The paper focuses on several misconceptions in frequentist inference that undermine the current discussions on replicability and the trustworthiness of empirical evidence, including, (a) the use/abuse of estimation-based effect sizes, (b) (mis)interpreting error probabilities as conditional on hypotheses giving rise to ostensible confusions between P(D|H0) and P(H0|D), and (c) the questionable nature

This paper proposes a new proof of the existence of constant threshold representations of semiorders on countably infinite sets. The construction treats each indifference-connected component of the semiorder separately. It uses a partition of such an indifference-connected component into indifference classes. Each element in the indifference-connected component is mirrored, using a “ghost” element

Physical colors, i.e. reflected or emitted lights entering the eyes from a visual environment, are converted into perceived colors sensed by humans by neurophysiological mechanisms. These processes involve both three types of photoreceptors, the LMS cones, and spectrally opponent and non-opponent interactions resulting from the activity rates of ganglion and lateral geniculate nucleus cells. Thus,

Inductive item tree analysis is an established method of Boolean analysis of questionnaires. By exploratory data analysis, from a binary data matrix, the method extracts logical implications between dichotomous test items. For example, assume that we have the problems i and j of a test that can be solved or failed by subjects. With inductive item tree analysis, an implication i→j between the items

In this paper, the completeness (completion) of attribution functions is introduced and a general way is given to derive an attribution function from a knowledge structure on an arbitrary domain. With the help of these, this paper establishes a Galois connection (f,g) between the collection K of all knowledge structures and the collection F of all attribution functions, where knowledge spaces and complete

Stefanutti (2019) recently developed procedures and a related theory for deriving learning spaces from problem spaces. The approach provides a deterministic model for partially ordering individuals, on the basis of their performances in problem-solving tasks. This deterministic model accounts for both the accuracy of the responses and, especially, the sequence of ”moves” (observable solution process)

The Wiener diffusion model with two absorbing barriers is frequently used in modeling decisions and decision latencies jointly. We derive representations of the partial derivatives of the density and cumulative distribution function of first-passage times. Different representations, based on infinite series, differ in convergence for small and large times, and we provide methods that control the approximation

Signal detection theory (SDT) and the sequential probability ratio test (SPRT) are two leading models for binary perceptual decision-making in psychology and neuroscience. For initiates in this research area, the foundational relationship between SDT and the SPRT, or between statistical inference models and their mechanistic counterparts, can be unclear because many decision-making models in use today

Bivariate Markov processes (BMPs) described by Ephraim and Mark (2012) consist of a pair of stochastic processes in the continuous time, one observable and the other latent, that are jointly Markov. In the present article, the navigation behavior and the learning process of a user of a web-based tutoring system are jointly modeled as BMPs constrained by assumptions that are coherent with the concepts

Motivation can counteract the effects of mental fatigue. However, the underlying mechanism by which motivation affects performance in mentally fatiguing tasks is obscure. In this paper, we propose goal competition as a paradigm to understand the role of motivation and built three models of mental fatigue studies to demonstrate the mechanism in a cognitive architecture named PRIMs. Each of these studies

In most of the work on probabilistic knowledge structures, no restrictions apply to the probability distribution on the collection of knowledge states. The number of parameters needed to describe this distribution can thus be very large. An exception is provided by the Simple Learning Model (SLM) in which, by means of assumptions on the learning process, the distribution is built from other parameters

It has been established in the fields of computer science and physics that many NP-hard and NP-complete graph-theoretic problems can be formulated and solved as Ising spin models. We discuss several problems that have a history in mathematical psychology, most notably max-cut clustering, graph coloring, a linear ordering problem related to paired comparison ranking and directed acyclic graphs, and

Human beings can perceive depth by using binocular disparity, namely the difference between a stereo-pair of retinal images. It is commonly believed that the visual system requires oculomotor information about the relative orientation between the two eyes to perceive depth on the basis of binocular disparity. Such oculomotor information can be obtained from the efference copy of the oculomotor signal

