Drawing movements have been shown to comply with a power law constraining local curvature and instantaneous speed. In particular, ellipses have been extensively studied, enjoying a 2/3 exponent. While the origin of such a non-trivial relationship remains debated, it has been proposed to be an outcome of the least action principle whereby mechanical work is minimized along 2/3 power law trajectories

Multisensory information can benefit perceptual, memory, and decision-making processes. These benefits commonly manifest in superior detection and discrimination of multisensory stimuli, as well as improved perception and subsequent memory of unisensory representation of an object previously encoded in a multisensory context. However, the vast majority of studies to date analyze accuracy, sensitivity

Gaussian graphical models (GGM; partial correlation networks) have become increasingly popular in the social and behavioral sciences for studying conditional (in)dependencies between variables. In this work, we introduce exploratory and confirmatory Bayesian tests for partial correlations. For the former, we first extend the customary GGM formulation that focuses on conditional dependence to also consider

In recent years two classes of knowledge structures received particular attention. They are, respectively, forward-graded and backward-graded knowledge structures. Their importance is related to the fact that the basic local independence model applied to such structures turns out to be locally unidentifiable. Spoto et al. (2012) established some sufficient conditions for a skill multimap to delineate

Integrating information across our various sensory modalities results in striking behavioral benefits. This integration depends on a variety of factors, among which are the effectiveness of the stimuli and the relative timing between them. Both of these factors physically vary as a function of the distance between stimuli and the observer: intensity decreases as a function of distance for both auditory

I provide a characterization of weakly pseudo-rationalizable choice functions – that is, choice functions rationalizable by a set of acyclic relations – in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity

Building intelligent tutoring systems (ITSs) that are aware of the students’ misconceptions has been one of the ambitions for many of the approaches to computerized assessment of knowledge and learning. In the present article we extend knowledge space theory (KST) to mistakes and misconceptions. The proposed approach completes and extends the work initiated by J. Lukas (1997, Modellierung von Fehlkonzepten

In a simple reaction time task in which auditory and visual stimuli are presented in random sequence alone (A or V) or together (AV), there is a so-called reaction time (RT) cost on trials in which sensory modality switches (A→V) compared to when it repeats (A→A). This is always true for unisensory trials, whereas RTs to AV stimuli preceded by unisensory stimuli are statistically comparable with the

Nilsson, Rieskamp, and Wagenmakers (2011) implemented a hierarchical Bayesian estimation procedure for cumulative prospect theory (CPT; Tversky and Kahneman (1992)). Nilsson et al. used a simplified version of CPT that holds for choice options with mixed outcomes, that is, one positive and one negative payoff. However, for choice options with only gains or only losses, the model specification does

Use of Multinomial Processing Tree (MPT) models is illustrated by fitting one to data of Dhir (2017). Her experiment examined age and association type in a paired-associate recall task. Age and Pair-Type had interactive effects on probability of a correct response. A natural interpretation of the interaction would be that both factors impact the same mental process. However, fitting an MPT leads to

Information processing underlying human perceptual decision-making is inherently noisy and identifying sources of this noise is important to understand processing. Ratcliff, Voskuilen, and McKoon (2018) examined results from five experiments using a double-pass procedure in which stimuli were repeated typically a hundred trials later. Greater than chance agreement between repeated tests provided evidence

Multinomial processing tree (MPT) models are commonly used in cognitive psychology to disentangle and measure the psychological processes underlying behavior. Various estimation approaches have been developed to estimate the parameters of MPT models for a group of participants. These approaches are implemented in various programs (e.g., MPTinR, TreeBUGS) and differ with regard to how data are pooled

This paper introduces the bi-separability of items in knowledge structures as a bidirectional separability of items. Let (Q,K) be the knowledge structure delineated by the skill multimap (Q,S,μ). This paper gives some necessary and sufficient conditions, expressed in terms of competencies of μ, ensuring that (Q,K) is discriminative (resp. bi-discriminative), which generalizes the discussion of the

Audiovisual integration can facilitate speech comprehension by integrating information from lip-reading with auditory speech perception. When incongruent acoustic speech is dubbed onto a video of a talking face, this integration can lead to the McGurk illusion of hearing a different phoneme than that spoken by the voice. Several computational models of the information integration process underlying

The cardinal secretary search problem confronts the decision maker with more or less candidates who have identically and independently distributed values and appear successively in a random order without recall of earlier candidates. Its benchmark solution implies monotonically decreasing sequences of optimal value aspirations (acceptance thresholds) for any number of remaining candidates. We compare

In a variety of real-world forecasting contexts, researchers have demonstrated that the unweighted average forecast is reasonably accurate and difficult to improve upon with more complex, model-based aggregation methods. We investigate this phenomenon by systematically examining the relationship between individual forecaster characteristics (e.g., bias, consistency) and aspects of the criterion being

