lra-ord {ordr}

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:

• svThe r-1 singular values

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

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

• row.weightsThe weights used to scale the row coordinates.

• column.weightsThe 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))

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