The structure of short-term memory scanning: an investigation using response time distribution models

A classic question in cognitive psychology concerns the nature of memory search in short-term recognition. Despite its long history of investigation, however, there is still no consensus on whether memory search takes place serially or in parallel or is based on global access. In the present investigation, we formalize a variety of models designed to account for detailed response time distribution data in the classic Sternberg (Science 153: 652-654, 1966) memory-scanning task. The models vary in their mental architectures (serial exhaustive, parallel self-terminating, and global access). Furthermore, the component processes within the architectures that make match/mismatch decisions are formalized as linear ballistic accumulators (LBAs). In fast presentation rate conditions, the parallel and global access models provide far better accounts of the data than does the serial model. LBA drift rates are found to depend almost solely on the lag between study items and test probes, whereas response thresholds change with memory set size. Under slow presentation rate conditions, even simple versions of the serial-exhaustive model provide accounts of the data that are as good as those of the parallel and global access models. We provide alternative interpretations of the results in our General Discussion.     

Hick's Law in a Stochastic Race Model with Speed-Accuracy Tradeoff

We present an analytic solution for a race model of n stochastic accumulators for multiple choice reaction time. We show that to maintain a constant level of accuracy, the response criterion needs to be increased approximately logarithmically with n, to compensate for the increase with n in the likelihood that an incorrect alternative will be most active after any fixed amount of time accumulating information. Assuming that participants monitor and maintain a constant level of performance can then explain the logarithmic dependency of the response latency on n as specified by Hick's law. Moreover, we show that for short time intervals, the Shannon information that observers extract from a stimulus, is predicted to increase linearly with processing time.     

Multi-attribute,multi-alternative models of choice: Choice,reaction time,and process tracing

The first aim of this research is to compare computational models of multi-alternative, multi-attribute choice when attribute values are explicit. The choice predictions of utility (standard random utility & weighted valuation), heuristic (elimination-by-aspects, lexicographic, & maximum attribute value), and dynamic (multi-alternative decision field theory, MDFT, & a version of the multi-attribute linear ballistic accumulator, MLBA) models are contrasted on both preferential and risky choice data. Using both maximum likelihood and cross-validation fit measures on choice data, the utility and dynamic models are preferred over the heuristic models for risky choice, with a slight overall advantage for the MLBA for preferential choice. The response time predictions of these models (except the MDFT) are then tested. Although the MLBA accurately predicts response time distributions, it only weakly accounts for stimulus-level differences. The other models completely fail to account for stimulus-level differences. Process tracing measures, i.e., eye and mouse tracking, were also collected. None of the qualitative predictions of the models are completely supported by that data. These results suggest that the models may not appropriately represent the interaction of attention and preference formation. To overcome this potential shortcoming, the second aim of this research is to test preference-formation assumptions, independently of attention, by developing the models of attentional sampling (MAS) model family which incorporates the empirical gaze patterns into a sequential sampling framework. An MAS variant that includes attribute values, but only updates the currently viewed alternative and does not contrast values across alternatives, performs well in both experiments. Overall, the results support the dynamic models, but point to the need to incorporate a framework that more accurately reflects the relationship between attention and the preference-formation process.     

Drawing conclusions from choice response time models: A tutorial using the linear ballistic accumulator

Cognitive models of choice and response times can lead to deeper insights into the processes underlying decisions than standard analyses of accuracy and response time data. The application of these models, however, has historically been reserved for the authors of the models, and their associates. Recently, choice response time models have become more accessible through the release of user-friendly software for estimating their parameters. The aim of this tutorial is to provide guidance about the process of using these parameter estimates and associated model fits to make conclusions about experimental data. We use an application of one response time model, the linear ballistic accumulator, as an example to demonstrate the steps required to select an appropriate parametric characterization of a data set. We also discuss how to evaluate the quality of the agreement between model and data, including guidelines for presenting model predictions for group-level data.     

