LRA {easyCODA}

Logratio analysis

Description

Computation of weighted or unweighted logratio analysis of a samples-by-parts compositional data table.

Usage

LRA(data, nd = 2, weight = TRUE, suprow = NA, row.wt = NA, amalg = NA, supamalg = FALSE)

Arguments

data

A data frame or matrix of compositional data, with no zero values

nd

Number of dimensions for summary solution if not 2 (default)

weight

TRUE (default) for part weighting, FALSE for unweighted analysis, or a vector of user-defined part weights

suprow

Indices of rows that are supplementary points

row.wt

Optional user-defined set of positive weights for the rows (samples) (default: equal weights)

amalg

Optional list of amalgamated parts

supamalg

FALSE (default) when amalgamations are active and their subparts supplementary, TRUE when amalgamations are supplementary and their parts active

Details

The function LRA computes a log-ratio analysis of a table of compositional data based on the singular value decomposition. By default the weighted log-ratio analysis is computed (Greenacre & Lewi 2009). For the unweighted logratio analysis (Aitchison & Greenacre 2002), specify the option weight=FALSE.

User-specified weights can be supplied, for the rows and/or the columns. Usually row weights are not specified, and are equal unless intentional weighting of the samples is desired. Default column weights (if weight = TRUE) are the part means of the true compositional table, thus summing to 1. User-specified part weights can be provided using the same weight option.

Supplementary rows can be declared (also known as passive points) – these do not contribute to the solution but are positioned on the solution axes.

Amalgamations can be defined and can either replace their constituent parts (default) or be declared supplementary using the supamalg option: supamalgamate = FALSE (default), = TRUE if all declared amalgamations are supplementary.

The function borrows the structure and functions of the ca package, which is required, and produces a ca object, and the same print, summary and plot methods can be used, as for a ca object.

Value

sv

Singular values

nd

Number of dimensions in solution results

rownames

Row names

rowmass

Row weights

rowdist

Row logratio distances to centroid

rowinertia

Row inertias

rowcoord

Row standard coordinates

rowpcoord

Row principal coordinates

rowsup

Indices of row supplementary points

colnames

Column names

colmass

Column weights

coldist

Column logratio distances to centroid

colinertia

Column inertias

colcoord

Column standard coordinates

colpcoord

Column principal coordinates

N

The compositional data table

Author(s)

Michael Greenacre

References

Aitchison, J. and Greenacre, M. (2002), Biplots of compositional data, Applied Statistics 51, 375-392.
Greenacre, M. and Lewi, P.J. (2009), Distributional equivalence and subcompositional coherence in the analysis of compositional data, contingency tables and ratio scale measurements. Journal of Classification 26, 29-54.

See Also

plot.ca, summary.ca, print.ca

Examples

# (weighted) LRA of the RomanCups data set, showing default symmetric map
data(cups)
PLOT.LRA(LRA(cups))
# all the examples below use the data set 'author' and the plot.ca function from 
# the ca package; alternatively, PLOT.LRA can be used (see first example below)
data(author)
which(author == 0, arr.ind = TRUE)
# row 5 (Farewell to Arms) and col 17 (Q) has a zero
# replace it with 0.5 for the logratio analysis
author[5,17] <- 0.5
# form compositional table of relative frequencies
author.comp <- author / apply(author, 1, sum)
# (weighted) logratio analysis (default is weighted = TRUE)
author.LRA1 <- LRA(author.comp)
plot(author.LRA1)	
PLOT.LRA(author.LRA1)
# unweighted logratio analysis
author.LRA2 <- LRA(author.comp, weight = FALSE)
plot(author.LRA2)
# identical to unweighted logratio analysis by specifying equal column weights
author.LRA3 <- LRA(author.comp, weight = rep(1/ncol(author), ncol(author)))
plot(author.LRA3)
# supplementary rows example (they are plotted with empty circle symbols)
# two books by Arthur C. Clark made supplementary
author.LRA4 <- LRA(author.comp, suprow = c(3,8))
plot(author.LRA4)
# make vowels an amalagamation
author.vowels <- c(1,5,9,15,21)
author.LRA5 <- LRA(author.comp, amalg = list(vowels = author.vowels))
# contribution biplot, just labels plotted, no symbols
plot(author.LRA5, labels=c(1,1), map="rowgreen")