Writing ξs(x) for the stimulus intensity judged greater (louder, heavier, brighter) than stimulus intensity x with criterion s, Iverson (2006b) proposed a law of similarity ξs(λx)=γ(λ,s)ξη(λ,s)(x) to model the dependence of ξs(x) on x. This model, which has η(λ,s) and γ(λ,s) as parameters, is quite general and may be applied in a number of situations in psychophysics. Iverson (2006b) analyzed this

Forecasts are generated by both human experts and statistical models, and their forecast accuracy can be understood using error decompositions. However, the assumptions that underlie decompositions used in the analysis of human error differ substantially from those used in the analysis of models. The lens model, one of the most popular error decompositions for human errors, treats the beliefs of the

The ACT-R cognitive architecture is a computational framework for developing, simulating and testing comprehensive theories of cognition. By far, the most common method of evaluating ACT-R models involves generating predictions through Monte Carlo simulation and comparing those predictions to aggregated human data. This approach has several limitations, including computational inefficiency, the potential

Invariant item ordering refers to the statement that if one item is harder than another for one person, then it is harder for all people. Whether item ordering holds is a psychological statement because it describes how people may qualitatively vary. Yet, modern item response theory (IRT) makes an a priori commitment to item ordering. The Rasch model, for example, posits that items must order. Conversely

In traditional multinomial processing tree (MPT) models for aggregate frequency data, parameters have usually been validated by means of experimental manipulations, thereby testing selective effects of discrete independent variables on specific model parameters. More recently, hierarchical MPT models which account for parameter heterogeneity between participants have been introduced. These models offer

The purpose of this paper is to formally outline a sequence of propositions that describe the connections between five linearly additive measurement error models commonly used in disciplines from psychometrics and test theory to economics to epidemiology, and one new model formerly proposed in Kroc & Zumbo (2018). We show that although these models are deceptively similar in their general algebraic

Complementary symmetry was derived before under particular theories, and used to test those. Progressively general results were published. This paper proves the condition in full generality, providing a one-line proof, and shedding new light on its empirical implications.

The detection response task (DRT) is a measure of workload that can assess the cognitive demands of real-world multitasking. It can be configured to present simple stimuli of several modalities, including auditory and visual signals. However, the concurrent presentation of the DRT stimuli alongside another task could cause dual-task interference, and the extent of this interference could be different

Multinomial processing tree (MPT) models are a class of stochastic models for categorical data that have recently been extended to account for heterogeneity in individuals by assuming separate parameters per participant. These extensions enable the estimation of correlations among model parameters and correlations between model parameters and external covariates. The present study compares different

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

Stephens, Matzke, and Hayes (SMH; 2019) used state-trace analysis to re-analyze databases of studies of reasoning and category learning. They found that many behavioral dissociations that had been viewed as support for distinct cognitive processes (or systems) were consistent with the operation of only one latent psychological variable. Ashby (2019) discussed several concerns about the application

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

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

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

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

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

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

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

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

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

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

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

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,

In a matching test, a test taker is presented with a list of test items and a list of response alternatives and asked to match each response alternative with a test item. The response alternatives can be given as a response to at most one test item. As a result, the response a test taker offers to one test item depends on his or her responses to all of the other test items. This violates the “local

We model word-list learning over sequences of immediate and delayed free recall tasks to study the impact of memory impairment on episodic memory. We use a previously developed Multinomial Processing Tree (MPT) model of encoding, retrieval, and learning (Alexander et al., 2016), and apply it to behavioral data from thousands of patients tested tens of thousands of times in a cognitive disorders clinic

Stimulated by William H. Batchelder’s seminal contributions in the 1980s and 1990s, multinomial processing tree (MPT) modeling has become a powerful and frequently used method in various research fields, most prominently in cognitive psychology and social cognition research. MPT models allow for estimation of, and statistical tests on, parameters that represent psychological processes underlying responses

Circular data are encountered throughout a variety of scientific disciplines, such as in eye movement research as the direction of saccades. Motivated by such applications, mixtures of peaked circular distributions are developed. The peaked distributions are a novel family of Batschelet-type distributions, where the shape of the distribution is warped by means of a transformation function. Because

In the redundant signals task, participants respond, in the same way, to stimuli of several sources, which are presented either alone or in combination (redundant signals). The responses to the redundant signals are typically much faster than to the single signals. Several models explain this effect, including race and coactivation models of information processing. Race models assume separate channels

Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a

The basic local independence model (BLIM) is one of the most widely applied probabilistic models in knowledge space theory. It is known that the BLIM is not identifiable in general and that its identifiability strictly depends on the properties of the knowledge structure to which it is applied. If the knowledge structure is either forward- or backward-graded in one or more items, then the BLIM is not