A memory-based model of Hick's law

We propose and evaluate a memory-based model of Hick’s law, the approximately linear increase in choice reaction time with the logarithm of set size (the number of stimulus–response alternatives). According to the model, Hick’s law reflects a combination of associative interference during retrieval from declarative memory and occasional savings for stimulus–response repetitions due to non-retrieval. Fits to existing data sets show that the model accounts for the basic set-size effect, changes in the set-size effect with practice, and stimulus–response-repetition effects that challenge the information-theoretic view of Hick’s law. We derive the model’s prediction of an interaction between set size, stimulus fan (the number of responses associated with a particular stimulus), and stimulus–response transition, which is subsequently tested and confirmed in two experiments. Collectively, the results support the core structure of the model and its explanation of Hick’s law in terms of basic memory effects.     

Time and rate measures in choice transitions

Three experiments with pigeons studied the relation between time and rate measures of behavior under conditions of changing preference. Experiment 1 studied a concurrent chain schedule with random-interval initial links and fixed-interval terminal links; Experiment 2 studied a multiple chained random-interval fixed-interval schedule; and Experiment 3 studied simple concurrent random-interval random-interval schedules. In Experiment 1, and to a lesser extent in the other two experiments, session-average initial-link wait-time differences were linearly related to session-average response-rate differences. In Experiment 1, and to a lesser extent in Experiment 3, ratios of session-average initial-link wait times and response rates were related by a power function. The weaker relations between wait and response measures in Experiment 2 appear to be due to the absence of competition between responses. In Experiments 1 and 2, initial-link changes lagged behind terminal-link changes. These findings may have implications for the relations between fixed- and variable-interval procedures and suggest that more attention should be paid to temporal measures in studies of free-operant choice.     

Preference as a function of active interresponse times: a test of the active time model

In this article, we describe a test of the active time model for concurrent variable interval (VI) choice. The active time model (ATM) suggests that the time since the most recent response is one of the variables controlling choice in concurrent VI VI schedules of reinforcement. In our experiment, pigeons were trained in a multiple concurrent similar to that employed by Belke (1992), with VI 20-s and VI 40-s schedules in one component, and VI 40-s and VI 80-s schedules in the other component. However, rather than use a free-operant design, we used a discrete-trial procedure that restricted interresponse times to a range of 0.5-9.0 s. After 45 sessions of training, unreinforced probe periods were mixed with reinforced training periods. These probes paired the two stimuli associated with the VI 40-s schedules. Further, the probes were defined such that during their occurrence, interresponse times were either "short" (0.5-3.0 s) or "long" (7.5-9.0 s). All pigeons showed a preference for the stimulus associated with the relatively rich VI 40-s schedule--a result mirroring that of Belke. We also observed, though, that this preference was more extreme during long probes than during short probes--a result predicted by ATM.     

整合模型还是占优启发式模型? 从齐当别模型视角进行的检验

实验从齐当别模型的视角,通过对决策过程反应时的考察分别对以累积预期理论(cumulative prospect theory)为代表的整合模型和启发式模型家族的重要成员--占优启发式模型(priority heuristic)--进行检验。结果表明,决策过程反应时并未随着占优启发式模型所假定的决策步骤的增加而变慢;也未随着选项之间整体值差值的变大而变快;模糊决策过程的反应时反而快于风险决策过程的反应时。无论是以累积预期理论为代表的整合模型还是占优启发式模型均不能满意地描述和解释人们的实际决策过程,而齐当别模型则能解释大部分实验结果。文章建议多角度、多指标探讨人们的决策过程,检验、修改、完善,以及建立新的启发式模型或决策过程模型(process model),以增进对人们如何进行风险决策的理解。     

The time course of perceptual choice: the leaky, competing accumulator model

The time course of perceptual choice is discussed in a model of gradual, leaky, stochastic, and competitive information accumulation in nonlinear decision units. Special cases of the model match a classical diffusion process, but leakage and competition work together to address several challenges to existing diffusion, random walk, and accumulator models. The model accounts for data from choice tasks using both time-controlled (e.g., response signal) and standard reaction time paradigms and its adequacy compares favorably with other approaches. A new paradigm that controls the time of arrival of information supporting different choice alternatives provides further support. The model captures choice behavior regardless of the number of alternatives, accounting for the log-linear relation between reaction time and number of alternatives (Hick's law) and explains a complex pattern of visual and contextual priming in visual word identification.     

