The measurement of individual differences in cognitive processes and the advancement of multinomial processing tree (MPT) models were two of William H. Batchelder’s major research interests. Inspired by his work, we investigated developmental differences between 7-year-old children, 10-year-old children, and young adults, in free recall with the pair-clustering model by Batchelder and Riefer (1980

The validity of survey-based reports of social relationships is a critical assumption for much social network research. Research on informant accuracy has shown that observational data and recalled behavior by informants are imperfectly correlated, which calls into question whether complex relations like friendship and advice-seeking can be accurately measured from individual reports. A class of network

The Extended Condorcet Model allows us to explore interindividual consensus concerning culturally held knowledge. Also, it enables a process-level description of interindividual differences in the knowledge a person has of the consensus, their willingness to guess in the absence of knowledge, and their bias in guessing. These person-specific characteristics might be tied to one’s everyday life experiences

In many forensic psychiatric hospitals, patients’ mental health is monitored at regular intervals. Typically, clinicians score patients using a Likert scale on multiple criteria including hostility. Having an overview of patients’ scores benefits staff members in at least three ways. First, the scores may help adjust treatment to the individual patient; second, the change in scores over time allows

We aim to provide a theoretical framework to explain the discrete transitions of mood connecting ideas from network theory and dynamical systems theory. It was recently shown how networks (graphs) can be used to represent psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could transition into a depression. To analyse changes

We consider a situation in which a group of respondents answers a set of questions and the aim is to identify any consensus among the respondents—that is, shared attitudes, beliefs, or knowledge. Consensus theory postulates that a latent trait determines the respondents’ probability to produce the consensus response. We propose a new version of the variable-response model, which implements consensus

To study linguistically coded concepts, researchers often resort to the Property Listing Task (PLT). In a PLT, participants are asked to list properties that describe a concept (e.g., for DOG, subjects may list “is a pet”, “has four legs”, etc.), which are then coded into property types (i.e., superficially dissimilar properties such as “has four legs” and “is a quadruped” may be coded as “four legs”)

Kruschke’s EXIT model (Kruschke, 2001b) has been very successful in explaining a variety of learning phenomena by means of selective attention. In particular, EXIT produces learned predictiveness effects (Le Pelley and McLaren, 2003), the inverse base rate effect (Kruschke, 1996; Medin and Edelson, 1988), inattention after blocking (Beesley and Le Pelley, 2011; Kruschke and Blair, 2000), differential

The modeling of multinomial data has seen tremendous progress since Riefer and Batchelder’s (1988) seminal paper. One recurring challenge, however, concerns the availability of relative performance measures that strike an ideal balance between goodness of fit and functional flexibility. One approach to the problem of model selection is Normalized Maximum Likelihood (NML), a solution derived from the

This report continues our probe of the fundamental properties of elementary psychological processes. In the present instance, we first distinguish between descriptive and state–space based parallel race models. Then we show, engaging previous results on stochastic dominance in Theorem 1, that descriptive race models can be designed that predict either faster ‘right’ channels or faster ‘wrong’ channels

Reporting descriptive statistics requires rounding the results. Experienced researchers typically round the numbers to one or two decimals, following the APA manual. However, this general recommendation ignores the sample size and the instrument’s precision. Herein, expressions are derived that indicate how many decimals are reliable and so at what point the results should be rounded. The derivations

Anderson (1970) introduced two models that are at the core of artificial neural network models as well as cognitive mathematical models of memory. The first, a simple summation of items, represented as vectors, can support rudimentary item-recognition. The second, a heteroassociative model consisting of a summation of outer products between paired item vectors, can support cued recall of associations

The Linear Ballistic Accumulator (LBA: Brown and Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters. Modern approaches use hierarchical Bayesian models and Markov chain Monte-Carlo (MCMC) methods to estimate the posterior distribution of the parameters. Although

This paper explores the role of social preferences in a competitive framework. More precisely, we study other-regarding strategic models where agents show Rawlsian preferences and, therefore, they care about the best interest of the worst-off agent. The representation of preferences proposed is the most appropriate when the utilities of the agents are vector-valued and their components are not compensable

