ordr.extra

This is an extension of the ordr package, a tidyverse extension for managing ordination models and rendering biplots. ordr provides methods for handling only some of the most common techniques, so ordr.extra provides methods for several additional techniques.

This package is like broom in that it can expand to accommodate additional models until they exceed the bandwidth of its maintainer(s). See this issue for additional discussion, and please comment with any additional suggestions!

installation

ordr.extra is not yet on CRAN. You can install the development version as follows:

# install.packages("devtools")
devtools::install_github("corybrunson/ordr.extra")

Note: This package extends tools from ordr to classes of ordination models from several additional packages, but it does not depend on these packages. The reason is so that someone interested in working with, say, candisc models does not have to also install ca, PMA, and the other packages ordr.extra supports. The trade-off is that this user must manually install candisc as well.

example

Joint correspondence analysis¹, implemented in the ca package, essentially applies PCA to a high-dimensional contingency table reformatted as a data frame with one observation per row. To illustrate the technique, recall the UC Berkeley admissions data set, reformatted here as a data frame of counts:

# inspect admissions data
head(as.data.frame(UCBAdmissions))
#>      Admit Gender Dept Freq
#> 1 Admitted   Male    A  512
#> 2 Rejected   Male    A  313
#> 3 Admitted Female    A   89
#> 4 Rejected Female    A   19
#> 5 Admitted   Male    B  353
#> 6 Rejected   Male    B  207

We can use ordr syntax to model these data using joint correspondence analysis with the function ca::mjca()², once we’ve ensured that ca is installed:

# install {ca} if not already installed
if (! "ca" %in% rownames(installed.packages())) install.packages("ca")
# fit JCA model to admissions data
(admissions_jca <- ordinate(UCBAdmissions, ca::mjca, lambda = "JCA"))
#> # A tbl_ord of class 'mjca': (4526 x 5) x (10 x 5)'
#> # 5 coordinates: Dim1, Dim2, ..., Dim5
#> # 
#> # Rows (standard): [ 4526 x 5 | 4 ]
#>    Dim1  Dim2     Dim3 ... |   name      mass    dist     inertia
#>                            |   <chr>    <dbl>   <dbl>       <dbl>
#> 1  2.77 -1.83 1153938.     | 1 1     0.000221 0.00672     9.97e-9
#> 2  2.77 -1.83 1153938. ... | 2 2     0.000221 0.00672     9.97e-9
#> 3  2.77 -1.83 1153938.     | 3 3     0.000221 0.00672     9.97e-9
#> 4  2.77 -1.83 1153938.     | 4 4     0.000221 0.00672     9.97e-9
#> 5  2.77 -1.83 1153938.     | 5 5     0.000221 0.00672     9.97e-9
#> # ℹ 4,521 more rows
#> # 
#> # Columns (standard): [ 10 x 5 | 6 ]
#>      Dim1    Dim2    Dim3 ... |    name    factor level   mass  dist
#>                               |    <chr>   <chr>  <chr>  <dbl> <dbl>
#>  1  0.934 -1.32    0.933      |  1 Admit:… Admit  Admi… 0.129  0.792
#>  2 -0.591  0.835  -0.591      |  2 Admit:… Admit  Reje… 0.204  0.502
#>  3 -1.12  -1.07    0.904      |  3 Gender… Gender Fema… 0.135  0.784
#>  4  0.765  0.732  -0.616      |  4 Gender… Gender Male  0.198  0.534
#>  5  1.65  -0.208  -0.0687 ... |  5 Dept:A  Dept   A     0.0687 1.22 
#>  6  1.86   0.354   0.687      |  6 Dept:B  Dept   B     0.0431 1.58 
#>  7 -0.884 -1.24   -1.73       |  7 Dept:C  Dept   C     0.0676 1.18 
#>  8 -0.354 -0.0487 -0.107      |  8 Dept:D  Dept   D     0.0583 1.26 
#>  9 -1.25  -0.619  -0.957      |  9 Dept:E  Dept   E     0.0430 1.54 
#> 10 -1.13   2.14    2.65       | 10 Dept:F  Dept   F     0.0526 1.39 
#> # ℹ 1 more variable: inertia <dbl>

We can then generate a monoplot³ of the group masses for each of the three categorical variables:

# build biplot of admissions JCA model with variance distributed to variables
admissions_jca %>%
  confer_inertia("colprincipal") %>%
  ggbiplot() +
  theme_bw() + theme_biplot() +
  geom_origin() +
  geom_cols_point(aes(color = factor, shape = factor, size = mass)) +
  geom_cols_text_repel(aes(label = level, color = factor), show.legend = FALSE) +
  scale_color_brewer(palette = "Dark2") +
  scale_size_area(guide = "none") +
  labs(color = "Factor level", shape = "Factor level")

acknowledgments

See the ordr repo for full acknowledgments.

Footnotes

1. Greenacre MJ (2005) “From Correspondence Analysis to Multiple and Joint Correspondence Analysis”. Available at SSRN: https://ssrn.com/abstract=847664 ↩

2. Note that the array is being passed as input. ca::mjca() can also take data frame input, but it requires a format that differs from that produced by as.data.frame(). ↩

3. This is a monoplot because JCA is based on the SVD of a case-by-variable matrix, and only variable elements are plotted here. ↩