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Measurement reliability is a fundamental concept in psychology. It is traditionally considered a stable property of a questionnaire, measurement device, or experimental task. Although intraclass correlation coefficients (ICC) are often used to assess reliability in repeated measure designs, their descriptive nature depends upon the assumption of a common within-person variance. This work focuses on the presumption that each individual is adequately described by the average within-person variance in hierarchical models. And thus whether reliability generalizes to the individual level, which leads directly into the notion of individually varying ICCs. In particular, we introduce a novel approach, using the Bayes factor, wherein a researcher can directly test for homogeneous within-person variance in hierarchical models. Additionally, we introduce a membership model that allows for classifying which (and how many) individuals belong to the common variance model. The utility of our methodology is demonstrated on cognitive inhibition tasks. We find that heterogeneous within-person variance is a defining feature of these tasks, and in one case, the ratio between the largest to smallest within-person variance exceeded 20. This translates into a tenfold difference in person-specific reliability! We also find that few individuals belong to the common variance model, and thus traditional reliability indices are potentially masking important individual variation. We discuss the implications of our findings and possible future directions. The methods are implemented in the R package vICC

Missing data are ubiquitous in psychological research. They may come about as an unwanted result of coding or computer error, participants' non-response or absence, or missing values may be intentional, as in planned missing designs. We discuss the effects of missing data on χ²-based goodness-of-fit indices in Structural Equation Modeling (SEM), specifically on the Root Mean Squared Error of Approximation (RMSEA). We use simulations to show that naive implementations of the RMSEA have a downward bias in the presence of missing data and, thus, overestimate model goodness-of-fit. Unfortunately, many state-of-the-art software packages report the biased form of RMSEA. As a consequence, the scientific community may have been accepting a much larger fraction of models with non-acceptable model fit. We propose a bias-correction for the RMSEA based on information-theoretic considerations that take into account the expected misfit of a person with fully observed data. The corrected RMSEA is asymptotically independent of the proportion of missing data for misspecified models. Importantly, results of the corrected RMSEA computation are identical to naive RMSEA if there are no missing data.

Ordinal variables, while extremely common in Psychology, are almost exclusively analysed with statistical models that falsely assume them to be metric. This practice can lead to distorted effect size estimates, inflated error rates, and other problems. We argue for the application of ordinal models that make appropriate assumptions about the variables under study. In this tutorial article, we first explain the three major ordinal model classes; the cumulative, sequential and adjacent category models. We then show how to fit ordinal models in a fully Bayesian framework with the R package brms, using data sets on stem cell opinions and marriage time courses. Two appendices provide detailed mathematical derivations of the models, and a third practical example that connects ordinal models to Signal Detection Theory with confidence rating data. Ordinal models provide better theoretical interpretation and numerical inference from ordinal data, and we recommend their widespread adoption in Psychology.

[Correction Notice: An Erratum for this article was reported in Vol 115(6) of Journal of Personality and Social Psychology (see record 2018-63189-002). In the article, the original supplemental material has been revised to include a clarifying note to the Tests of model fit over larger sample (Samples C-G) section and post-peer review analyses added to the Post-peer review Factor Analytic Tests section. All versions of this article have been corrected.] Philosophers and behavioral scientists refer to wisdom as unbiased reasoning that guides one toward a balance of interests and promotes a good life. However, major instruments developed to test wisdom appear biased, and it is unclear whether they capture balance-related tendencies. We examined whether shifting from global, de-contextualized reports to state-level reports about concrete situations provides a less biased method to assess wise reasoning (e.g., intellectual humility, recognition of uncertainty and change, consideration of the broader context at hand and perspectives of others, integration of these perspectives or compromise), which may be aligned with the notion of balancing interests. Results of a large-scale psychometric investigation (N = 4,463) revealed that the novel Situated WIse Reasoning Scale (SWIS) is reliable and appears independent of psychological biases (attribution bias, bias blind spot, self-deception, and impression management), whereas global wisdom reports are subject to such biases. Moreover, SWIS scores were positively related to indices of living well (e.g., adaptive emotion regulation, mindfulness), and balancing of cooperative and self-protective interests, goals (influence-vs.-adjustment), and causal inferences about conflict (attribution to the self-vs.-other party). In contrast, global wisdom reports were unrelated or negatively related to balance-related measures. Notably, people showed modest within-person consistency in wise reasoning across situations or over time, suggesting that a single-shot measurement may be insufficient for whole understanding of trait-level wisdom. We discuss theoretical and practical implications for research on wisdom, judgment and decision making, well-being, and prosociality. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Background. Studies investigating the link between depressive symptoms and inflammation have yielded inconsistent results, which may be due to two factors. First, studies differed regarding the specific inflammatory markers studied and covariates accounted for. Second, specific depressive symptoms may be differentially related to inflammation. We address both challenges using network psychometrics.Methods. We estimated seven regularized mixed graphical models in the NESDA data (N=2321) to explore shared variances among 1) depression severity, modeled via depression sum-score, 9 DSM-5 symptoms, or 28 individual depressive symptoms; 2) inflammatory markers C-reactive protein (CRP), interleukin 6 (IL-6), and tumor necrosis factor α (TNF-α); 3) before and after adjusting for sex, age, body mass index (BMI), exercise, smoking, alcohol, and chronic diseases.Results. The depression sum-score was related to both IL-6 and CRP before, and only to IL-6 after covariate adjustment. When modeling the DSM-5 symptoms and CRP in a conceptual replication of Jokela et al. (2016), CRP was associated with ‘sleep problems’, ‘energy level’, and ‘weight/appetite changes’; only the first two links survived covariate adjustment. In a conservative model with all 38 variables, symptoms and markers were unrelated. Following recent psychometric work, we re-estimated the full model without regularization: the depressive symptoms ‘insomnia, ‘hypersomnia’, and ‘aches and pain’ showed unique positive relations to all inflammatory markers.Conclusions. We found evidence for differential relations between markers, depressive symptoms, and covariates. Associations between symptoms and markers were attenuated after covariate adjustment; BMI and sex consistently showed strong relations with inflammatory markers.

