Some notes on Goodman's marginal-free correspondence analysis

TL;DR

This paper clarifies that Goodman's marginal-free correspondence analysis is a special case of weighted correspondence analysis and a first-order approximation of logratio analysis, connecting different methods for analyzing contingency tables.

Contribution

It demonstrates that marginal-free correspondence analysis is a specific instance of weighted correspondence analysis and relates it to logratio analysis, providing theoretical insights.

Findings

Shows marginal-free correspondence analysis as a case of weighted correspondence analysis.

Establishes the connection between marginal-free correspondence analysis and logratio analysis.

Provides a unified view of different analytical methods for contingency tables.

Abstract

In his seminal paper Goodman (1996) introduced marginal-free correspondence analysis; where his principal aim was to reconcile Pearson correlation measure with Yule's association measure in the analysis of contingency tables. We show that marginal-free correspondence analysis is a particular case of correspondence analysis with prespecified weights studied in the beginning of the 1980s by Benz\'ecri and his students. Furthermore, we show that it is also a particular first-order approximation of logratio analysis with uniform weights. Key words: Marginal-free correspondence analysis; logratio analysis; interactions; scale invariance; taxicab singular value decomposition.