Category-based induction is an inferential mechanism that uses knowledge of conceptual relations in order to estimate how likely is for a property to be projected from one category to another. During the last decades, psychologists have identified several features of this mechanism, and they have proposed different formal models of it. In this article; we propose a new mathematical model for category-based

Active Inference is a theory arising from theoretical neuroscience which casts action and planning as Bayesian inference problems to be solved by minimizing a single quantity — the variational free energy. The theory promises a unifying account of action and perception coupled with a biologically plausible process theory. However, despite these potential advantages, current implementations of Active

Consumers’ preferences and choices are traditionally described by appealing to two classical tenets of rationality: transitivity and completeness. In 1971, Schmeidler proved a striking result on the interplay between these properties: On a connected topological space, a nontrivial bi-semicontinuous preorder is complete. Here we reformulate and extend this well-known theorem. First, we show that the

Ordered item response models that are in common use can be divided into three groups, cumulative, sequential and adjacent categories model. The derivation and motivation of the models is typically based on the assumed presence of latent traits or underlying process models. In the construction frequently binary models play an important role. The objective of this paper is to give motivations for the

In the free energy principle (FEP) proposed by Friston, it is supposed that agents seek to minimize the “surprise” – the negative log (marginal) likelihood of observations (i.e., sensory stimuli) – given the agents’ current belief. This is achieved by minimizing the free energy, which provides an upper bound on the surprise. The FEP has been applied to action selection in a framework called “active

Our ability to detect temporal asynchrony is sometimes an obstacle to multisensory integration. A seamless multisensory experience occurs when the temporal misalignment of two signals is within the allowance for subjective synchrony, referred to as the temporal window of integration (TWI). The TWI is most commonly measured with the temporal-order judgment task or the synchrony judgment task, which

The availability of signals from multiple senses is often beneficial for perceptual decisions. To study such benefits, models of multisensory decision-making are typically fed with the behavioural performance as measured separately with unisensory component signals. Critically, by doing so, the approach implicitly makes the so-called context invariance assumption, which states that processing of a

This paper develops a generalized framework which allows for the use of parametric classical test theory inference with non-normal models. Using the theory of natural exponential families and Bayesian theory of their conjugate priors, theoretical properties of test scores under the framework are derived, including a formula for parallel-test reliability in terms of the test length and a parameter of

This paper introduces a new solution concept for non-cooperative games in normal form with no ties and pure strategies: the Perfectly Transparent Equilibrium. The players are rational in all possible worlds and know each other’s strategies in all possible worlds — which, together, we refer to as Perfect Prediction. The anticipation of a player’s decision by their opponents is counterfactually dependent

Many models of response time that base choices on the first evidence accumulator to win a race to threshold rely on statistical independence between accumulators to achieve mathematical tractability (e.g., Brown and Heathcote, 2008; Logan et al., 2014; Van Zandt et al., 2000). However, it is psychologically plausible that trial-to-trial fluctuations can cause both positive correlations (e.g., variability

The response-time extended multinomial processing tree (RT-MPT; Klauer and Kellen, 2018) model class and its implementation (rtmpt; Hartmann et al., in press) in the programming language R enable one to estimate process-completion times and encoding plus motor-execution times along with the process probabilities of traditional multinomial processing tree (MPT) models via an MCMC algorithm in a hierarchical

Knowledge Space Theory (KST) aims at modeling the hierarchical relations between items or skills in a learning process. For example, when studying mathematics in school, students first need to master the rules of summation before being able to learn multiplication. In KST, the knowledge states of individuals are represented by means of partially ordered latent classes. In probabilistic KST models,

Modelling intentions in large groups is cognitively costly. Not alone must first order beliefs be tracked ('what does A think about X?'), but also beliefs about beliefs ('what does A think about B's belief concerning X?'). Thus linear increases in group size impose non-linear increases in cognitive processing resources. At the same time, however, large groups offer coordination advantages relative

In the redundant signals task, two target stimuli are associated with the same response. If both targets are presented together, redundancy gains are observed, as compared with single-target presentation. Different models explain these redundancy gains, including race and coactivation models (e.g., the Wiener diffusion superposition model, Schwarz, 1994, Journal of Mathematical Psychology, and the