This article introduces the NetworkToolbox package for R. Network analysis offers an intuitive perspective on complex phenomena via models depicted by nodes (variables) and edges (correlations). The ability of networks to model complexity has made them the standard approach for modeling the intricate interactions in the brain. Similarly, networks have become an increasingly attractive model for studying the complexity of psychological and psychopathological phenomena. NetworkToolbox aims to provide psychological researchers with state-of-the-art methods and measures for estimating and analyzing brain, cognitive, and psychometric data. In this article, I introduce NetworkToolbox and provide a manual for applying the package’s functions to psychometric (personality) data.

Psychological data often violate the normality assumptions made by commonly used statistical methods. These violations are addressed in a variety of ways such as transformations or assuming the employed method is robust to violations. Here we argue that data transformations are unnecessary at best and severely misleading at worst. An alternative approach is to use a Bayesian model that permits skewness and other perturbations to classical assumptions (e.g., heteroskedasticity). Through simulation, we demonstrate that a Bayesian skew-normal model has optimal frequentist properties (i.e., "type 1" error, "power", unbiasedness) compared to normal-assumptive models with or without transformation. Furthermore, the Bayesian skew-normal model has greater predictive utility, as indicated by posterior predictive checking and approximate leave-one-out cross-validation. After an applied example, we discuss practical implications of our findings for psychological science in general, and specifically how Bayesian modeling can improve reproducibility in psychology.

A test score on a psychological test is usually expressed as a normed score, representing its position relative to test scores in a reference population. These typically depend on predictor(s) such as age. The test score distribution conditional on predictors is estimated using regression, which may need large normative samples to estimate the relationships between the predictor(s) and the distribution characteristics properly. In this study, we examine to what extent this burden can be alleviated by using prior information in the estimation of new norms with Bayesian Gaussian distributional regression. In a simulation study, we investigate to what extent this norm estimation is more efficient and how robust it is to prior model deviations. We varied the prior type, prior misspecification and sample size. In our simulated conditions, using a fixed effects prior resulted in more efficient norm estimation than a weakly informative prior as long as the prior misspecification was not age dependent. With the proposed method and reasonable prior information, the same norm precision can be achieved with a smaller normative sample, at least in empirical problems similar to our simulated conditions. This may help test developers to achieve cost-efficient high-quality norms. The method is illustrated using empirical normative data from the IDS-2 intelligence test.

Over the last decade, the Bayesian estimation of evidence-accumulation models has gained popularity, largely due to the advantages afforded by the Bayesian hierarchical framework. Despite recent advances in the Bayesian estimation of evidence-accumulation models, model comparison continues to rely on suboptimal procedures, such as posterior parameter inference and model selection criteria known to favor overly complex models. In this paper, we advocate model comparison for evidence-accumulation models based on the Bayes factor obtained via Warp-III bridge sampling. We demonstrate, using the linear ballistic accumulator (LBA), that Warp-III sampling provides a powerful and flexible approach that can be applied to both nested and non-nested model comparisons, even in complex and high-dimensional hierarchical instantiations of the LBA. We provide an easy-to-use software implementation of the Warp-III sampler and outline a series of recommendations aimed at facilitating the use of Warp-III sampling in practical applications.

Decision making is a vital aspect of our everyday functioning, from simple perceptual demands to more complex and meaningful decisions. The strategy adopted to make such decisions is often viewed as balancing elements of speed and caution, i.e. making fast or careful decisions. Using sequential sampling models to analyse decision making data can allow us to tease apart strategic differences, such as being more or less cautious, from processing differences, which would otherwise be indistinguishable in behavioural data. Our study used a multiple object tracking task where student participants and a highly skilled military group were compared on their ability to track several items at once. Using a mathematical model of decision making (the linear ballistic accumulator), we show the underpinnings of how two groups differ in performance. Results showed a large difference between the groups on accuracy, with the Royal Australian Air Force (RAAF) group outperforming students. An interaction effect was observed between groups and level of difficulty in response times, where RAAF response times slowed at a greater rate than the student group as difficulty increased. Model results indicated that the RAAF personnel were more cautious in their decisions than students, and had faster processing in some conditions. Our study shows the strength of sequential sampling models, as well as providing a first attempt at fitting a sequential sampling model to data from a multiple object tracking task.

Network psychometrics is undergoing a time of methodological reflection. In part, this was spurred by the revelation that l1-regularization does not reduce spurious associations in partial correlation networks. In this work, we address another motivation for the widespread use of regularized estimation: the thought that it is needed to mitigate overfitting. We first clarify important aspects of overfitting and the bias-variance tradeoff that are especially relevant for the network literature, where the number of nodes or items in a psychometric scale are not largecompared to the number of observations (i.e., a low p/n ratio). This revealed that bias and especially variance are most problematic in p=n ratios rarely encountered. We then introduce a nonregularized method, based on classical hypothesis testing, that fulfills two desiderata: (1) reducing or controlling the false positives rate and (2) quelling concerns of overfitting by providing accurate predictions. These were the primary motivations for initially adopting the graphical lasso (glasso). In several simulation studies, our nonregularized method provided more than competitive predictive performance, and, in many cases, outperformed glasso. Itappears to be nonregularized, as opposed to regularized estimation, that best satisfies these desiderata. We then provide insights into using our methodology. Here we discuss the multiple comparisons problem in relation to prediction: stringent alpha levels, resulting in a sparse network, can deteriorate predictive accuracy. We end by emphasizing key advantages of our approach that make it ideal for both inference and prediction in network analysis.

