Hierarchical Bayesian Modeling: Does it Improve Parameter Stability?

摘要: Hierarchical Bayesian Modeling: Does it Improve Parameter Stability? Benjamin Scheibehenne (benjamin.scheibehenne@unibas.ch) Economic Psychology, Department of Missionsstrasse 62a 4055 Basel, Switzerland Thorsten Pachur (pachur@mpib-berlin.mpg.de) Center for Adaptive Rationality, Max Planck Institute Human Development, Lentzeallee 94 14195 Berlin, Germany Abstract Fitting multi-parameter models to the behavior individual participants is a popular approach in cognitive science measuring differences. This assumes that model parameters capture psychologically meaningful and stable characteristics person. If so, estimated should show, some extent, stability across time. Recently, has been proposed hierarchical procedures might provide more reliable parameter estimates than non- procedures. Here, we examine benefits estimation assessing using techniques. Using transfer-of- attention-exchange (TAX; Birnbaum & Chavez, 1997), highly successful account risky decision making, compare based on hierarchically versus non-hierarchically parameters. Surprisingly, find TAX not improved by as compared approach. Further analyses suggest this because shrinkage induced overcorrects extreme yet values. We techniques may be limited particular conditions, such sparse data level or very homogenous samples. Keywords: modeling; consistency; choice; transfer-of-attention- exchange Introduction In science, describing understanding develop with adjustable can fitted data. As are usually supposed represent aspects processing, they often used study, measure, describe differences between people. For illustration, consider cumulative prospect theory (CPT; Tversky Kahneman, 1992), one most prominent making under risk. According CPT, responses alternative (which lead different outcomes probabilities) function several factors including person’s sensitivity probability information her relative overweighting losses gains (“loss aversion”). model, both loss aversion quantified parameters, studies have employed CPT investigate how age (Harbaugh, Krause, Vesterlund, 2002), gender (e.g., Fehr-Duda, Gennaro, Schubert, 2006), personality (Pachur, Hanoch, Gummerum, 2010) affect making. Cognitive modeling thus allows decomposed into underlying components. individually measure relies assumption stability—that is, values person remain relatively invariant time (Yechiam Busemeyer, 2008). applies when where assumed people’s choices their underpinnings reflect preferences Ert, 2011). principle, however, possible people simply unsystematic variability (i.e., noise) rather characteristics. case, fitting would useful results obtained generalize beyond given task situation. Glockner (2012) found evidence temporal CPT: participants’ at each two separate experimental sessions were (moderately) correlated. But does finding also extend other making? And—more importantly—do conclusions regarding model’s depend estimated? Whereas traditionally independently single participant, recently achieved procedures, which exploit group-level distributions inform individual-level Gelman Hill, 2007; Lee Webb, 2005). Our goal whether affected statistical method obtain estimates. particular, against decision-making context. issue claimed better risk (Birnbaum, example, (2008) showed correctly violations gain–loss separability, coalescing,