Three representations of the Ising model

TL;DR

This paper demonstrates that three mathematically equivalent representations of the Ising model offer different interpretative perspectives on observed variable associations, enriching understanding of their underlying mechanisms.

Contribution

It introduces three equivalent Ising model representations, enabling multiple interpretations of the same data and clarifying conceptual issues.

Findings

Three equivalent Ising model representations identified

Different interpretations can be applied to the same data

Conceptual issues are clarified through alternative explanations

Abstract

Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense.