Provenance studies rely on the identification of probable sources, such that the variability between two sources is greater than the internal variability of a single source (the so-called provenance postulate, Weigand, Harbottle, and Sayre 1977). This assumes that a unique signature can be identified for each source on the basis of several criteria.

nexus is designed for chemical fingerprinting and source tracking of ancient materials. It provides provides tools for exploration and analysis of compositional data in the framework of Aitchison (1986).

## Get started

You can install the released version of nexus from CRAN with:

install.packages("nexus")

Once installed, load the package and start working:

library(nexus)
#>
#> Attaching package: 'nexus'
#> The following object is masked from 'package:stats':
#>
#>     biplot

nexus provides a set of S4 classes that represent different special types of matrix. The most basic class represents a compositional data matrix, i.e. quantitative (nonnegative) descriptions of the parts of some whole, carrying relative, rather than absolute, information (Aitchison 1986; Greenacre 2021).

It assumes that you keep your data tidy: each variable must be saved in its own column and each observation (sample) must be saved in its own row.

This class is of simple use as it inherits from base matrix:

## Mineral compositions of rock specimens
data("hongite")
#>       A    B    C    D    E
#> H1 48.8 31.7  3.8  6.4  9.3
#> H2 48.2 23.8  9.0  9.2  9.8
#> H3 37.0  9.1 34.2  9.5 10.2
#> H4 50.9 23.8  7.2 10.1  8.0
#> H5 44.2 38.3  2.9  7.7  6.9
#> H6 52.3 26.2  4.2 12.5  4.8

## Coerce to compositional data
coda <- as_composition(hongite)
#> <CompositionMatrix: 6 x 5>
#>        A     B     C     D     E
#> H1 0.488 0.317 0.038 0.064 0.093
#> H2 0.482 0.238 0.090 0.092 0.098
#> H3 0.370 0.091 0.342 0.095 0.102
#> H4 0.509 0.238 0.072 0.101 0.080
#> H5 0.442 0.383 0.029 0.077 0.069
#> H6 0.523 0.262 0.042 0.125 0.048

A CompositionMatrix represents a closed composition matrix: each row of the matrix sum up to 1 (only relative changes are relevant in compositional data analysis).

The original row sums are kept internally, so that the source data can be restored:

## Coerce to count data
counts <- as_amounts(coda)

all.equal(hongite, as.data.frame(counts))
#> [1] TRUE

get_totals(x) and set_totals(x) <- value allow to retrieve or modify row sums of an existing CompositionMatrix.

### Working with (reference) groups

Provenance studies typically rely on two approaches, which can be used together:

• Identification of groups among the artifacts being studied, based on mineralogical or geochemical criteria (clustering).
• Comparison with so-called reference groups, i.e. known geological sources or productive contexts (classification).

nexus allows to specify whether an observation belongs to a specific group (or not). When coercing a data.frame to a CompositionMatrix object, an attempt is made to automatically detect groups by mapping column names.

## Create a data.frame
X <- data.frame(
groups = c("A", "A", "B", "A", "B", "C", "C", "C", "B"),
Ca = c(7.72, 7.32, 3.11, 7.19, 7.41, 5, 4.18, 1, 4.51),
Fe = c(6.12, 5.88, 5.12, 6.18, 6.02, 7.14, 5.25, 5.28, 5.72),
Na = c(0.97, 1.59, 1.25, 0.86, 0.76, 0.51, 0.75, 0.52, 0.56)
)

## Coerce to a compositional matrix
Y <- as_composition(X)
has_groups(Y)
#> [1] TRUE

This behavior can be disabled by setting options(nexus.autodetect = FALSE) or overridden by explicitly specifying the column to be used with the groups argument of as_composition().

get_groups(x) and set_groups(x) <- value allow to retrieve or set groups of an existing CompositionMatrix (NA can be used to specify that a sample does not belong to any group):

## Set groups (NA means no group)
set_groups(Y) <- c("X", "X", "Y", "X", "Y", NA, NA, NA, "Y")

## Retrieve groups
get_groups(Y)
#> [1] "X" "X" "Y" "X" "Y" NA  NA  NA  "Y"

Once groups have been defined, they can be used by further methods (e.g. plotting).

### Working with repeated measurements

In some situations, measurements may have been repeated (e.g. multiple chemical analyses on the same sample). The presence of repeated measurements can be specified by giving several observations the same sample name.

When coercing a data.frame to a CompositionMatrix object, an attempt is made to automatically detect samples by mapping column names. If no matching column is found, row names will be used by default.

## Create a data.frame
X <- data.frame(
samples = c("A", "A", "A", "B", "B", "B", "C", "C", "C"),
Ca = c(7.72, 7.32, 3.11, 7.19, 7.41, 5, 4.18, 1, 4.51),
Fe = c(6.12, 5.88, 5.12, 6.18, 6.02, 7.14, 5.25, 5.28, 5.72),
Na = c(0.97, 1.59, 1.25, 0.86, 0.76, 0.51, 0.75, 0.52, 0.56)
)

## Coerce to a compositional matrix
Y <- as_composition(X)
has_replicates(Y)
#> [1] TRUE

This behavior can be disabled by setting options(nexus.autodetect = FALSE) or overridden by explicitly specifying the column to be used with the samples argument of as_composition().

get_samples(x) and set_samples(x) <- value allow to retrieve or set sample names of an existing CompositionMatrix (missing values are not allowed):

## Set sample names
set_samples(Y) <- c("A", "B", "C", "D", "E", "F", "G", "H", "I")

## Retrieve groups
get_samples(Y)
#> [1] "A" "B" "C" "D" "E" "F" "G" "H" "I"

Note that the presence of repeated measurements may affect some calculations (read the documentation carefully).

## References

Aitchison, J. 1986. The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Londres, UK ; New York, USA: Chapman and Hall. http://dx.doi.org/10.1007/978-94-009-4109-0.
Greenacre, Michael. 2021. “Compositional Data Analysis.” Annual Review of Statistics and Its Application 8 (1): 271–99. https://doi.org/10.1146/annurev-statistics-042720-124436.
Weigand, P. C., G. Harbottle, and E. Sayre. 1977. “Turquoise Sources and Source Analysisis: Mesoamerica and the Southwestern U.S.A.” In Exchange Systems in Prehistory, edited by J. Ericson and T. K. Earle, 15–34. New York, NY: Academic Press.