The Balloon Analogue Risk Task (BART) is a popular task used to measure risk-taking behavior. To identify cognitive processes associated with choice behavior on the BART, a few computational models have been proposed. However, the extant models either fail to capture choice patterns on the BART or show poor parameter recovery performance. Here, we propose a novel computational model, the exponential-weight

Cash-out products offered by bookmakers allow a bettor to liquidate, for a small fee, an existing bet prior to “game end”. Previous research has found that bettors are likely to hold preferences consistent with cumulative prospect theory (CPT). We obtain analytic expressions for the ‘optimal’ proportion of the bet to cash-out for bettors with CPT preferences. Diminishing sensitivity or marginal utility

The area of mathematical psychology concerning knowledge spaces is complemented by the theoretical notion of a “curriculum space,” which is developed as a mathematical model for curriculum design in order to illuminate the interplay between learners and the curricula in which they enroll. The analysis is carried out in terms of concepts from graph theory and order theory, yielding a precise language

In recent years, Bayesian causal inference has emerged as a computational principle for multisensory integration; it considers the causal relationships of multisensory stimuli and combines stimuli only when they are causally related. Many empirical studies have confirmed the predictions of Bayesian causal inference models and have begun to reveal the neural mechanisms of their computations. However

In knowledge space theory, the (latent) knowledge state of a student consists of the subset of test items that he masters in principle. Even at a given stage of apprenticeship, the student’s knowledge state may vary in a given collection of subsets. The collection of all possible states of all potential students forms a knowledge structure. In the modeling of student answer production, the probabilities

We describe a modified sequential probability ratio test that can be used to reduce the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Examples are provided for z tests, t tests, and tests of binomial success probabilities. A description of a software package to implement the test designs is provided. We compare the sample sizes required

This paper combines two aspects in the construction of knowledge spaces. The first is to utilize a partial order of skills which belong to a given domain of knowledge to find items or problems which finally constitute a knowledge space or a learning space. Secondly the orders of skills of different (related) areas are coalesced by well known order operations to construct larger spaces. In the first

Based on the celebrated Birkhoff theorem, Doignon and Falmagne (1985) establish a one-to-one correspondence between certain binary relations on a domain of (dichotomous) items and the quasi-ordinal knowledge spaces defined on it. It is shown that this construction can be generalized to apply to polytomous response formats, where response values are partially ordered so that they form a lattice. Polytomous

The ALEKS (Assessment and LEarning in Knowledge Spaces) educational software system is an instantiation of knowledge space theory (KST) that has been used by millions of students in mathematics, chemistry, statistics and accounting. The software employs a probabilistic assessment based on KST for placement into an appropriate course or curriculum, a learning mode in which students are guided through

In the redundant signals task, participants respond in the same way to stimuli of different sources, for example, to auditory as to visual signals. The stimuli are presented either alone (single signals) or in combination (redundant signals). In this task, one often observes substantially faster responses to redundant signals than to single signals. Different mechanisms may underlie this so-called

Since the influential work of Schelling, binary choice games with externalities (situations in which the consequences of the choices of an agent are affected by the actions of other agents) have become central within social dilemma literature. Previous literature has developed models with agents mainly based on classic probability theory where populations formed by impulsive agents (i.e., they tend

The attentional blink (AB) basically refers to a deficit in the processing of the second stimulus, which is revealed when two target stimuli are presented in a rapid serial visual presentation (RSVP) stream. We propose a mathematical model of the AB based on a logistic model with first-order difference system, and give a maximum likelihood method for estimating the parameters of our model. Validity

Learning about the statistics of one’s environment is a fundamental requirement of adaptive behaviour. In this experiment we probe whether pupil dilation in response to brief auditory stimuli reflects automatic statistical learning about the underlying stimulus distributions. Specifically, we consider whether pupil dilation reflects automatic (task-irrelevant) learning about the precision of Gaussian

