Interpreting the Ising Model: The Input Matters
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The Ising model is a widely used model for multivariate binary data. It has been first introduced as a theoretical model for the alignment between positive (+1) and negative (-1) atom spins, but is now estimated from data in many applications. A popular way to estimate the Ising model is the pseudo-likelihood approach which reduces estimation to a sequence of logistic regression problems. However, the latter is defined on the domain {0,1}. In this paper we investigate the subtleties of using {0,1} instead of {-1, 1} as the domain for the Ising model. We show that the two domains are statistically equivalent, but imply different interpretations of both threshold and interaction parameters and discuss in which situation which domain is more appropriate. Next, we show that the qualitative behavior of the dynamic Ising model depends on the choice of domains. Finally, we present a transformation that allows to obtain the parameters in one domain from the parameters in the other domain.
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