Working with Groups

## Install extra packages (if needed)
# install.packages("folio")

library(nexus)
#> Loading required package: dimensio

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 archaeological contexts (classification).

When coercing a data.frame to a CompositionMatrix object, nexus allows to specify whether an observation belongs to a specific group (or not):

## Data from Wood and Liu 2023
data("bronze", package = "folio")

## Use the third column (dynasties) for grouping
coda <- as_composition(bronze, groups = 3)

groups(x) and groups(x) <- value allow to retrieve or set groups of an existing CompositionMatrix. Missing values (NA) or empty strings can be used to specify that a sample does not belong to any group.

Once groups have been defined, they can be used by further methods (e.g. plotting). Note that for better readability, you can select only some of the parts (e.g. major elements):

## Select major elements
major <- coda[, is_element_major(coda)]

## Compositional bar plot
barplot(major, order_rows = "Cu", space = 0)

## Compositional mean by artefact
coda <- condense(coda, by = list(bronze$dynasty, bronze$reference))

Multivariate Analysis

Log-Ratio Analysis

## CLR
clr <- transform_clr(coda, weights = TRUE)

## PCA
lra <- pca(clr)

## Visualize results
viz_individuals(lra, color = c("#004488", "#DDAA33", "#BB5566"))
viz_hull(x = lra, border = c("#004488", "#DDAA33", "#BB5566"))

viz_variables(lra)

References

Aitchison, J. (1986). The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Londres, UK ; New York, USA: Chapman and Hall.

Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G. and Barceló-Vidal, C. (2003). Isometric Logratio Transformations for Compositional Data Analysis. Mathematical Geology, 35(3): 279-300. DOI: 10.1023/A:1023818214614.

Greenacre, M. (2021). Compositional Data Analysis. Annual Review of Statistics and Its Application, 8(1): 271-299. DOI: 10.1146/annurev-statistics-042720-124436.

Hron, K., Filzmoser, P., de Caritat, P., Fišerová, E. and Gardlo, A. (2017). Weighted Pivot Coordinates for Compositional Data and Their Application to Geochemical Mapping. Mathematical Geosciences, 49(6): 797-814. DOI : 10.1007/s11004-017-9684-z.

Weigand, P. C., Harbottle, G. and Sayre, E. (1977). Turquoise Sources and Source Analysisis: Mesoamerica and the Southwestern U.S.A. In J. Ericson & T. K. Earle (Eds.), Exchange Systems in Prehistory, 15-34. New York, NY: Academic Press.