On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.     

Transformation of a three-mode multidimensional scaling solution to indscal form

Relations between Tucker's three-mode multidimensional scaling and Carroll and Chang's INDSCAL are discussed. The possibility is raised that it may be profitable to attempt to transform a three-mode solution to the general form of an INDSCAL solution. Operationally, this involves transforming the three-mode core matrix so that each section is, as nearly as possible, a diagonal matrix. A technique is developed for accomplishing such a transformation, and is applied to two sets of data from the literature. Results indicate that the process is both feasible and valuable, providing useful information on the relative appropriateness of the two models.     

How a high working memory capacity can increase proactive interference

Previous findings suggested that a high working memory capacity (WMC) is potentially associated with a higher susceptibility to proactive interference (PI) if the latter is measured under high cognitive load. To explain such a finding, we propose to consider susceptibility to PI as a net effect of individual executive processes and the intrinsic potential for PI. With the latter, we refer to the amount of information that is activated at a given time and that has the potential to exert PI subsequently. In two studies deploying generalized linear mixed models, susceptibility to PI was modeled as the decline of performance over trials of a complex span task. The results revealed that a higher WMC was associated with a higher susceptibility to PI. Moreover, the number of stimuli recalled in one trial as a proxy variable for the intrinsic potential for PI negatively affected memory performance in the subsequent trial.     

Simulation of Preference Information in an Interactive Reference Point‐Based Method for the Bi‐Objective Inventory Routing Problem

In the research area of multiple criteria decision making, very few publications exist that explicitly design the simulation of a decision maker (DM) in an interactive approach. For this reason, we outline some methods widely used in the literature to identify common assumptions of simulating the DM's responses and the required input preference information. Our paper aims at covering the identified gap by introducing experimental concepts. Such concepts are used for theoretical analyses of a combined search‐and‐decision‐making procedure. Simulating the DM is a fruitful idea because the algorithm can be tested without integrating a human decision maker. Finally, we conduct experiments based on the proposed settings for a multiobjective inventory routing problem, which is a relevant and challenging logistic problem. Copyright © 2014 John Wiley & Sons, Ltd.     

A note on computing Louis’ observed information matrix identity for IRT and cognitive diagnostic models

Using Louis’ formula, it is possible to obtain the observed information matrix and the corresponding large-sample standard error estimates after the expectation–maximization (EM) algorithm has converged. However, Louis’ formula is commonly de-emphasized due to its relatively complex integration representation, particularly when studying latent variable models. This paper provides a holistic overview that demonstrates how Louis’ formula can be applied efficiently to item response theory (IRT) models and other popular latent variable models, such as cognitive diagnostic models (CDMs). After presenting the algebraic components required for Louis’ formula, two real data analyses, with accompanying numerical illustrations, are presented. Next, a Monte Carlo simulation is presented to compare the computational efficiency of Louis’ formula with previously existing methods. Results from these presentations suggest that Louis’ formula should be adopted as a standard method when computing the observed information matrix for IRT models and CDMs fitted with the EM algorithm due to its computational efficiency and flexibility.     

Adversary effects and the tactics of violent offenders

We examine the implication of adversary effects for target choice, lethal intent, and the use of weapons and allies in violent incidents. Adversary effects refer to the tendency of offenders to make tactical decisions based on the coercive power of victims and potential victims. Using the victim's gender as a proxy for coercive power, we analyzed violent incidents from the National Incident‐Based Reporting System (2005–2014). The sample included over six million assaults, robberies, and homicides. Consistent with adversary effects, offenders who attack males (vs. females) are more likely to (a) kill victims; (b) use guns, knives, blunt objects, poison, and automobiles; (c) use male (but not female) allies; and (d) use multiple allies. The evidence for target choice is mixed: unarmed female offenders, but not unarmed male offenders, are more likely to target females than males. The evidence shows how a simple theoretical principle can parsimoniously account for basic patterns of violence in society related to gender, weapons, and group violence.     

