Mixtures of peaked power Batschelet distributions for circular data with application to saccade directions
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): Kees Mulder, Irene Klugkist, Daan van Renswoude, Ingmar VisserAbstractCircular 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 the Inverse Batschelet distribution features an implicit inverse th...
Source: Journal of Mathematical Psychology - February 2, 2020 Category: Psychiatry & Psychology Source Type: research
Testing the race model in a difficult redundant signals task
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): Matthias Gondan, Dawa Dupont, Steven P. BlurtonAbstractIn 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 for the two components of a redundant signal, with the response time determine...
Source: Journal of Mathematical Psychology - January 27, 2020 Category: Psychiatry & Psychology Source Type: research
New Handbook of Mathematical Psychology: Volume I: Foundations and Methodology; Volume II: Modeling and Measurement (Cambridge Handbooks in Psychology), Batchelder William H., Colonius Hans, Dzhafarov Ehtibar N., Myung Jay (Eds.) (2016–2018)
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): Reinhard Suck (Source: Journal of Mathematical Psychology)
Source: Journal of Mathematical Psychology - January 25, 2020 Category: Psychiatry & Psychology Source Type: research
Bayesian parameter estimation for the SWIFT model of eye-movement control during reading
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): Stefan A. Seelig, Maximilian M. Rabe, Noa Malem-Shinitski, Sarah Risse, Sebastian Reich, Ralf EngbertAbstractProcess-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 spatial, pseudo-marginal lik...
Source: Journal of Mathematical Psychology - January 25, 2020 Category: Psychiatry & Psychology Source Type: research
BLIM’s identifiability and parameter invariance under backward and forward transformations
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): Luca Stefanutti, Andrea SpotoAbstractThe 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 identifiable. In such cases, there exist continuous transformations of the model’s parameters, ...
Source: Journal of Mathematical Psychology - January 22, 2020 Category: Psychiatry & Psychology Source Type: research
Editorial Board
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): (Source: Journal of Mathematical Psychology)
Source: Journal of Mathematical Psychology - January 21, 2020 Category: Psychiatry & Psychology Source Type: research
On complementary symmetry under Cumulative Prospect Theory
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): J. ChudziakAbstractComplementary symmetry has been proved to be fulfilled in Cumulative Prospect Theory with random reference, regardless of the form of the utility function. Furthermore an alternative model, in which complementary symmetry generally does not hold, is discussed. (Source: Journal of Mathematical Psychology)
Source: Journal of Mathematical Psychology - January 15, 2020 Category: Psychiatry & Psychology Source Type: research
Calibrating generative models: The probabilistic Chomsky–Schützenberger hierarchy
Publication date: April 2020Source: Journal of Mathematical Psychology, Volume 95Author(s): Thomas F. IcardAbstractA probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. ...
Source: Journal of Mathematical Psychology - January 6, 2020 Category: Psychiatry & Psychology Source Type: research
A systematic exploration of temporal bisection models across sub- and supra-second duration ranges
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Nicholas A. Lusk, Elijah A. Petter, Warren H. MeckAbstractAn integral component to the validity of timing models is their ability to accurately fit behavioral data from detection and discrimination tasks such as the temporal bisection procedure. Two of the most prominent timing models are the Sample Known Exactly (SKE), based on scalar timing theory, and the pseudo-logistic model (PLM). Recently, evidence accumulation models based on drift–diffusionprocesses (DDM) have been utilized for modeling temporal bisection data. Current...
Source: Journal of Mathematical Psychology - December 31, 2019 Category: Psychiatry & Psychology Source Type: research
The Hitchhiker’s guide to nonlinear filtering
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Anna Kutschireiter, Simone Carlo Surace, Jean-Pascal PfisterAbstractNonlinear filtering is used in online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We start our review of the theory on nonlinear filtering from the simplest ‘filtering’ task we can think of, namely static Bayesian inference. From there we continue our journey through discrete-time models, which are usually encountere...
Source: Journal of Mathematical Psychology - December 28, 2019 Category: Psychiatry & Psychology Source Type: research
Inhibited Elements Model — Implementation of an associative learning theory
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Anna Thorwart, Harald LachnitAbstractThe Inhibited Elements Model (IEM) is an associative learning theory with an elemental stimulus representation and normalised amount of activation. At present, an evaluation of the model has been difficult as the IEM was originally described and specified only for one learning task (biconditional discriminations) and later discussions also concerned only selected learning problems and stimulus configurations. The main aim of the current paper is to derive a complete mathematical description of...
Source: Journal of Mathematical Psychology - December 21, 2019 Category: Psychiatry & Psychology Source Type: research
On the polytomous generalization of knowledge space theory
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Luca Stefanutti, Pasquale Anselmi, Debora de Chiusole, Andrea SpotoAbstractOne of the core assumptions of knowledge space theory (KST) is that the answer of a subject to an item can be dichotomously classified as correct or incorrect. Schrepp (1997) provided a very first attempt to generalize the main KST concepts to items with more than two response alternatives, but his work has not had a strong impact on the subsequent research on KST. The aim of the present article is to introduce a new formulation of the polytomous KST, star...
Source: Journal of Mathematical Psychology - November 24, 2019 Category: Psychiatry & Psychology Source Type: research
Regression methods for metacognitive sensitivity
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Simon Bang Kristensen, Kristian Sandberg, Bo Martin BibbyAbstractMetacognition is an important component in basic science and clinical psychology, often studied through complex, cognitive experiments. While Signal Detection Theory (SDT) provides a popular and pervasive framework for modelling responses from such experiments, a shortfall remains that it cannot in a straightforward manner account for the often complex designs. Additionally, SDT does not provide direct estimates of metacognitive ability. This latter shortcoming has ...
Source: Journal of Mathematical Psychology - November 16, 2019 Category: Psychiatry & Psychology Source Type: research
Algebraic aspects of Bayesian modeling in psychology
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Luigi Burigana, Michele VicovaroAbstractSeveral Bayesian models in perceptual and cognitive psychology show a complex organization that is only partly captured by referring to Bayes rule and the associated concepts of prior, likelihood, and posterior distributions. In this article, an algebraic framework is constructed that may serve as a guide for representing and analyzing the internal organization of these models. The construction begins by defining a comprehensive class of probabilistic structures, called probability kernels,...
Source: Journal of Mathematical Psychology - November 16, 2019 Category: Psychiatry & Psychology Source Type: research
Comparison of magnitude-sensitive sequential sampling models in a simulation-based study
Publication date: February 2020Source: Journal of Mathematical Psychology, Volume 94Author(s): Thomas Bose, Angelo Pirrone, Andreagiovanni Reina, James A.R. MarshallAbstractModelling plays a key role in explaining data in psychology and neuroscience and helps elucidate neural computations. Recent observations of magnitude-sensitivity (i.e. sensitivity to overall magnitudes and magnitude differences) in both humans engaged in perceptual decision making and monkeys engaged in value-based decisions have shown that new assumptions (such as the inclusion of noise that is proportional to magnitudes of external stimuli) in routin...
Source: Journal of Mathematical Psychology - November 16, 2019 Category: Psychiatry & Psychology Source Type: research
