Mixed-Effects Regression Weights for Advice Taking and Related Phenomena of Information Sampling and Utilization

Abstract

Advice taking and related research are dominated by deterministic weighting indices such as ratio-of-differences-based formulas for investigating informational influence. They are intuitively simple but entail various measurement problems and restrict research to a certain paradigmatic approach. As a solution, we propose process-consistent mixed-effects regression modeling for specifying how strongly peoples’ judgment is influenced by external information. Our formal derivation of the proposed weighting measures is accompanied by a detailed elaboration on their most important technical and statistical subtleties. Essentially, the approach differentiates between components of endogenous (i.e., final judgment) and exogenous (e.g., initial judgment and advice) nature by relying on accordingly specified multilevel models. Corresponding mixed-effects regression coefficients of various exogenous sources of information hence also reflect individual weighting but are based on a conceptually consistent representation of the endogenous judgment process. We use this modeling approach to revisit empirical findings from sequential collaboration and advice taking paradigms. Specifically, whereas we do not obtain evidence for systematic order effects in sequential collaboration, we document recency effects in the weighting of sequentially sampled advice. We argue that process-consistent modeling of information sampling and utilization has the potential to increase the replicability of our science and opens up new avenues for innovative research. Moreover, the proposed method is relevant beyond sequential collaboration and advice taking. Mixed-effects regression weights can also inform research on related cognitive phenomena such as multidimensional belief updating, anchoring effects, hindsight biases, or attitude change.

Mixed‐effects regression weights for advice taking and related phenomena of information sampling and utilization

“…Descriptively, however, advice of intermediate distance, $$$ {A}_2 $$$, was on average weighted somewhat more strongly than relatively close advice, $$$ {A}_1 $$$, which again was weighted somewhat more strongly than relatively distant advice, $$$ {A}_3 $$$. This finding is in line with empirical evidence for an inverse‐U‐shaped relation between advice distance and weighting, where advice of intermediate distance is weighted the most both according to ROD‐WOA in the traditional paradigm (Moussaïd et al, 2013; Schultze et al, 2015), as well as according to separate MER‐WOAs of sequentially sampled advice (Rebholz, 2023, Chapter 4).…”

“…Compared to the inter‐individual differences in advice weighting $$$ {\hat{\tau}}_{A_k,S} $$$, there was notably less variability for different items as measured by $$$ {\hat{\tau}}_{A_k,T} $$$. Also in comparison to other judgment tasks, such as product carbon footprint or quantity estimation (Rebholz & Hütter, 2022; see also Rebholz, 2023, Chapter 3, for MER‐WOAs), the differences between items were rather negligible. In contrast to the item‐wise random effects, we indeed found significant differences between some of the participant‐wise random effects.…”

“…Often people combine different sources of information in a nonlinear way (e.g., Ganzach, 1995, for clinical judgment). Actually, ROD‐WOA usually features an inverse‐U‐shaped relation with advice distance in many empirical studies: Close and more distant advice is typically taken less than advice of “intermediate” distance (Hütter & Ache, 2016; Moussaïd et al, 2013; Rebholz, 2023; Schultze et al, 2015). As the regression framework allows to incorporate any number and type of additional predictors at any level, researchers no longer have to assume linear processing of advice for calculating the weights.…”

Bayesian Advice Taking: Adaptive Strategy Selection in Sequential Advice Seeking

“…Weighted averaging is more in line with Information Integration Theory according to which the "diagnosticity" of a certain piece of advice is proportional to its serial positioning in the sample (Anderson, 1971;Shanteau, 1970Shanteau, , 1972. The multilevel regression-based model of Rebholz et al (2023) enables the estimation of individual weights per individually sampled advice despite the lack of intermediate judgments. Instead of implicitly imposing equal-weighting constraints, they propose a multilevel modeling framework for "estimating" advice-or advisor-specific weights as sampling-related deviations (i.e., random effects) from the overall weighting tendency (i.e., fixed effect; Bates et al, 2015;Brown et al, 2018;Raudenbush & Bryk, 2002).…”

“…Specifically, also relatively small shifts from E 0 are still better described by choosing-self 7 Sum-to-one constraining implies that the Bayesian account does not allow for over-or underweighting of advice. Therefore, Bayesian updating has similar conceptual problems as the ratio-of-differences formula (see Equation 5) with absolute distances or post-hoc truncation to the [0, 1] interval (Rebholz et al, 2023).…”