A 3D shape of an object is N-fold rotational-symmetric if the shape is invariant for 360/N degree rotations about an axis. Human observers are sensitive to the 2D rotational-symmetry of a retinal image, but they are less sensitive than they are to 2D mirror-symmetry, which involves invariance to reflection across an axis. Note that perception of the mirror-symmetry of a 2D image and a 3D shape has

Bayesian nonparametric (BNP) models are becoming increasingly important in psychology, both as theoretical models of cognition and as analytic tools. However, existing tutorials tend to be at a level of abstraction largely impenetrable by non-technicians. This tutorial aims to help beginners understand key concepts by working through important but often omitted derivations carefully and explicitly

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices). For both representations, we describe a general Gibbs

Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and convex polyhedral set, or polytope. Polyhedral combinatorics have thus played a key role in studying the mathematical structure of these models. However, standard

One of the more principled methods of performing model selection is via Bayes factors. However, calculating Bayes factors requires marginal likelihoods, which are integrals over the entire parameter space, making estimation of Bayes factors for models with more than a few parameters a significant computational challenge. Here, we provide a tutorial review of two Monte Carlo techniques rarely used in

To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are characterized by long temporal correlations, and evidence used to make a present choice is often relevant to future decisions. To understand decision-making under

The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable and must be approximated using numerical methods. Here we provide a tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), a reliable and relatively straightforward

A fundamental challenge in cognitive neuroscience is to develop theoretical frameworks that effectively span the gap between brain and behavior, between neuroscience and psychology. Here, we attempt to bridge this divide by formalizing an integrative cognitive neuroscience approach using dynamic field theory (DFT). We begin by providing an overview of how DFT seeks to understand the neural population

The selective integration model of Tsetsos et al. (2016a) is a biologically motivated computational framework that aims to model intransitive preference and choice. Tsetsos et al. (2016a) concluded that a noisy system can lead to violations of transitivity in otherwise rational agents optimizing a task. We show how their model can be interpreted from a Fechnerian perspective and within a random utility

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common assumption of these models is that decision parameters, e.g., the rate of accumulation

Optimality studies and studies of decision-making in monkeys have been used to support a model in which the decision boundaries used to evaluate evidence collapse over time. This article investigates whether a diffusion model with collapsing boundaries provides a better account of human data than a model with fixed boundaries. We compared the models using data from four new numerosity discrimination

Perceptual decision making can be accounted for by drift-diffusion models, a class of decision-making models that assume a stochastic accumulation of evidence on each trial. Fitting response time and accuracy to a drift-diffusion model produces evidence accumulation rate and non-decision time parameter estimates that reflect cognitive processes. Our goal is to elucidate the effect of attention on visual

Accumulator models explain decision-making as an accumulation of evidence to a response threshold. Specific model parameters are associated with specific model mechanisms, such as the time when accumulation begins, the average rate of evidence accumulation, and the threshold. These mechanisms determine both the within-trial dynamics of evidence accumulation and the predicted behavior. Cognitive modelers

This paper provides an easy to follow tutorial on the free-energy framework for modelling perception developed by Friston, which extends the predictive coding model of Rao and Ballard. These models assume that the sensory cortex infers the most likely values of attributes or features of sensory stimuli from the noisy inputs encoding the stimuli. Remarkably, these models describe how this inference

Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a sample. The practical problems of such inference are substantial: the brain has limited data and restricted computational resources. But there is a more fundamental question:

Studies of the primate visual system have begun to test a wide range of complex computational object-vision models. Realistic models have many parameters, which in practice cannot be fitted using the limited amounts of brain-activity data typically available. Task performance optimization (e.g. using backpropagation to train neural networks) provides major constraints for fitting parameters and discovering

The development of mathematical models to characterize perceptual and cognitive processes dates back almost to the inception of the field of psychology. Since the 1990s, human functional neuroimaging has provided for rapid empirical and theoretical advances across a variety of domains in cognitive neuroscience. In more recent work, formal modeling and neuroimaging approaches are being successfully

