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.     

Integrating Covariates into Social Relations Models: A Plausible Values Approach for Handling Measurement Error in Perceiver and Target Effects

The Social Relations Model (SRM) is a conceptual and analytical approach to examining dyadic behaviors and interpersonal perceptions within groups. In an SRM, the perceiver effect describes a person's tendency to perceive other group members in a certain way, whereas the target effect measures the tendency to be perceived by others in certain ways. In SRM research, it is often of interest to relate these individual SRM effects to covariates. However, the estimated individual SRM effects might not provide a very reliable measure of the true, unobserved SRM effects, resulting in distorted estimates of associations with other variables. This article introduces a plausible values approach that allows users to correct for measurement error when assessing the association of individual SRM effects with other individual difference variables. In the plausible values approach, the latent, true individual SRM effects are treated as missing values and are imputed from an imputation model by applying Bayesian estimation techniques. In a simulation study, the statistical properties of the plausible values approach are compared with two approaches that have been used in previous research. A data example from educational psychology is presented to illustrate how the plausible values approach can be implemented with the software WinBUGS.     

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.     

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.     

Do Bettors Correctly Perceive Odds? Three Studies of How Bettors Interpret Betting Odds as Probabilistic Information

This paper reports on three studies investigating how accurately bettors (=people who regularly bet on sports events) interpret the probabilistic information implied by betting odds. All studies were based on data collected by web surveys prompting a total of 186 experienced bettors to convert sets of representative odds into frequency judgments. Bayesian statistical methods were used to analyze the data. From the results, the following conclusions were made: (i) On the whole, the bettors produced well‐calibrated judgments, indicating that they have realistic perceptions of odds. (ii) Bettors were unable to consciously adjust judgments for different margins. (iii) Although their interval judgments often covered the estimates implied by the odds, the bettors tended to overestimate the variation of expected profitable bets between months. The results are consistent with prior research showing that people tend to make accurate probability judgments when faced with tasks characterized by constant and clear feedback. Copyright © 2015 John Wiley & Sons, Ltd.     

A Duet for one

This paper considers communication in terms of inference about the behaviour of others (and our own behaviour). It is based on the premise that our sensations are largely generated by other agents like ourselves. This means, we are trying to infer how our sensations are caused by others, while they are trying to infer our behaviour: for example, in the dialogue between two speakers. We suggest that the infinite regress induced by modelling another agent – who is modelling you – can be finessed if you both possess the same model. In other words, the sensations caused by others and oneself are generated by the same process. This leads to a view of communication based upon a narrative that is shared by agents who are exchanging sensory signals. Crucially, this narrative transcends agency – and simply involves intermittently attending to and attenuating sensory input. Attending to sensations enables the shared narrative to predict the sensations generated by another (i.e. to listen), while attenuating sensory input enables one to articulate the narrative (i.e. to speak). This produces a reciprocal exchange of sensory signals that, formally, induces a generalised synchrony between internal (neuronal) brain states generating predictions in both agents. We develop the arguments behind this perspective, using an active (Bayesian) inference framework and offer some simulations (of birdsong) as proof of principle.     

Identifying expectations about the strength of causal relationships

When we try to identify causal relationships, how strong do we expect that relationship to be? Bayesian models of causal induction rely on assumptions regarding people’s a priori beliefs about causal systems, with recent research focusing on people’s expectations about the strength of causes. These expectations are expressed in terms of prior probability distributions. While proposals about the form of such prior distributions have been made previously, many different distributions are possible, making it difficult to test such proposals exhaustively. In Experiment 1 we used iterated learning—a method in which participants make inferences about data generated based on their own responses in previous trials—to estimate participants’ prior beliefs about the strengths of causes. This method produced estimated prior distributions that were quite different from those previously proposed in the literature. Experiment 2 collected a large set of human judgments on the strength of causal relationships to be used as a benchmark for evaluating different models, using stimuli that cover a wider and more systematic set of contingencies than previous research. Using these judgments, we evaluated the predictions of various Bayesian models. The Bayesian model with priors estimated via iterated learning compared favorably against the others. Experiment 3 estimated participants’ prior beliefs concerning different causal systems, revealing key similarities in their expectations across diverse scenarios.     

Polytomous multilevel testlet models for testlet‐based assessments with complex sampling designs

A pplications of standard item response theory models assume local independence of items and persons. This paper presents polytomous multilevel testlet models for dual dependence due to item and person clustering in testlet‐based assessments with clustered samples. Simulation and survey data were analysed with a multilevel partial credit testlet model. This model was compared with three alternative models – a testlet partial credit model (PCM), multilevel PCM, and PCM – in terms of model parameter estimation. The results indicated that the deviance information criterion was the fit index that always correctly identified the true multilevel testlet model based on the quantified evidence in model selection, while the Akaike and Bayesian information criteria could not identify the true model. In general, the estimation model and the magnitude of item and person clustering impacted the estimation accuracy of ability parameters, while only the estimation model and the magnitude of item clustering affected the item parameter estimation accuracy. Furthermore, ignoring item clustering effects produced higher total errors in item parameter estimates but did not have much impact on the accuracy of ability parameter estimates, while ignoring person clustering effects yielded higher total errors in ability parameter estimates but did not have much effect on the accuracy of item parameter estimates. When both clustering effects were ignored in the PCM, item and ability parameter estimation accuracy was reduced.     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.