Three representations of the Ising model

Statistical models that analyse (pair-wise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that for the Ising model three representations exist that, while mathematically equivalent, each propose a theoretically distinct explanation for the observed associations. 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.