In recent years, open science practices have become increasingly popular in psychology and related sciences. These practices aim to increase rigour and transparency in science as a potential response to the challenges posed by the replication crisis. Many of these reforms—including the increasingly usedpreregistration—have been designed for purely experimental work that tests straightforward hypotheses with standard inferential statistical analyses, such as assessing whether an experimental manipulation has an effect on a variable of interest. But psychology is a diverse field of research. The somewhat narrow focus of the prevalent discussions surrounding and templates for preregistration has led to debates on how appropriate these reforms are for areas of research with more diverse hypotheses and more intricate methods of analysis, such as cognitive modelling research within mathematical psychology. Our article attempts to bridge the gap between open science and mathematical psychology, focusing on the type of cognitive modelling that Crüwellet al.(Crüwell S, Stefan AM, Evans NJ. 2019 Robust standards in cognitive science.Comput. Brain Behav.2, 255–265) labelledmodel application, where researchers apply a cognitive model as ameasurement toolto test hypotheses about parameters of the cognitive model. Specifically, we (i) discuss several potential researcher degrees of freedom within model application, (ii) provide the first preregistration template for model application and (iii) provide an example of a preregistered model application using our preregistration template. More broadly, we hope that our discussions and concrete proposals constructively advance the mostly abstract current debate surrounding preregistration in cognitive modelling, and provide a guide for how preregistration templates may be developed in other diverse or intricate research contexts.

This dissertation deals with the problem of modeling psychopathology. Its first part focuses on statistical (data) models and introduces a number of models for cross-sectional and time series data that can be visualized as a network. This includes Mixed Graphical Models (MGMs), which allow one to include variables of different types in a statistical network model, Moderated Network Models (MNMs) which allow pairwise interactions to be moderated by other variables in the model, and time-varying Vector Autoregressive (VAR) models and MGMs that relax the standard assumption of stationarity. In addition, I discuss several methodological issues related to statistical network models such as the importance of considering predictability, model selection between AR and VAR models, and how the interpretation of the Ising model depends on its domain. The second part focuses on formal theories of psychopathology and how to develop them using data models. I first illustrate the fundamental difficulties in obtaining a formal theory with a purely statistical approach, by trying to recover an assumed bistable system for emotion dynamics with currently popular time series analyses. Next, I present a formal theory of panic disorder, based on an extensive review of the literature on the phenomenology of panic disorder and existing theories. Finally, I discuss three different ways to use data models to construct formal theories about psychopathological phenomena. Based on this discussion, I put forward an abductive framework for constructing formal theories for psychological and psychopathological phenomena.

Uncertainty plays a critical role in reinforcement learning and decision making. However, exactly how it influences behavior remains unclear. Multiarmed-bandit tasks offer an ideal test bed, since computational tools such as approximate Kalman filters can closely characterize the interplay between trial-by-trial values, uncertainty, learning, and choice. To gain additional insight into learning and choice processes, we obtained data from subjects’ overt allocation of gaze. The estimated value and estimation uncertainty of options influenced what subjects looked at before choosing; these same quantities also influenced choice, as additionally did fixation itself. A momentary measure of uncertainty in the form of absolute prediction errors determined how long participants looked at the obtained outcomes. These findings affirm the importance of uncertainty in multiple facets of behavior and help delineate its effects on decision making.

The positive manifold of intelligence has fascinated generations of scholars in human ability. In the past century, various formal explanations have been proposed, including the dominant g factor, the revived sampling theory, and the recent multiplier effect model and mutualism model. In this article, we propose a novel idiographic explanation. We formally conceptualize intelligence as evolving networks in which new facts and procedures are wired together during development. The static model, an extension of the Fortuin–Kasteleyn model, provides a parsimonious explanation of the positive manifold and intelligence’s hierarchical factor structure. We show how it can explain the Matthew effect across developmental stages. Finally, we introduce a method for studying growth dynamics. Our truly idiographic approach offers a new view on a century-old construct and ultimately allows the fields of human ability and human learning to coalesce.

Agents that can make better use of computation, experience, time, and memory can solve a greater range of problems more effectively. A crucial ingredient for managing such finite resources is intelligently chosen abstract representations. But, how do abstractions facilitate problem solving under limited resources? What makes an abstraction useful? To answer such questions, we review several trends in recent reinforcement-learning research that provide insight into how abstractions interact with learning and decision making. During learning, abstraction can guide exploration and generalization as well as facilitate efficient tradeoffs---e.g., time spent learning versus the quality of a solution. During computation, good abstractions provide simplified models for computation while also preserving relevant information about decision-theoretic quantities. These features of abstraction are not only key for scaling up artificial problem solving, but can also shed light on what pressures shape the use of abstract representations in humans and other organisms.

A wide variety of effect size indices have been proposed for quantifying the magnitude of treatment effects in single-case designs. Commonly used measures include parametric indices such as the standardized mean difference as well as nonoverlap measures such as the percentage of nonoverlapping data, improvement rate difference, and nonoverlap of all pairs. Currently, little is known about the properties of these indices when applied to behavioral data collected by systematic direct observation, even though systematic direct observation is the most common method for outcome measurement in single-case research. This study uses Monte Carlo simulation to investigate the properties of several widely used single-case effect size measures when applied to systematic direct observation data. Results indicate that the magnitude of the nonoverlap measures and of the standardized mean difference can be strongly influenced by procedural details of the study's design, which is a significant limitation to using these indices as effect sizes for meta-analysis of single-case designs. A less widely used parametric index, the log response ratio, has the advantage of being insensitive to sample size and observation session length, although its magnitude is influenced by the use of partial interval recording. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

