A note on residual M-distances for identifying aberrant response patterns

Although a statistical model might fit well to a large proportion of the individuals of a random sample, some individuals might give ‘unusual’ responses that are not well explained by the hypothesized model. If individual responses are given as continuous response vectors, M-distances can be used to produce real valued indicators of how well an individual's response vector corresponds to a covariance structure implied by a psychometric model. In this note, we focus on the so-called one-factor model. Two M-distances, d_si and d_ri, which are sensitive to different aspects of the assumed factor model, have been proposed. While one of the M-distances, d_ri, has been derived based on Bartlett factor scores, in this note we show that the second M-distance, d_si, can be derived in an analogous fashion based on Thomson factor scores.     

A latent topic model with Markov transition for process data

We propose a latent topic model with a Markov transition for process data, which consists of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem-solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem-solving item in the 2012 version of the Programme for International Student Assessment (PISA).     

Reducing tunnel vision with a pen‐and‐paper tool for the weighting of criminal evidence

In order to prevent tunnel vision, and ultimately miscarriages of justice, police, prosecutors, and judges must remain open to alternative scenarios in which the suspect is in fact innocent. However, it is not evident from the literature that people are sufficiently aware of how alternative scenarios should be employed in the decision‐making process. In the present research, participants read a case vignette and formed an impression of the suspect's guilt. Some participants were made familiar with an alternative scenario. Others were not only presented with an alternative scenario but were also instructed to score (with pen and paper) the extent to which every piece of evidence fitted in the primary and the alternative scenario. Findings suggest that this pen‐and‐paper task helped to reduce tunnel vision.     

Discounting model selection with area‐based measures: A case for numerical integration

A novel method for analyzing delay discounting data is proposed. This newer metric, a model‐based Area Under Curve (AUC) combining approximate Bayesian model selection and numerical integration, was compared to the point‐based AUC methods developed by Myerson, Green, and Warusawitharana (2001) and extended by Borges, Kuang, Milhorn, and Yi (2016). Using data from computer simulation and a published study, comparisons of these methods indicated that a model‐based form of AUC offered a more consistent and statistically robust measurement of area than provided by using point‐based methods alone. Beyond providing a form of AUC directly from a discounting model, numerical integration methods permitted a general calculation in cases when the Effective Delay 50 (ED50) measure could not be calculated. This allowed discounting model selection to proceed in conditions where data are traditionally more challenging to model and measure, a situation where point‐based AUC methods are often enlisted. Results from simulation and existing data indicated that numerical integration methods extended both the area‐based interpretation of delay discounting as well as the discounting model selection approach. Limitations of point‐based AUC as a first‐line analysis of discounting and additional extensions of discounting model selection were also discussed.     

The natural mathematics of behavior analysis

Models that generate event records have very general scope regarding the dimensions of the target behavior that we measure. From a set of predicted event records, we can generate predictions for any dependent variable that we could compute from the event records of our subjects. In this sense, models that generate event records permit us a freely multivariate analysis. To explore this proposition, we conducted a multivariate examination of Catania's Operant Reserve on single VI schedules in transition using a Markov Chain Monte Carlo scheme for Approximate Bayesian Computation. Although we found systematic deviations between our implementation of Catania's Operant Reserve and our observed data (e.g., mismatches in the shape of the interresponse time distributions), the general approach that we have demonstrated represents an avenue for modelling behavior that transcends the typical constraints of algebraic models.     

Non‐Bayesian Noun Generalization in 3‐ to 5‐Year‐Old Children: Probing the Role of Prior Knowledge in the Suspicious Coincidence Effect

It is unclear how children learn labels for multiple overlapping categories such as “Labrador,” “dog,” and “animal.” Xu and Tenenbaum (2007a) suggested that learners infer correct meanings with the help of Bayesian inference. They instantiated these claims in a Bayesian model, which they tested with preschoolers and adults. Here, we report data testing a developmental prediction of the Bayesian model—that more knowledge should lead to narrower category inferences when presented with multiple subordinate exemplars. Two experiments did not support this prediction. Children with more category knowledge showed broader generalization when presented with multiple subordinate exemplars, compared to less knowledgeable children and adults. This implies a U‐shaped developmental trend. The Bayesian model was not able to account for these data, even with inputs that reflected the similarity judgments of children. We discuss implications for the Bayesian model, including a combined Bayesian/morphological knowledge account that could explain the demonstrated U‐shaped trend.     

Comparing Data Sets: Implicit Summaries of the Statistical Properties of Number Sets

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of means, coefficient of variation, and number of observations, by measuring eye fixations, accuracy, and confidence when assessing differences between number sets. Results indicated that participants implicitly create and compare approximate summary values that include information about mean and variance, with no evidence of explicit calculation. Accuracy and confidence increased, while the number of fixations decreased as sets became more distinct (i.e., as mean ratios increase and variance decreases), demonstrating that the statistical properties of datasets were highly related to comparisons. The discussion includes a model proposing how reasoners summarize and compare datasets within the architecture for approximate number representation.     

Examining the association between psychological wellbeing with daily and intra-individual variation in subjective wellbeing

A number of studies identify distinct dimensions of psychological and subjective wellbeing. However, few investigations have examined how these distinctive wellbeing dimensions may be related over time. The present study aimed to contribute to this growing body of research by adopting a measurement burst design to examine the association between psychological functioning with daily and intra-individual variation in affect over a 14-day period, controlling for personality. Participants (N = 45) comprised a sample of Australian adults from Canberra, Australia who were observed on up to 14 days over a 2-week period (Mobs = 10.9 (SD = 3.1)). Maximum Likelihood (ML) estimates from a multi-level structural equation model identified psychological functioning as only weakly associated with daily positive affect, and unrelated to daily levels of negative affect and intra-individual variation in both affect domains when adjusting for demographic, personality and daily stressors. Positive and negative daily events were most strongly associated with positive and negative feelings, respectively. Post-hoc analysis within a Bayesian context confirmed our ML results whilst a Monte Carlo simulation identified sufficient statistical power of significant parameters. Overall, evidence for an association between psychological functioning and daily affect was not identified.