Abstract In everyday life, our behavior varies on a continuum from automatic and habitual to deliberate and goal-directed. Recent evidence suggests that habit formation and relearning of habits operate in a context-dependent manner: Habit formation is promoted when actions are performed in a specific context, while breaking off habits is facilitated after a context change. It is an open question how

Abstract Vision and touch interact in spatial perception. How vision exerts online influences on tactile spatial perception is well-appreciated, but far less is known regarding how recent visual experiences modulate tactile perception offline, particularly in a bimanual context. Here, we investigated how visual cues exert both online and offline biases in bimanual tactile spatial perception. In a series

Abstract Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of these approaches depends on the assumptions about the model space M . Also, traditional methods like leave-one-out cross-validation (LOO-CV) estimate the

Abstract We introduce a set of models designed to analyze datasets involving responses from multiple subjects on pairwise comparisons from a fixed discrete set of alternatives. These models are part of a greater body of work known as Cultural Consensus Theory (CCT). Like other CCT models, these simultaneously infer each individual’s tendency toward aligning with the group consensus, level of agreement

Abstract For testing categorical scaling, psychologists ordered subjects to consider the categories as equally spaced. This need not be mandated. This note shows that equally spaced categories will naturally emerge whenever subjects aim at providing maximum or equal information to the experimenter.

Abstract An experienced event has many distinctively different qualitative attributes. Besides the informational content, such as which word was presented on an experimental list at a specific temporal instant, there is also information about the ordinal properties of the event relative to other events. A multinomial processing tree (MPT) model is provided for measuring four different states for the

Abstract To form a coherent presentation of the world, the brain needs to combine multiple sensory modalities accurately together in the temporal domain. Judgements on the relative timing of audio–visual stimuli are complex, due to the differing propagation speeds of light and sound through the environment and the nervous system, and the dependence of processing latencies on stimulus intensity (Pieron

This work is a continuation of Mallahi-Karai and Diederich (2019), where the authors introduced and studied the cube model as a multi-dimensional extension of the diffusion model in binary choice model. The aim of this note is to introduce and study the disk model, which can be viewed as a variation of the model introduced in the aforementioned paper. Here, we consider a choice situation with three

We continue to analyze basic constraints on the human decision making from the viewpoint of quantum measurement theory (QMT). As it has been found, the conventional QMT based on the projection postulate cannot account for the combination of the question order effect (QOE) and the response replicability effect (RRE). This was an alarming finding for quantum-like modeling of decision making. Recently

Abstract Psychological theory should guide the method. A method should not dictate theory. Extraneous assumptions entering psychological theories through the backdoor of a method may differentially affect the analysis of different data sets. This introduces noise and jeopardizes successful replication of valid theoretical claims. Auxiliary theoretical assumptions can also bias substantive conclusions

Humans and other animals are constantly learning new categories and making categorization decisions in their everyday life. However, different individuals may focus on different information when learning categories, which can impact the category representation and the information that is used when making categorization decisions. This article used computational modeling of behavioral data to take a

A family of models of individual discrete choice are constructed by means of statistical averaging of choices made by a subject in a reinforcement learning process, where the subject has short, k-term memory span. The choice probabilities in these models combine in a non-trivial, non-linear way the initial learning bias and the experience gained through learning. The properties of such models are discussed

Abstract 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

Abstract 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,

Abstract 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

Abstract 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

Abstract 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

Abstract 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)

Abstract 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

Abstract 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

Abstract 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

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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract Writing ξ s ( x ) for the stimulus intensity judged greater (louder, heavier, brighter) than stimulus intensity x with criterion s , Iverson (2006b) proposed a law of similarity ξ s ( λ x ) = γ ( λ , s ) ξ η ( λ , s ) ( x ) to model the dependence of ξ s ( 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

Abstract 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

Abstract 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

Abstract 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