Our understanding of cognition has been advanced by two traditionally nonoverlapping and non-interacting groups. Mathematical psychologists rely on behavioral data to evaluate formal models of cognition, whereas cognitive neuroscientists rely on statistical models to understand patterns of neural activity, often without any attempt to make a connection to the mechanism supporting the computation. Both

This special issue explores the growing intersection between mathematical psychology and cognitive neuroscience. Mathematical psychology, and cognitive modeling more generally, has a rich history of formalizing and testing hypotheses about cognitive mechanisms within a mathematical and computational language, making exquisite predictions of how people perceive, learn, remember, and decide. Cognitive

Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over 50 years. We propose, as an alternative, the use of the odds of a correct rejection of the null hypothesis to incorrect rejection. Both pre-experimental versions

W.K. Estes often championed an approach to model development whereby an existing model was augmented by the addition of one or more free parameters, and a comparison between the simple and more complex, augmented model determined whether the additions were justified. Following this same approach we utilized Estes' (1950) own augmented learning equations to improve the fit and plausibility of a win-stay-lose-shift

An inordinate amount of computation is required to evaluate predictions of simulation-based models. Following Myung et al (2007), we derived an analytic form expression of the REM model of recognition memory using a Fourier transform technique, which greatly reduces the time required to perform model simulations. The accuracy of the derivation is verified by showing a close correspondence between its

A half-century ago, at the dawn of the all-or-none learning era, Estes showed that finite Markov chains supply a tractable, comprehensive framework for discrete-change data of the sort that he envisioned for shifts in conditioning states in stimulus sampling theory. Shortly thereafter, such data rapidly accumulated in many spheres of human learning and animal conditioning, and Estes' work stimulated

Experimentation is ubiquitous in the field of psychology and fundamental to the advancement of its science, and one of the biggest challenges for researchers is designing experiments that can conclusively discriminate the theoretical hypotheses or models under investigation. The recognition of this challenge has led to the development of sophisticated statistical methods that aid in the design of experiments

A critical component of how we understand a mental process is given by measuring the effect of varying the workload. The capacity coefficient (Townsend & Nozawa, 1995; Townsend & Wenger, 2004) is a measure on response times for quantifying changes in performance due to workload. Despite its precise mathematical foundation, until now rigorous statistical tests have been lacking. In this paper, we demonstrate

Although a fully general extension of ROC analysis to classification tasks with more than two classes has yet to be developed, the potential benefits to be gained from a practical performance evaluation methodology for classification tasks with three classes have motivated a number of research groups to propose methods based on constrained or simplified observer or data models. Here we consider an

We present a predictive account on adaptive sequential sampling of stimulus-response relations in psychophysical experiments. Our discussion applies to experimental situations with ordinal stimuli when there is only weak structural knowledge available such that parametric modeling is no option. By introducing a certain form of partial exchangeability, we successively develop a hierarchical Bayesian

Computational Cognitive Neuroscience (CCN) is a new field that lies at the intersection of computational neuroscience, machine learning, and neural network theory (i.e., connectionism). The ideal CCN model should not make any assumptions that are known to contradict the current neuroscience literature and at the same time provide good accounts of behavior and at least some neuroscience data (e.g.,

The survivor interaction contrasts (SIC) is a powerful measure for distinguishing among candidate models of human information processing. One class of models to which SIC analysis can apply are the coactive, or channel summation, models of human information processing. In general, parametric forms of coactive models assume that responses are made based on the first passage time across a fixed threshold

Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models

Systems Factorial Technology is a powerful framework for investigating the fundamental properties of human information processing such as architecture (i.e., serial or parallel processing) and capacity (how processing efficiency is affected by increased workload). The Survivor Interaction Contrast (SIC) and the Capacity Coefficient are effective measures in determining these underlying properties,

Young men's errors in sexual perception have been linked to sexual coercion. The current investigation sought to explicate the perceptual and decisional sources of these social perception errors, as well as their link to risk for sexual violence. General Recognition Theory (GRT; [Ashby, F. G., & Townsend, J. T. (1986). Varieties of perceptual independence. Psychological Review, 93, 154-179]) was used