Discerning Mouse Trajectory Features With the Drift Diffusion Model

Mouse tracking, a new action-based measure of behavior, has advanced theories of decision making with the notion that cognitive and social decision making is fundamentally dynamic. Implicit in this theory is that people's decision strategies, such as discounting delayed rewards, are stable over task design and that mouse trajectory features correspond to specific segments of decision making. By applying the hierarchical drift diffusion model and the Bayesian delay discounting model, we tested these assumptions. Specifically, we investigated the extent to which the “mouse-tracking” design of decision-making tasks (delay discounting task, DDT and stop-signal task, SST) deviate from the standard “keypress” design of decision making tasks. We found remarkable agreement in delay discounting rates (intertemporal impatience) obtained in the keypress and mouse-tracking versions of DDT (ρ = 0.90) even though these tasks were given about 1 week apart. Rates of evidence accumulation converged well in the two versions (DDT, ρ = .86; SST, ρ = .55). Omission/commission error in SST showed high agreement (ρ = .42, ρ = .53). Mouse-motion features such as maximum velocity and AUC (area under the curve) correlated well with nondecision time (ρ = −.42) and boundary separation (ρ = .44)—the amount of information needed to accumulate prior to making a response. These results indicate that the response time (RT) and motion-based decision tasks converge well at a fundamental level, and that mouse-tracking features such as AUC and maximum velocity do indicate the degree of decision conflict and impulsivity.     

Dynamics Versus Development in Numerosity Estimation: A Computational Model Accurately Predicts a Developmental Reversal

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model—a situation in which children's estimates of numerosity would be better than those of adults. Consistent with the model simulations, task contexts led to a clear developmental reversal: children made more adult-like, linear estimates when to-be-estimated numbers were descending over trials (i.e., backward condition), whereas adults became more like children with logarithmic estimates when numbers were ascending (i.e., forward condition). In addition, adults’ estimates were subject to inter-trial differences regardless of stimulus order. In contrast, children were not able to use the trial-to-trial dynamics unless stimuli varied systematically, indicating the limited cognitive capacity for dynamic updates. Together, the model adequately predicts both developmental and trial-to-trial changes in number-line tasks.     

Choosing what to choose from: Preference for inclusion over exclusion when constructing consideration sets from large choice sets

Decision making is a two‐stage process, consisting of, first, consideration set construction and then final choice. Decision makers can form a consideration set from a choice set using one of two strategies: including the options they wish to further consider or excluding those they do not wish to further consider. The authors propose that decision makers have a relative preference for an inclusion (vs. exclusion) strategy when choosing from large choice sets and that this preference is driven primarily by a lay belief that inclusion requires less effort than exclusion, particularly in large choice sets. Study 1 demonstrates that decision makers prefer using an inclusion (vs. exclusion) strategy when faced with large choice sets. Study 2 replicates the effect of choice set size on preference for consideration set construction strategy and demonstrates that the belief that exclusion is more effortful mediates the relative preference for inclusion in large choice sets. Studies 3 and 4 further support the importance of perceived effort, demonstrating a greater preference for inclusion in large choice sets when decision makers are primed to think about effort (vs. accuracy; Study 3) and when the choice set is perceived as requiring more effort because of more information being presented about each alternative (vs. more alternatives in the choice set; Study 4). Finally, Study 5 manipulates consideration set construction strategy, showing that using inclusion (vs. exclusion) in large choice sets leads to smaller consideration sets, greater confidence in the decision process, and a higher quality consideration set.     

What could be My Next Job? Using Flat Information Structures to Generate Creative Future Career Ideas

In a dynamic labor market, it is important to help people combine information and generate creative solutions to cope with complex career challenges. In the present research, we apply the theory of information structure to creative career idea generation and hypothesize that flat information structures—that is, structures in which the information is disorganized—are more conducive to creativity than hierarchical information structures—that is, structures in which information is organized in higher‐order categories. In two experimental studies, participants had to combine career information related to self and work preferences that was presented either in flat or hierarchical structures. We found that flat information structures, compared with hierarchical information structures, led to future career ideas that were more creative on average. Our results suggest that cognitive flexibility explains the effect of information structure on the creativity of career ideas. Theoretical implications and suggestions for career management practices are discussed.