Hierarchical Bayesian Modeling: Does it Improve Parameter Stability?

Fitting multi-parameter models to the behavior of individual participants is a popular approach in cognitive science to measuring individual differences. This approach assumes that the model parameters capture psychologically meaningful and stable characteristics of a person. If so, the estimated parameters should show, to some extent, stability across time. Recently, it has been proposed that hierarchical procedures might provide more reliable parameter estimates than nonhierarchical procedures. Here, we examine the benefits of hierarchical parameter estimation for assessing parameter stability using Bayesian techniques. Using the transfer-ofattention-exchange model (TAX; Birnbaum & Chavez, 1997), a highly successful account of risky decision making, we compare parameter stability based on hierarchically versus non-hierarchically estimated parameters. Surprisingly, we find that parameter stability for TAX is not improved by using a hierarchical Bayesian as compared to a nonhierarchical Bayesian approach. Further analyses suggest that this is because the shrinkage induced by hierarchical estimation overcorrects for extreme yet reliable parameter values. We suggest that the benefits of hierarchical techniques may be limited to particular conditions, such as sparse data on the individual level or very homogenous samples.