lra-ord | R Documentation |
Represent log-ratios between variables based on their values on a population of cases.
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)), ...)
x |
A numeric matrix or rectangular data set. |
compositional |
Logical; whether to normalize rows of |
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 |
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 ( |
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.
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.
Greenacre MJ (2010) Biplots in Practice. Fundacion BBVA, ISBN: 978-84-923846. https://www.fbbva.es/microsite/multivariate-statistics/biplots.html
# 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))
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