时间知觉在老年人跨期选择中的作用

随着人口老龄化速度的加快,老年人的跨期选择问题受到越来越多的关注。时间知觉是影响跨期选择的重要因素之一。然而,目前从时间知觉的角度来探讨老年人跨期选择的研究比较有限。本文在总结国内外相关研究的基础之上,试图分析时间知觉的随龄变化如何影响老年人的跨期选择。具体而言,本文从时间长度知觉、时间成本知觉以及时间知觉相关心理动机三个方面进行探讨,并指出了时间知觉视角的局限性及今后的研究方向。     

时间洞察力特质对食品选择偏好的影响:解释水平对内隐偏好的作用

探索两类时间洞察力特质个体外显与内隐食物选择偏好。实验1用《津巴多时间洞察力问卷》选出"现在享乐"和"未来定向"两类个体,考察其外显食物选择偏好,结果发现,与"未来定向"组相比,"现在享乐"个体选择更多垃圾食品。实验2中,两类个体分别接受不同的解释水平操作,之后完成单靶内隐联想测验,以考察其对垃圾食品的内隐态度,并检验解释水平的调节作用。结果发现,与未来定向组相比,现在享乐组对"垃圾食品"存在内隐偏好。此外,对现在享乐者,解释水平改变会对食物选择偏好有显著影响;而对未来定向者,其影响不显著。这表明与未来时间定向者比,现在享乐者在外显、内隐层面对"垃圾食品"有选择偏好,并且解释水平会通过改变心理距离对其内隐选择偏好产生影响。     

A tuned-trace theory of interval-timing dynamics

Animals on interval schedules of reinforcement can rapidly adjust a temporal dependent variable, such as wait time, to changes in the prevailing interreinforcement interval. We describe data on the effects of impulse, step, sine-cyclic, and variable-interval schedules and show that they can be explained by a tuned-trace timing model with a one-back threshold-setting rule. The model can also explain steady-state timing properties such as proportional and Weber law timing and the effects of reinforcement magnitude. The model assumes that food reinforcers and other time markers have a decaying effect (trace) with properties that can be derived from the rate-sensitive property of habituation (the multiple-time-scale model). In timing experiments, response threshold is determined by the trace value at the time of the most recent reinforcement. The model provides a partial account for the learning of multiple intervals, but does not account for scalloping and other postpause features of responding on interval schedules and has some problems with square-wave schedules.     

项目间多维测验作答时间数据分析：潜在特质速度间效应建模

随着计算机测验使用的普及化,被试在心理与教育测验上的作答反应时的获取也越发便利。为了充分利用项目反应时信息,单维与多维的反应时模型相继被提出。然后,在项目间多维反应时数据中,潜在特质速度之间可能存在共同关系（比如,层阶关系）,此时现有的反应时模型并不能适用。基于此,本研究提出了高阶对数正态反应时模型与双因子对数正态反应时模型。在模拟研究中,高阶对数正态反应时模型与双因子对数正态反应时模型的各参数都能被准确估计。在瑞文标准推理测验的三组测验项目的反应时数据中,双因子对数正态反应时模型表现出更为优秀的拟合效果,同时基于多个统计量说明了局部与全局潜在特质速度同时存在的必要性。因此,在项目间多维测验反应时数据分析中,非常有必要考虑多维潜在特质速度之间的共同效应。     

Bounded Ornstein-Uhlenbeck models for two-choice time controlled tasks

The Ornstein-Uhlenbeck (O-U) model has been successfully applied to describe the response accuracy and response time in 2-alternative choice tasks. This paper analyses properties and performance of variants of the O-U model with absorbing and reflecting boundary conditions that limit the range of possible values of the integration variable. The paper focuses on choice tasks with pre-determined response time. The type of boundary and the growth/decay parameter of the O-U model jointly determine how the choice is influenced by the sensory input presented at different times throughout the trial. It is shown that the O-U models with two types of boundary are closely related and can achieve the same performance under certain parameter values. The value of the growth/decay parameter that maximizes the accuracy of the model has been identified. It is shown that when the boundaries are introduced, the O-U model may achieve higher accuracy than the diffusion model. This suggests that given the limited range of the firing rates of integrator neurons, the neural decision circuits could achieve higher accuracy employing leaky rather than linear integration in certain tasks. We also propose experiments that could distinguish between different models of choice in tasks with pre-determined response time.     

