  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.