In eye-movement control during reading, advanced process-oriented models have been developed to reproduce behavioral data. So far, model complexity and large numbers of model parameters prevented rigorous statistical inference and modeling of interindividual differences. Here we propose a Bayesian approach to both problems for one representative computational model of sentence reading (SWIFT; Engbert et al., Psychological Review, 112, 2005, pp. 777-813). We used experimental data from 36 subjects who read the text in a normal and one of four manipulated text layouts (e.g., mirrored and scrambled letters). The SWIFT model was fitted to subjects and experimental conditions individually to investigate between-subject variability. Based on posterior distributions of model parameters, fixation probabilities and durations are reliably recovered from simulated data and reproduced for withheld empirical data, at both the experimental condition and subject levels. A subsequent statistical analysis of model parameters across reading conditions generates model-driven explanations for observable effects between conditions. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

State trace analyses assess the latent dimensionality of a cognitive process by asking whether the means of two dependent variables conform to a monotonic function across a set of conditions. Using an assumption of independence between the measures, recently proposed statistical tests address bivariate measurement error, allowing both frequentist and Bayesian analyses of monotonicity (e.g., Davis-Stober, Morey, Gretton, & Heathcote, 2016; Kalish, Dunn, Burdakov, & Sysoev, 2016). However, statistical inference can be biased by unacknowledged dependencies between measures, particularly when the data are insufficient to overwhelm an incorrect prior assumption of independence. To address this limitation, we developed a hierarchical Bayesian model that explicitly models the separate roles of subject, item, and trial-level dependencies between two measures. Assessment of monotonicity is then performed by fitting separate models that do or do not allow a non-monotonic relation between the condition effects (i.e., same versus different rank orders). The Widely Applicable Information Criterion (WAIC) and Pseudo Bayesian Model Averaging – both cross validation measures of model fit – are used for model comparison, providing an inferential conclusion regarding the dimensionality of the latent psychological space. We validated this new state trace analysis technique using model recovery simulation studies, which assumed different ground truths regarding monotonicity and the direction/magnitude of the subject- and trial-level dependence. We also provide an example application of this new technique to a visual object learning study that compared performance on a visual retrieval task (forced choice part recognition) versus a verbal retrieval task (cued recall).

25 pags., 11 figs., 8 tabs., We check the robustness of a recently proposed dynamical model of associative Pavlovian learning that extends the Rescorla–Wagner (RW) model in a natural way and predicts progressively damped oscillations in the response of the subjects. Using the data of two experiments, we compare the dynamical oscillatory model (DOM) with an oscillatory model made of the superposition of the RW learning curve and oscillations. Not only do data clearly show an oscillatory pattern but they also favor the DOM over the added oscillation model, thus pointing out that these oscillations are the manifestation of an associative process. The latter is interpreted as the fact that subjects make predictions on trial outcomes more extended in time than in the RW model, but with more uncertainty., This study is supported by grant PSI2016-80082-P from Ministerio de Economía y Competitividad, Secretaría de Estado de Investigación, Desarrollo e Innovación, Spanish Government (R.P. Principal Investigator).

A majority of statistically educated scientists draw incorrect conclusions based on the most commonly used statistical technique: null hypothesis significance testing (NHST). Frequentist techniques are often claimed to be incorrectly interpreted as Bayesian outcomes, which suggests that a Bayesian framework may fit better to inferences researchers frequently want to make (Briggs, 2012). The current study set out to test this proposition. Firstly, we investigated whether there is a discrepancy between what researchers think they can conclude and what they want to be able to conclude from NHST. Secondly, we investigated to what extent researchers want to incorporate prior study results and their personal beliefs in their statistical inference. Results show the expected discrepancy between what researchers think they can conclude from NHST and what they want to be able to conclude. Furthermore, researchers were interested in incorporating prior study results, but not their personal beliefs, into their statistical inference.

Steinley, Hoffman, Brusco, and Sher (2017) proposed a new method for evaluating the performance of psychological network models: fixed-margin sampling. The authors investigated LASSO regularized Ising models (eLasso) by generating random datasets with the same margins as the original binary dataset, and concluded that many estimated eLasso parameters are not distinguishable from those that would be expected if the data were generated by chance. We argue that fixed-margin sampling cannot be used for this purpose, as it generates data under a particular null-hypothesis: a unidimensional factor model with interchangeable indicators (i.e., the Rasch model). We show this by discussing relevant psychometric literature and by performing simulation studies. Results indicate that while eLasso correctly estimated network models and estimated almost no edges due to chance, fixed-margin sampling performed poorly in classifying true effects as “interesting” (Steinley et al. 2017, p. 1004). Further simulation studies indicate that fixed-margin sampling offers a powerful method for highlighting local misfit from the Rasch model, but performs only moderately in identifying global departures from the Rasch model. We conclude that fixed-margin sampling is not up to the task of assessing if results from estimated Ising models or other multivariate psychometric models are due to chance.

A key assumption of models of human cognition is that there is variability in information processing. Evidence accumulation models (EAMs) commonly assume 2 broad variabilities in information processing: within-trial variability, which is thought to reflect moment-to-moment fluctuations in perceptual processes, and between-trial variability, which is thought to reflect variability in slower-changing processes like attention, or systematic variability between the stimuli on different trials. Recently, Ratcliff, Voskuilen, and McKoon (2018) claimed to "provide direct evidence that external noise is, in fact, required to explain the data from five simple two-choice decision tasks" (p. 33), suggesting that at least some portion of the between-trial variability in information processing is due to "noise." However, we argue that Ratcliff et al. (2018) failed to distinguish between 2 different potential sources of between-trial variability: random (i.e., "external noise") and systematic (e.g., item effects). Contrary to the claims of Ratcliff et al. (2018), we show that "external noise" is not required to explain their findings, as the same trends of data can be produced when only item effects are present. Furthermore, we contend that the concept of "noise" within cognitive models merely serves as a convenience parameter for sources of variability that we know exist but are unable to account for. Therefore, we question the usefulness of experiments aimed at testing the general existence of "random" variability and instead suggest that future research should attempt to replace the random variability terms within cognitive models with actual explanations of the process. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

The Extended Condorcet Model allows us to explore interindividual consensus concerning culturally held knowledge. At the same time, 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 potentially have an influence on one's everyday life experiences. Here, we develop a cognitive latent variable model in which dynamic process parameters from intensive longitudinal daily life data are systematically linked to parameters of the Extended Condorcet Model. We apply this joint model of consensus and longitudinal dynamics to study whether subjective beliefs on what makes people feel loved are linked to daily life experiences of love.

