Measuring the mixture of rule-based and exemplar-based processes in judgment: A hierarchical Bayesian approach.

Abstract

Based on theoretical and empirical considerations, Bröder et al. (2017) proposed the RulEx-J model to quantify the relative contribution of rule-and exemplar-based processes in numerical judgments. In their original article, a least-squares (LS) optimization procedure was used to estimate the model parameters. Despite general evidence for the validity of the model, the authors suggested that a strong bias in favoring the rule module could arise when there is noise in the data. In this article, we present a hierarchical Bayesian implementation of the RulEx-J model with the goal to rectify this problem. In a series of simulation studies, we demonstrate the ability of the hierarchical Bayesian RulEx-J model to recover parameters accurately and to be more robust against noise in the data, compared to an LS estimation routine. One further advantage of the hierarchical Bayesian approach is the direct implementation of hypotheses about group differences in the model structure. A validation experiment as well as reanalyses of two experiments from different labs demonstrate the usefulness of the approach for testing hypotheses about processing differences. Further applications for judgment research are discussed.

What is the airspeed velocity of an unladen swallow? modeling numerical judgments of realistic stimuli

“…As preregistered and as in the validation study, the judgment data were analyzed using the hierarchical Bayesian version of the RulEx-J model (Bröder, Gräf, & Kieslich, 2017 ; Izydorczyk, & Bröder , 2022 ) extended for continuous cues. The RulEx-J model proposes a continuous mixture between rule-based and exemplar-based processes in quantitative judgments.…”

“…The hierarchical Bayesian implementation of the RulEx-J model proposed in Izydorczyk and Bröder ( 2022 ) directly incorporates the difference in the parameter between two conditions via the parameter which reflects the differences of between both conditions on a standardized scale. Hence, it reflects the effect size of the fixed effect between experimental conditions.…”

“…1 by investigating whether the experimentally created attribute structure of artificial stimuli would be recovered by an MDS analysis (e.g., Nosofsky , 1989 ) and more importantly, whether the cues extracted from the MDS analysis could be used to model empirical judgment data. The judgment data we used for this purpose are data from the validation experiment reported in Izydorczyk and Bröder ( 2022 ), 3 where = 238 participants judged the selling price of 16 fictitious flowers that varied on four binary attributes (see Fig. 1 for some examples).…”

“…Building on the early classification and categorization literature, in this article we demonstrate in two studies how to combine multidimensional scaling analysis (MDS, Hout, Papesh, & Goldinger , 2013 ; Kruskal , 1964 ; Shepard , 1962 ) with a current state-of-the-art model for quantitative judgments to investigate the underlying processes of judgments of complex, natural stimuli where the cues are not known beforehand. We will use the cues extracted by a MDS to model data with the RulEx-J model (Bröder, Gräf, & Kieslich, 2017 ; Izydorczyk, & Bröder , 2022 ) which measures the relative contribution of rule- and exemplar-based processes. We will use different kinds of stimuli (simple artificial vs. complex and naturalistic) and manipulate different learning regimes (different information during judgment task vs. different tasks during learning) to affect the kind of processing people predominantly use.…”

“…Finally, a computational model (6) can be applied to judgment data (5), using the MDS dimensions as cues. The flowers are examples of stimuli used in Izydorczyk and Bröder ( 2022 ) …”