Journal of Mathematical Psychology最新文献

In the past years, several theories for assessment have been developed within the overlapping fields of Psychometrics and Mathematical Psychology. The most notable are Item Response Theory (IRT), Cognitive Diagnostic Assessment (CDA), and Knowledge Structure Theory (KST). In spite of their common goals, these frameworks have been developed largely independently, focusing on slightly different aspects. Yet various connections between them can be found in literature. In this contribution, Part I of a three-part work, a unified perspective is suggested that uses two primitives (structure and process) and two operations (factorization and reparametrization) to derive IRT, CDA, and KST models. A Taxonomy of models is built using a two-processes sequential approach that captures the similarities between the conditional probabilities featured in these models and separates them into a first process modeling the effects of individual ability on item mastering, and a second process representing the effects of pure chance on item solving.

The APA encourages authors to thoroughly report their results, including confidence intervals. However, considerable debate exists regarding the computation of confidence intervals in within-subject designs. Nathoo et al.’s (2018) recently proposed a Bayesian within-subject credible interval, which has faced criticism for not accounting for the uncertainty associated with estimating subject-specific effects. In this article, we show how Nathoo et al.’s within-subject credible interval can be easily corrected by utilizing the theory of degrees of freedom. This correction obviates the necessity for estimates of subject-specific effects that offer shrinkage. Instead, it involves a straightforward adjustment in degrees of freedom in both the interaction mean squares and the $t$-distribution used to compute the interval. Therefore, our proposed interval, being easily computable through a simple formula, eliminates the need for fully Bayesian approaches. It accurately represents uncertainty and offers the interpretational benefit of Bayesian intervals.

Think about a thought. Easy to do but where does the thought come from? How is it created? Can it be measured? If so what in the mind is measured? This presentation describes a method for answering these basic questions. The answers derive from a new experimental method called Directly Measured Stimulus Differences (DMSD) and a new theory of mental measurement, a cybernetic process, for the creation of thought. The ideas of Prime Thought and Prime Mind are introduced.

This paper explores a relationship between lexicographic and majority preferences as a novel explanation of preference cycles in choice. Already May (1954) notes that, among subjects in his experiment who did not display a (majority) preference cycle, a vast majority ordered alternatives according to an attribute that they found overridingly important, suggesting that a lexicographic heuristic was used. Our model, Lexicographic Majority, reconciles these findings by providing a unified framework for lexicographic and simple majority preferences. We justify lexicographic majority preferences by providing an axiomatization in terms of behavioral properties.

The Rasch model is the most prominent member of the class of latent trait models that are in common use. The main reason is that it can be considered as a measurement model that allows to separate person and item parameters, a feature that is referred to as invariance of comparisons or specific objectivity. It is shown that the property is not an exclusive trait of Rasch type models but is also found in alternative latent trait models. It is distinguished between separability in the theoretical measurement model and empirical separability with empirical separability meaning that parameters can be estimated without reference to the other group of parameters. A new type of pairwise estimator with this property is proposed that can be used also in alternative models. Separability is considered in binary models as well as in polytomous models.

A sequence of visual or auditory events may be perceived as a single continuing sequence or as two or more separate sequences occurring in parallel. The latter percept occurs when the perceived distance between events is large, and the timing is fast, and is referred to as “streaming.” Several researchers have previously argued that streaming indicates a velocity constraint on the movement of attention. To test this hypothesis the present experiment measured tradeoffs between distance and timing for the onset or loss of streaming in a rectangular pattern of displayed lights. Two linear tradeoffs were found, one corresponding to the loss of streaming when the light pattern was slowed down, and one corresponding to the onset of streaming when the light pattern was sped up. The slopes of these linear relations are interpreted as integer multiples of the velocity of spatio-temporal attention waves. A process model postulates that participants adjust the wavelength of their spatio-temporal attentional traveling wave to match the height of the displayed rectangle. Streaming is assumed to occur when peaks in the attentional traveling wave coincide with the onsets of lights at the top and bottom of the displayed rectangle. Additional supporting evidence for temporal and spatial attention waves is reviewed. This model may be useful for understanding some forms of attentional deficits as well as expert attentional skills arising in musical performance, sports, meditation, and other tasks.

The multiplicative inequality (MI) introduced by Sattath and Tversky (1976) is a rare example of a simple and intuitively appealing condition relating choice probabilities across choice sets of different sizes. It is also a testable implication of two models of stochastic discrete choice: the Elimination by Aspects model of Tversky (1972b) and the independent random utility model. We prove several results on the multiplicative inequality and its relationship to the regularity condition. One major result illustrates how little the MI constrains binary choice probabilities: it implies that every system of binary choice probabilities on a universe of choice objects can be extended to a complete system of choice probabilities satisfying the MI. In this sense, the MI is complementary to axioms for binary choice probabilities, of which many have been proposed. We also discuss choice environments where the multiplicative inequality is implausible.

The human’s capacity to perceptually entrain to an auditory rhythm has been repeatedly modeled as a dynamical system consisting of one or more forced oscillators. However, a more recent perspective, closely related to the popular theory of Predictive Processing, treats auditory entrainment as an inference process in which the observer infers the phase, tempo, and/or metrical structure of an auditory stimulus based on event timing. Here, we propose a close relationship between these two perspectives. We show for the first time that a system performing variational Bayesian inference about the circular phase underlying a rhythmic stimulus takes the form of a forced, damped oscillator with a specific nonlinear phase response function corresponding to the internal metrical model of the underlying rhythm. This algorithm can be extended to simultaneous inference on both phase and tempo using one of two possible approximations that closely align with the two most prominent models of auditory entrainment: one yields a single oscillator with an adapting period, and the other yields a networked bank of oscillators. We conclude that an inference perspective on rhythm perception can offer similar descriptive power and flexibility to a dynamical systems perspective while also plugging into the fertile unifying framework of Bayesian Predictive Processing.

We propose an extension of the widely used class of multinomial processing tree models by incorporating response times via diffusion-model kernels. Multinomial processing tree models are models of categorical data in terms of a number of cognitive and guessing processes estimating the probabilities with which each process outcome occurs. The new method allows one to estimate completion times of each process along with outcome probability and thereby provides process-oriented accounts of accuracy and latency data in all domains in which multinomial processing tree models have been applied. Furthermore, the new models are implemented hierarchically so that individual differences are explicitly accounted for and do not bias the population-level estimates. The new approach overcomes a number of shortcomings of previous extensions of multinomial models to incorporate response times. We evaluate the new method’s performance via a recovery study and simulation-based calibration. The method allows one to test hypotheses about processing architecture, and it provides an extension of traditional diffusion model analyses where multinomial models have been proposed for the modeled paradigm. We illustrate these and other benefits of the new model class using five existing data sets from recognition memory.