International audience; We elaborated an index, the Interference Distribution Index, which allows quantifying the relation between response times and the size of the interference effect. This index is associated with an intuitive graphical representation, the Lorenz-interference plot. We show that this index has some convenient properties in terms of sensitivity to changes in the distribution of the interference effect and to aggregation of individual data. Moreover, it turns out that this index is the only one (up to an arbitrary increasing transformation) possessing these properties. The relevance of this index is illustrated through simulations of a cognitive model of interference effects and reanalysis of experimental data.

This study develops a new way to model the emotional impact on a particular individual (person, group,...) that may have feelings, to any event or any information. The significance of an event or an information depends on the person undergoing it. Each person reacts emotionally differently to a same situation in terms of intensity and/or type of emotion. A particular same event is therefore perceived subjectively different by each individual. The reason is that each person has his own personality, his own experience, his own history, his own education and tradition ... In this study, we assume that all the Events / Information have common interpretable points relative to each individual: Who is in the event ?, What is done? When it is done? Where it is done? How often/much it is done? Why it is done? and How it is done? Each element of the vector [Who; What; When; Where; How Much; Why; How] will be called as an emotional stimulus and will be mathematically modeled relatively to the studied individual. These stimuli, interpreted differently by each individual, will be the starting point for the creation of emotions at different intensities. The objective of this study is to mathematically link these different stimuli to the intensity of the resulting emotions following an event relatively to an individual.

The mind and consciousness are pretty complex to observe and analyze quantitatively since the complexity of neuron and mystery of consciousness. Recent years, many scientists try to explain our mind from physical viewpoint or elucidate the physics of the mind. In the paper, we reveal a new approach to understand our mind and present a tentative theory to describe how our mind works respect to physics. Two significant concept of time, namely, the internal time of mind and external time of the outside are introduced to measure our mind quantitatively on some degree. The related law of these two types of time is similar to the special relativity proposed by Einstein. Our theory aims to provide a new perspective to understand and know ourselves and lead our life better. At the end of paper, we design an experiment to check the correctness of our results.

This paper presents a new idea to understand human's thoughts and behaviors. Here, we propose a tentative theory of human's thoughts and behaviors, including the relativity of the thoughts, the relativity of the behaviors with thoughts, the inertia of the behaviors with thoughts and its corollary, the spiral advance of the human's thoughts, the procedure of the behaviors with thoughts, and a universal identity. This paper aims to provide a new method to know ourselves and lead human's life better. We design some experiments to check the theory lastly.

Contemporary theories of choice posit that decision making is a constructive process in which a decision maker uses information about the choice options to generate support for various decisions and judgments, then uses these decisions and judgments to reduce their uncertainty about their own preferences. Here we examine how these constructive processes unfold by tracking dynamic changes in preference strength. Across two experiments, we observed that mean preference strength oscillated over time and found that eliciting a choice strongly affected the pattern of oscillation. Preferences following choices oscillated between being stronger than those without prior choice (bolstering) and being weaker than those without choice (suppression). An open system model, merging epistemic uncertainty about how a person reacts to options and ontic uncertainty about how their preference is affected by choice, accounts for the oscillations resulting in both bolstering and suppression effects.

In many workplace contexts, accurate predictions of a human’s fatigue state can drastically improve system safety. Biomathematical models of fatigue (BMMs) are a family of dynamic phenomenological models that predict the neurobehavioural outcomes of fatigue (e.g., sleepiness, performance impairment) based on sleep/wake history (Dawson, Darwent, & Roach, 2017). However, to-date there are no open source implementations of BMMs, and this presents a significant barrier to their broadscale adoption by researchers and industry practitioners. FIPS is an open source R package (R Core Team, 2020) to facilitate BMM research and simulation. FIPS has implementations of several published bio-mathematical models and includes functions for easily manipulating sleep history data into the required data structures. FIPS also includes default plot and summary methods to aid model interpretation. Model objects follow tidy data conventions (Wickham, 2014), enabling FIPS to be integrated into existing research workflows of R users.

We recently discussed several limitations of Bayesian leave-one-out cross-validation (LOO) for model selection. Our contribution attracted three thought-provoking commentaries. In this rejoinder, we address each of the commentaries and identify several additional limitations of LOO-based methods such as Bayesian stacking. We focus on differences between LOO-based methods versus approaches that consistently use Bayes' rule for both parameter estimation and model comparison. We conclude that LOO-based methods do not align satisfactorily with the epistemic goal of mathematical psychology.

