Interpreting the Ising Model: The Input Matters

Abstract: The Ising model is a model for pairwise interactions between binary variables that has become popular in the psychological sciences. It has been first introduced as a theoretical model for the alignment between positive (+1) and negative (-1) atom spins. In many psychological applications, however, the Ising model is defined on the domain ${0,1}$ instead of the classical domain ${-1,1}$. While it is possible to transform the parameters of a given Ising model in one domain to obtain a statistically equivalent model in the other domain, the parameters in the two versions of the Ising model lend themselves to different interpretations and imply different dynamics, when studying the Ising model as a dynamical system. In this tutorial paper, we provide an accessible discussion of the interpretation of threshold and interaction parameters in the two domains and show how the dynamics of the Ising model depends on the choice of domain. Finally, we provide a transformation that allows to transform the parameters in an Ising model in one domain into a statistically equivalent Ising model in the other domain.