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.     

Choice, time allocation, and response rate during stimulus generalization

Six pigeons were trained to discriminate between two noise intensities using a procedure that assessed choice, time allocation, and response rate simultaneously and independently. Responses on the left or right key (R1 or R2) were respectively correct in the presence of two different intensities, S1 and S2. After a correct response, reinforcement became available for pecks on the center key. Reinforcement density for R1¦S1 relative to R2¦S2 was varied across experimental conditions. Generalization tests followed extensive training at each condition. As a function of stimulus intensity, proportions of initial choices of R2, of time spent in R2-initiated components, and of center-key responses emitted in R2-initiated components all yielded sigmoidal gradients of similar slope, which shifted slightly in location when relative reinforcement density changed. Changeovers were maximal where initial choice proportions approximated 0.5. Gradients relating the absolute number of center-key responses to stimulus intensity were also roughly sigmoidal, but were more sensitive to changes in reinforcement density. Gradients of momentary response rate also depended on reinforcement density. During training, large but transitory shifts in choice responding occurred when reinforcement density changed, while differences in momentary response rate developed slowly, suggesting separate control of choice and response rate by the contingencies of reinforcement.     

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.     

The effect of rearing environments on the contrafreeloading phenomenon in rats

Eight naive rats were reared in enriched or impoverished environments for 39 days after weaning and then lived in operant chambers, in which they could obtain food pellets freely or by lever pressing, for 25 or 30 days. The animals raised in an impoverished environment acquired the bar-press response quickly when placed in the operant chambers and maintained a preference for obtaining food via bar pressing. Animals raised in an enriched environment did not learn to lever press, as demonstrated by low levels of responding and the lack of bar pressing when free food was subsequently removed. It was concluded that restricting animals' postweaning environments facilitated learning in a choice situation, probably because of increased activity levels. The results are interpreted in relation to previous studies on rearing environments and on contrafreeloading.     

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.     

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.     

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.     

Adaptations in driver deceleration behaviour with automatic incident detection: A naturalistic driving study

Traffic congestion and crash rates can be reduced by introducing variable speed limits (VSLs) and automatic incident detection (AID) systems. Previous findings based on loop detector measurements have revealed that drivers reduce their speeds while approaching traffic congestion when the AID system is active. Notwithstanding these behavioural effects, most microscopic traffic flow models assessing the impact of VSLs do not describe driver response accurately.This study analyses the main factors that influence driver deceleration behaviour while approaching traffic congestion with and without VSLs. The Dutch VSL database was linked to the driver behaviour data collected in the UDRIVE naturalistic driving study. Driver engagement in secondary tasks and glance behaviour were extracted from the video data. Linear mixed-effects models predicting the characteristics of deceleration events were estimated.The results show that the maximum deceleration is high when approaching a slower leader, when driving at high speeds and short distance headways, and close to the beginning of traffic congestion. The minimum time headway is short when driving at high speeds and changing lanes. Certain drivers showed higher decelerations and shorter time headways than others. Controlled for these main factors, smaller maximum decelerations were found when the VSLs were present and visible, and when the gantries were within close proximity. These factors could be incorporated into microscopic traffic simulations to evaluate the impact of AID systems on traffic congestion more realistically. Further research is needed to clarify the link between engagement in secondary tasks, glance behaviour and deceleration behaviour.     

Trust and intention to use autonomous vehicles: Manufacturer focus and passenger control

Autonomous Vehicle (AV) research has focused on public acceptance of and intention to use AVs, with trust emerging as important to these variables. Research on AV trust has centered on trust in vehicle performance. However, trust evaluation may include AV manufacturers and developers, and regulation pertaining to AVs; thus, we expand our measurement of trust to include beliefs based on manufacturers and regulation. In this experiment, we manipulate information regarding manufacturer focus (i.e., an emphasis on standards, regulations, and research (SRR) versus speed to market) to determine its effect on trust. When information focused on SRR, we found higher levels of trust in AV performance and in manufacturers, compared to when it focused on speed to market. In addition, information regarding passenger control (i.e., the ability to take over for the vehicle and to determine privacy settings) was manipulated to yield either high or low passenger control conditions. Behavioral Intention (BI) to use AVs was lowest when speed to market was emphasized and when passenger control was low. Furthermore, trust was tested as a mediator between perceived risk and BI. Trust in AV performance partially mediated the relationship between perceived AV performance risk and BI. In addition, trust in AV regulation partially mediated the relationship between AV privacy/security risk and BI. Researchers should continue to examine trust beyond the AV itself to encompass trust in manufacturers and regulations. Those designing and marketing AVs should carefully consider decisions that influence manufacturer/developer reputation and passenger control due to their effect on intention to use AVs.