Computational implementations of Theory of Mind (ToM), the ability to attribute mental states to others, has been used to investigate a variety of issues. This includes the effect of framing effects on, or inter-species differences in, ability to do ToM (Devaine et al., 2014a, 2017), ToM in autists (d’Arc et al., 2018), or providing an explanation for the apparent limits on human ability to do ToM recursively (Devaine et al., 2014b). It has been implemented in the VBA package for Matlab (Daunizeau et al., 2014), but not in any free and open-source software. Therefore this thesis presents the Theory of Mind simulation using Python (tomsup) package. The tomsup package provides accessible tools for running agent-based models in a game theory context, and allows the implementation of a computational model of ToM, either in agent-based models or in interaction with a human player. The implementation of the ToM model was originally proposed by Yoshida et al. (2008), and was developed by drawing on the Free Energy Principle (Friston, 2010) to its current form as it is in Devaine et al. (2017), where it is generalized to any 2-player game which can be operationalized as a 2-by-2 payoff matrix. Importantly, the ToM implementation introduces a sophistication level k, which determines how many recursive simulations of its opponent it can perform, hereby assuming bounded rationality (Kahneman, 2003). An agent using the ToM model, denoted as k-ToM, uses a variational Bayes Laplace approximation (Daunizeau, 2017b) on a turn-by-turn basis to infer its opponent’s model parameters and sophistication level, based on which it predicts the opponent’s choice and acts accordingly. An agent-based model simulation using the competitive matching pennies game was done to perform a prelim- inary investigation of the behaviour of the k-ToM model. Most importantly, it was found that k-ToM’s prior beliefs about its opponent have a notable effect on its performance, even over many trials, warranting further research into how its priors should be formed. Various ways are suggested in which the tomsup package and the k-ToM model could be applied and developed further, as well as a discussion on how to make it broadly available, so as to scaffold future research using computational ToM models.

Evidence accumulation models (EAMs) have become the dominant explanation of how the decision-making process operates, proposing that decisions are the result of a process of evidence accumulation. The primary use of EAMs has been as "measurement tools" of the underlying decision-making process, where researchers apply EAMs to empirical data to estimate participants' task ability (i.e., the "drift rate"), response caution (i.e., the "decision threshold"), and the time taken for other processes (i.e., the "non-decision time"), making EAMs a powerful tool for discriminating between competing psychological theories. Recent studies have brought into question the mapping between the latent parameters of EAMs and the theoretical constructs that they are thought to represent, showing that emphasizing urgent responding -- which intuitively should selectively influence decision threshold -- may also influence drift rate and/or non-decision time. However, these findings have been mixed, leading to differences in opinion between experts in the field. The current study aims to provide a more conclusive answer to the implications of emphasizing urgent responding, providing a re-analyse of 6 data sets from previous studies using two different EAMs -- the diffusion model and the linear ballistic accumulator (LBA) -- with state-of-the-art methods for model selection based inference. The findings display clear evidence for a difference in conclusions between the two models, with the diffusion model suggesting that decision threshold and non-decision time decrease when urgency is emphasized, and the LBA suggesting that decision threshold and drift rate decrease when urgency is emphasized. Furthermore, although these models disagree regarding whether non-decision time or drift rate decrease under urgency emphasis, both show clear evidence that emphasizing urgency does not selectively influence decision threshold. These findings suggest that researchers should revise their assumptions about certain experimental manipulations, the specification of certain EAMs, or perhaps both.

What kind of dynamic decision process do humans use to make decisions? In this article, two different types of processes are reviewed and compared: Markov and quantum. Markov processes are based on the idea that at any given point in time a decision maker has a definite and specific level of support for available choice alternatives, and the dynamic decision process is represented by a single trajectory that traces out a path across time. When a response is requested, a person's decision or judgment is generated from the current location along the trajectory. By contrast, quantum processes are founded on the idea that a person's state can be represented by a superposition over different degrees of support for available choice options, and that the dynamics of this state form a wave moving across levels of support over time. When a response is requested, a decision or judgment is constructed out of the superposition by "actualizing" a specific degree or range of degrees of support to create a definite state. The purpose of this article is to introduce these two contrasting theories, review empirical studies comparing the two theories, and identify conditions that determine when each theory is more accurate and useful than the other. This article is categorized under: Economics > Individual Decision-Making Psychology > Reasoning and Decision Making Psychology > Theory and Methods.

Recent results have challenged the widespread assumption of dual process models of belief bias that sound reasoning relies on slow, careful reflection, whereas biased reasoning is based on fast intuition. Instead, parallel process models of reasoning suggest that rule- and belief-based problem features are processed in parallel and that reasoning problems that elicit a conflict between rule- and belief-based problem features may also elicit more than one Type 1 response. This theoretical developmental has important implications for individual-differences research on reasoning, because rule-based responses by certain individuals may reflect that these individuals were either more likely to give a rule-based default response or that they successfully inhibited and overrode a belief-based default response. In two studies, we used the diffusion model to describe decision making during syllogistic reasoning and related model parameters to individual differences in cognitive abilities and thinking styles. We found that individuals with a greater need for cognition showed a smaller decrease in drift rates when confronted with a conflict between rule- and belief-based problem features under conflict instruction, which suggests that a greater disposition to engage in reflective thinking facilitated the inhibition and successful override of Type 1 responses. More intelligent individuals, however, showed a greater decrease in drift rates when confronted with a conflict between rule- and belief-based problem features under belief instruction, which suggests that their quickly generated logical response interfered with their ability to evaluate lower-level intrinsic problem features. Taken together, this double dissociation suggests that cognitive abilities and thinking styles affect the processing of conflict information through different mechanisms and at different stages of information-processing: Greater cognitive abilities facilitate the efficient creation of decoupled problem representations, whereas a greater disposition to engage in critical thinking facilitates the successful detection and override of Type 1 responses.

