Splitting-Coalescence-Estimation Method (SCEM) for archaeological time series.

Source: R/SCEM.R

This function performs the clustering algorithm SCEM on the bivariate time series data – where one series is the distance from the cementum-enamel junction, and the other series is the value of the oxygen-18 isotope at that distance. It returns the class assignments and birth seasonality estimates for all the individuals.

The SCEM assumes that the oxygen isotope values \((z(t))\) can be expressed as a function of \(x(t)\), the natural logarithm of the distance from the CEJ for each of the incremental samples, scaled down by the period (\(X\), the length of the tooth crown). In other words,

\[z(t) = f(x(t)/X) + e(t)\]

where the form of \(f\) is unknown and \(e(t)\) is an error process. Also, following our definition, it assumes that the value of \(x(t)/X\) that maximizes \(z(t)\) is the estimated birth seasonality.

Birth seasonality is estimated using the combined data from all individuals in a single cluster, but birth seasonality estimates for individuals in a cluster are based on individual estimates of the length of the tooth crown (\(X_{k}\)).

For a detailed description of the algorithm, please see Chazin et al. 2019, Supplemental Materials 1.

SCEM(paths, bandwidth)

Arguments

paths

A list of data frames, where each frame contains the data for one individual. There should be two columns with names 'distance' and 'oxygen'.
bandwidth

Denotes the order of the bandwidth that should be used in the splitting-coalescence (SC) clustering algorithm. A value k will mean that the bandwidth used in the algorithm is n^k.

Value

A list containing the following components:

results

A data frame that has the individual information (ID, species, number of observations in the time series), cluster assignment, estimated period, delay and the birth seasonality estimate for every individual.

groups

The groups formed by the clustering algorithm

References

Chazin, Hannah, Soudeep Deb, Joshua Falk, and Arun Srinivasan. 2019. “New Statistical Approaches to Intra-Individual Isotopic Analysis and Modeling Birth Seasonality in Studies of Herd Animals.” Archaeometry 61 (2): 478–93.

Examples

armenia_split = split(armenia,f = armenia$ID)
results = SCEM(armenia_split,bandwidth = -0.33)

#> Warning: step factor 0.000488281 reduced below 'minFactor' of 0.000976562