On the choice of weights in aggregate compositional data analysis

TL;DR

This paper explores how to select appropriate weights in the analysis of aggregate compositional data, proposing methods for visualization and approximation based on data structure distinctions.

Contribution

It introduces a distinction between elementary and aggregate compositional data, and proposes two novel approaches for analyzing and visualizing aggregate compositional vectors.

Findings

Different weight choices affect log interaction analysis results.

Proposed two approaches: log interaction of aggregates and aggregate of log interactions.

First-order approximation of log interaction varies with row and column weights.

Abstract

In this paper, we distinguish between two kinds of compositional data sets: elementary and aggregate. This fact will help us to decide the choice of the weights to use in log interaction analysis of aggregate compositional vectors. We show that in the aggregate case, the underlying given data form a paired data sets composed of responses and qualitative covariates; this fact helps us to propose two approaches for analysis-visualization of data named log interaction of aggregates and aggregate of log interactions. Furthermore, we also show the first-order approximation of log interaction of a cell for different choices of the row and column weights.