The analysis of longitudinal neuroimaging data within the massively univariate framework provides the opportunity to study empirical questions about neurodevelopment. Missing outcome data are an all-to-common feature of any longitudinal study, a feature that, if handled improperly, can reduce statistical power and lead to biased parameter estimates. The goal of this paper is to provide conceptual clarity of the issues and non-issues that arise from analyzing incomplete data in longitudinal studies with particular focus on neuroimaging data. This paper begins with a review of the hierarchy of missing data mechanisms and their relationship to likelihood-based methods, a review that is necessary not just for likelihood-based methods, but also for multiple-imputation methods. Next, the paper provides a series of simulation studies with designs common in longitudinal neuroimaging studies to help illustrate missing data concepts regardless of interpretation. Finally, two applied examples are used to demonstrate the sensitivity of inferences under different missing data assumptions and how this may change the substantive interpretation. The paper concludes with a set of guidelines for analyzing incomplete longitudinal data that can improve the validity of research findings in developmental neuroimaging research. Keywords: Neuroimaging, Missing data, Likelihood, Longitudinal data

An important tool in the advancement of cognitive science are quantitative models that represent different cognitive variables in terms of model parameters. To evaluate such models, their parameters are typically tested for relationships with behavioral and physiological variables that are thought to reflect specific cognitive processes. However, many models do not come equipped with the statistical framework needed to relate model parameters to covariates. Instead, researchers often revert to classifying participants into groups depending on their values on the covariates, and subsequently comparing the estimated model parameters between these groups. Here we develop a comprehensive solution to the covariate problem in the form of a Bayesian regression framework. Our framework can be easily added to existing cognitive models and allows researchers to quantify the evidential support for relationships between covariates and model parameters using Bayes factors. Moreover, we present a simulation study that demonstrates the superiority of the Bayesian regression framework to the conventional classification-based approach.

The Cognitive Reflection Test, measuring intuition inhibition and cognitive reflection, has become extremely popular because it reliably predicts reasoning performance, decision-making, and beliefs. Across studies, the response format of CRT items sometimes differs, based on the assumed construct equivalence of tests with open-ended versus multiple-choice items (the equivalence hypothesis). Evidence and theoretical reasons, however, suggest that the cognitive processes measured by these response formats and their associated performances might differ (the nonequivalence hypothesis). We tested the two hypotheses experimentally by assessing the performance in tests with different response formats and by comparing their predictive and construct validity. In a between-subjects experiment (n = 452), participants answered stem-equivalent CRT items in an open-ended, a two-option, or a four-option response format and then completed tasks on belief bias, denominator neglect, and paranormal beliefs (benchmark indicators of predictive validity), as well as on actively open-minded thinking and numeracy (benchmark indicators of construct validity). We found no significant differences between the three response formats in the numbers of correct responses, the numbers of intuitive responses (with the exception of the two-option version, which had a higher number than the other tests), and the correlational patterns of the indicators of predictive and construct validity. All three test versions were similarly reliable, but the multiple-choice formats were completed more quickly. We speculate that the specific nature of the CRT items helps build construct equivalence among the different response formats. We recommend using the validated multiple-choice version of the CRT presented here, particularly the four-option CRT, for practical and methodological reasons. Supplementary materials and data are available at https://osf.io/mzhyc/ .

This Tutorial explains the statistical concept known as likelihood and discusses how it underlies common frequentist and Bayesian statistical methods. The article is suitable for researchers interested in understanding the basis of their statistical tools and is also intended as a resource for teachers to use in their classrooms to introduce the topic to students at a conceptual level.

Evaluation of model fit is critically important for every structural equation model (SEM), and sophisticated methods have been developed for this task. Among them are the χ² goodness-of-fit test, decomposition of the χ², derived measures like the popular root mean square error of approximation (RMSEA) or comparative fit index (CFI), or inspection of residuals or modification indices. Many of these methods provide a global approach to model fit evaluation: A single index is computed that quantifies the fit of the entire SEM to the data. In contrast, graphical criteria like d-separation or trek-separation allow derivation of implications that can be used for local fit evaluation, an approach that is hardly ever applied. We provide an overview of local fit evaluation from the viewpoint of SEM practitioners. In the presence of model misfit, local fit evaluation can potentially help in pinpointing where the problem with the model lies. For models that do fit the data, local tests can identify the parts of the model that are corroborated by the data. Local tests can also be conducted before a model is fitted at all, and they can be used even for models that are globally underidentified. We discuss appropriate statistical local tests, and provide applied examples. We also present novel software in R that automates this type of local fit evaluation. (PsycINFO Database Record

Classical dynamic theories of decision making assume that responses are triggered by accumulating a threshold amount of information. Recently, there has been a growing appreciation that the passage of time also plays a role in triggering responses. We propose that decision processes are composed of two diffusive accumulation mechanisms---one evidence-based and one time-based---that compete in an independent race architecture. We show that this Timed Racing Diffusion Model (TRDM) provides a unified, comprehensive and quantitatively accurate explanation of key decision phenomena---including the effects of implicit and explicit deadlines and the relative speed of correct and error responses under speed-accuracy tradeoffs---without requiring additional mechanisms that have been criticized as being ad-hoc in theoretical motivation and difficult to estimate, such as trial-to-trial variability parameters, collapsing thresholds, or urgency signals. In contrast, our addition is grounded in a widely validated account of time-estimation performance, enabling the same mechanism to simultaneously account for interval estimation and decision making with an explicit deadline.

The topic of replicability has recently captivated the emerging field of networkpsychometrics. Although methodological practice (e.g., p-hacking) has been identified as aroot cause of unreliable research findings in psychological science, the statistical modelitself has come under attack in the partial correlation network literature. In a motivatingexample, I first describe how sampling variability inherent to partial correlations can merelygive the appearance of unreliability. For example, when going from zero-order to partialcorrelations there is necessarily more sampling variability that translates into reducedstatistical power. I then introduce novel methodology for deriving expected networkreplicability (ENR), wherein replication is modeled with the Poisson-binomial distribution.This analytic solution can be used with the Pearson, Spearman, Kendall, and polychoricpartial correlation coefficient. I first employed the method to estimate ENR for a variety ofdatasets from the network literature. Here it was determined that partial correlationnetworks do not have inherent limitations, given current estimates of replicability wereconsistent with ENR. I then highlighted sources that can reduce replicability, that is, whengoing from continuous to ordinal data with few categories and employing a multiplecomparisons correction. To address these challenges, I described a strategy for using theproposed method to plan for network replication. I end with recommendations that includethe importance of the network literature repositioning itself with gold-standard approachesfor assessing replication, including explicit consideration of type I and type II error rates.The method for computing ENR is implemented in the R package GGMnonreg.