时间感知差异对跨期选择倾向的影响作用

本研究从人格特质差异角度出发, 采用简单跨期选择任务考察了由时距复制任务筛选的两类时距估计倾向不同的群体(时间高估者和时间低估者)在跨期选择中行为倾向的差异, 旨在探讨时间感知在跨期决策中的影响作用。结果发现：(1)无论任务难易, 与时间低估者相比, 时间高估者在跨期选择时更倾向于选择即时兑现的较小奖赏。(2)时间高估者和低估者的跨期选择反应时没有明显的差异, 但二者的反应时受任务难度的影响程度明显不同, 时间高估者的跨期选择反应时不受任务难度的影响, 而时间低估者在任务困难时的反应时比任务容易时明显增长。这些结果表明, 在跨期选择过程中, 时间感知倾向差异明显地影响了个体的选择倾向。时间高估倾向个体对时距的高估可能会导致其在跨期选择权衡中对收益成本的高估, 进而做出冲动的选择行为。     

Hick’s law equivalent for reaction time to individual stimuli

Hick’s law, one of the few law-like relationships involving human performance, expresses choice reaction time as a linear function of the mutual information between the stimulus and response events. However, since this law was first proposed in 1952, its validity has been challenged by the fact that it only holds for the overall reaction time (RT) across all the stimuli, and does not hold for the reaction time (RT_i) for each individual stimulus. This paper introduces a new formulation in which RT_i is a linear function of (1) the mutual information between the event that stimulus i occurs and the set of all potential response events and (2) the overall mutual information for all stimuli and responses. Then Hick’s law for RT follows as the weighted mean of each side of the RT_i equation using the stimulus probabilities as the weights. The new RT_i equation incorporates the important speed–accuracy trade-off characteristic. When the performance is error-free, RT_i becomes a linear function of two entropies as measures of stimulus uncertainty or unexpectancy. Reanalysis of empirical data from a variety of sources provide support for the new law-like relationship.     

On choosing between movement sequences: comments on Rose (1988)

One method of investigating human motor programming is to determine how the choice reaction time for a memorized response sequence depends on the composition of that sequence as well as the other sequence that may be required. Using this method, Rose (1988) found that the total number of responses in the two possible response sequences predicts the choice reaction time to initiate either one. On the basis of this result, Rose claimed that the hierarchical editor (HED) model of motor programming, developed by Rosenbaum, Inhoff, and Gordon (1984), may have to be reevaluated. In this commentary I argue that Rose's results are inconsistent with a precursor of the HED model, not with the HED model itself, that the HED model actually provides a better fit to Rose's data than her total-number-of-responses model, that in general, choice reaction time does not increase with the total number of possible responses, and that structural relations between alternative movement sequences are the main determinants of choice reaction time. Taken as a whole, the results suggest that possible responses are not held in completely readied form before being selected for execution. A further implication is that the storage capacity of the motor output buffer (the MOB) is extremely limited.     

Bayes factors for the linear ballistic accumulator model of decision-making

Evidence accumulation models of decision-making have led to advances in several different areas of psychology. These models provide a way to integrate response time and accuracy data, and to describe performance in terms of latent cognitive processes. Testing important psychological hypotheses using cognitive models requires a method to make inferences about different versions of the models which assume different parameters to cause observed effects. The task of model-based inference using noisy data is difficult, and has proven especially problematic with current model selection methods based on parameter estimation. We provide a method for computing Bayes factors through Monte-Carlo integration for the linear ballistic accumulator (LBA; Brown and Heathcote, 2008), a widely used evidence accumulation model. Bayes factors are used frequently for inference with simpler statistical models, and they do not require parameter estimation. In order to overcome the computational burden of estimating Bayes factors via brute force integration, we exploit general purpose graphical processing units; we provide free code for this. This approach allows estimation of Bayes factors via Monte-Carlo integration within a practical time frame. We demonstrate the method using both simulated and real data. We investigate the stability of the Monte-Carlo approximation, and the LBA’s inferential properties, in simulation studies.