Modeling Psychological Systems with Ternary Spin Models

Han van der Maas, University of Amsterdam, SFI
In previous work in psychology, we have introduced network models as alternatives to traditional common cause models, such as the g-theory of general intelligence. For major depressive disorder and attitudinal change, we used variants of the Ising model, providing new explanations for phenomena such as sudden relapse and polarization. These theoretical insights were supported by extensive empirical research, demonstrating the successful application of network models to psychological data. However, the binary nature of the nodes in these models is a limitation, as many data sets include questions with a neutral or intermediate category (e.g., "don't know" or "not relevant"). In addition, the behavior of the Ising model is somewhat limited. Ternary spin models, such as the Blume-Capel model, offer a solution by introducing richer dynamics, including tricritical behavior, which is more consistent with various phenomena observed in clinical research, attitude studies, and intelligence research. We also discuss equivalence with existing statistical approaches (multidimensional nominal response model, IRT trees) for these data types. Finally, we present new R packages for fitting the Blume Capel model to psychological data.
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