> 4 -0.680  -0.367  0.0694 | 4 MgO   active  
#> 5 -0.0804  0.151 -0.941  | 5 CaO   active  
# symmetric biplot
glass_lda %>%
  confer_inertia(.5) %>%
  ggbiplot(aes(shape = grouping)) +
  theme_bw() + theme_biplot() +
  geom_rows_point() +
  stat_rows_density_2d(elements = "score", alpha = .5, color = "#444444") +
  stat_cols_rule(
    aes(label = name), geom = "axis", color = "#888888", num = 8L,
    ref_elements = "active", fun.offset = \(x) minabspp(x, p = .1),
    text_size = 2.5, text_dodge = .025
  ) +
  scale_shape_manual(values = c(16L, 17L, 15L, 18L)) +
  ggtitle(
    "LDA of Freestone glass measurements",
    "Symmetric biplot of contribution LDA"
  )