A model, driven by the theories of Special and General Relativity, is suggested. This model tends to correlate the relativistic view on time dilation with the current models and conclusions on time perception. The model uses energy ratios instead of geometrical transformations to explain time dilation. Brain mechanisms like the arousal mechanism and the attention mechanism are interpreted and combined. Matrices of order two are generated to contain the time dilation between two observers, from the point of view of a third observer. The matrices are used to transform an observer time to another observer time. Correlations with the official time dilation equations are given in the appendix.

Recently-developed models of decision behavior have provided richer accounts of the cognitive processes underlying choice by examining performance on tasks where responses can fall along a continuum, such as identifying the color or orientation of a stimulus. While these have laudably expanded models beyond simple binary and multi-alternative choice paradigms, critical concerns remain about the models lack of completeness, poor computational tractability, or inability to capture important characteristics of choice responses. Specifically, no model is yet able to predict a truly continuous distribution of responses that exhibit multimodality, where responses have more than one central tendency. This property appears frequently in real data where there is conflict between decision information favoring responses at different locations, such as a predecision cue that indicates a different response than the stimulus. These patterns of data are informative to psychological theory, making it critical to develop a better account of continuous response tasks. In this theoretical note, we use a geometric approach developed by Kvam (2019) to provide a solution to this issue and to reconcile the different existing models under a common framework. The resulting geometric diffusion model (GDM) yields a truly continuous joint distribution of responses and response times, produces multimodal distributions of responses, and offers much greater computational efficiency than models producing discrete approximations of continuous responses. We demonstrate that this model can be extended to account for behavior when alternatives are not arranged in a circle, including a case where responses can fall along a 2-dimensional plane such as identifying the location of an item on a computer screen.

The target article on robust modeling (Lee et al. in review) generated a lot of commentary. In this reply, we discuss some of the common themes in the commentaries; some are simple points of agreement while others are extensions of a practical or abstract nature. We also address a small number of disagreements or confusions.

People express quantities using a remarkably small set of units – digits. Confusing digits could be costly, and not all confusions are equal; confusing a price tag of 2 dollars with 9 dollars is naturally more costly than confusing 2 with 3. Confusion patterns are intimately related to the distances between mental representations, which are hypothetical internal symbols said to stand for, or represent, ‘real’ external stimuli. The distance between the mental representations of two digits could be determined by their numerical distance. Alternatively, it could be driven by visual similarity. In an English speaking cohort, we investigated the mental representations of familiar and unfamiliar numbers (4 sets: Arabic, Chinese, Thai, and non-symbolic dots) through a set of identification experiments, using multi-dimensional scaling and cluster analysis. We controlled for undesired effects of response bias using Luce’s choice model. Our findings show Arabic, Chinese and Thai numerals were represented in the mental space by perceptual similarities. We also find non-symbolic dots were represented by perceptual and numerical similarities. This work is a novel contribution to the literature and lays the foundation for further investigations into the mental representation of numerals across cultures.

Forensic handwriting examiners currently testify to the origin of questioned handwriting for legal purposes. However, forensic scientists are increasingly being encouraged to assign probabilities to their observations in the form of a likelihood ratio. This study is the first to examine whether handwriting experts are able to estimate the frequency of US handwriting features more accurately than novices. The results indicate that the absolute error for experts was lower than novices, but the size of the effect is modest, and the overall error rate even for experts is large enough as to raise questions about whether their estimates can be sufficiently trustworthy for presentation in courts. When errors are separated into effects caused by miscalibration and those caused by imprecision, we find systematic differences between individuals. Finally, we consider several ways of aggregating predictions from multiple experts, suggesting that quite substantial improvements in expert predictions are possible when a suitable aggregation method is used.

The additive clustering approach to modeling pairwise similarity of entities is a powerful tool for deriving featural stimulus representations. In a recent paper, Lee (2001) proposes a statistically principled measure for choosing between clustering models that accounts for model complexity as well as data fit. Importantly, complexity is understood to be a property, not merely of the number of clusters, but also their size and pattern of overlap. However, some caution is required when interpreting the measure, with regard to the applicability of the Hadamard inequality to the complexity matrix.

Systems Factorial Technology (SFT) is a popular framework for that has been used to investigate processing capacity across many psychological domains over the past 25+ years. To date, it had been assumed that no processing resources are used for sources in which no signal has been presented (i.e., in a location that can contain a signal but does not on a given trial). Hence, response times are purely driven by the ``signal-containing'' location or locations. This assumption is critical to the underlying mathematics of the capacity coefficient measure of SFT. In this manuscript, we show that stimulus locations influence response times even when they contain no signal, and that this influence has repercussions for the interpretation of processing capacity under the SFT framework, particularly in conjunctive (AND) tasks - where positive responses require detection of signals in multiple locations. We propose a modification to the AND task requiring participants to fully identify both target locations on all trials. This modification allows a new coefficient to be derived. We apply the new coefficient to novel experimental data and resolve a previously reported empirical paradox, where observed capacity was limited in an OR detection task but super capacity in an AND detection task. Hence, previously reported differences in processing capacity between OR and AND task designs are likely to have been spurious.

This paper develops a new representational model of similarity data that combines continuous dimensions with discrete features. An algorithm capable of learning these representations is described, and a Bayesian model selection approach for choosing the appropriate number of dimensions and features is developed. The approach is demonstrated on a classic data set that considers the similarities between the numbers 0 through 9.