LRA: Logratio analysis In easyCODA: Compositional Data Analysis in Practice

Description

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

Usage

 1 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.

Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 # (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")

Example output       