lra-ord: Log-ratio analysis

In ordr: A 'Tidyverse' Extension for Ordinations and Biplots

Log-ratio analysis

Description

Represent log-ratios between variables based on their values on a population of cases.

Usage

lra(x, compositional = FALSE, weighted = TRUE)

## S3 method for class 'lra'
print(x, nd = length(x$sv), n = 6L, ...)

## S3 method for class 'lra'
screeplot(x, main = deparse1(substitute(x)), ...)

## S3 method for class 'lra'
biplot(
  x,
  choices = c(1L, 2L),
  scale = c(0, 0),
  main = deparse1(substitute(x)),
  var.axes = FALSE,
  ...
)

## S3 method for class 'lra'
plot(x, main = deparse1(substitute(x)), ...)

Arguments

x	A numeric matrix or rectangular data set.
compositional	Logical; whether to normalize rows of x to sum to 1.
weighted	Logical; whether to weight rows and columns by their sums.
nd	Integer; number of shared dimensions to include in print.
n	Integer; number of rows of each factor to print.
main, var.axes, ...	Parameters passed to other plotting methods (in the case of main, after being force()d.
choices	Integer; length-2 vector specifying the components to plot.
scale	Numeric; values between 0 and 1 that control how inertia is conferred unto the points: Row (i = 1L) and column (i = 2L) coordinates are scaled by sv ^ scale[[i]]. If a single value scale is passed, it is assigned to the rows while 1 - scale is assigned to the columns.

Details

Log-ratio analysis (LRA) is based on a double-centering of log-transformed data, usually weighted by row and column totals. The technique is suitable for positive-valued variables on a common scale (e.g. percentages). The distances between variables' coordinates (in the full-dimensional space) are their pairwise log-ratios. The distances between cases' coordinates are called their log-ratio distances, and the total variance is the weighted sum of their squares.

LRA is not implemented in standard R distributions but is a useful member of the ordination toolkit. This is a minimal implementation following Greenacre's (2010) exposition in Chapter 7.

Value

Given an n * p data matrix and setting r=min(n,p), lra() returns a list of class "lra" containing three elements:

sv

The r-1 singular values

row.coords

The n * (r-1) matrix of row standard coordinates.

column.coords

The p * (r-1) matrix of column standard coordinates.

row.weights

The weights used to scale the row coordinates.

column.weights

The weights used to scale the column coordinates.

References

Greenacre MJ (2010) Biplots in Practice. Fundacion BBVA, ISBN: 978-84-923846. https://www.fbbva.es/microsite/multivariate-statistics/biplots.html

Examples

# U.S. 1973 violent crime arrests
head(USArrests)
# row and column subsets
state_examples <- c("Hawaii", "Mississippi", "North Dakota")
arrests <- c(1L, 2L, 4L)

# pairwise log-ratios of violent crime arrests for two states
arrest_pairs <- combn(arrests, 2L)
arrest_ratios <-
  USArrests[, arrest_pairs[1L, ]] / USArrests[, arrest_pairs[2L, ]]
colnames(arrest_ratios) <- paste(
  colnames(USArrests)[arrest_pairs[1L, ]], "/",
  colnames(USArrests)[arrest_pairs[2L, ]], sep = ""
)
arrest_logratios <- log(arrest_ratios)
arrest_logratios[state_examples, ]

# non-compositional log-ratio analysis
(arrests_lra <- lra(USArrests[, arrests]))
screeplot(arrests_lra)
biplot(arrests_lra, scale = c(1, 0), cex = c(2/3, 1))

# compositional log-ratio analysis
(arrests_lra <- lra(USArrests[, arrests], compositional = TRUE))
biplot(arrests_lra, scale = c(1, 0), cex = c(2/3, 1))

ordr documentation built on Aug. 8, 2025, 7:27 p.m.