A diffusion model explanation of the worst performance rule for reaction time and IQ

The worst performance rule for cognitive tasks [Coyle, T.R. (2003). IQ, the worst performance rule, and Spearman's law: A reanalysis and extension. Intelligence, 31, 567-587] in which reaction time is measured is the result that IQ scores correlate better with longer (i.e., 0.7 and 0.9 quantile) reaction times than shorter (i.e., 0.1 and 0.3 quantile) reaction times. We show that this pattern of correlations can be predicted by the diffusion model [Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59-108], in two ways: either assuming that the rate of accumulation of information toward a decision is higher for higher IQ subjects or assuming that the criterial amounts of information they require before a decision are lower. Importantly, the model explains both reaction times and accuracy, so the two possibilities can be distinguished.     

A review of the worst performance rule: Evidence, theory, and alternative hypotheses

This paper reviews evidence, theory, and alternative hypotheses for the worst performance rule (WPR), which states that on multitrial cognitive tasks, worst performance trials predict general intelligence (g) better than best performance trials. A review of the relevant evidence indicates that the WPR has been found for a variety of participants, tasks, and measures. A review of relevant theories reveals that the WPR appears to be related to cognitive factors (e.g., lapses in working memory) as well as biological factors (e.g., individual differences in neural oscillations). A review of alternative hypotheses shows that the WPR cannot be attributed to statistical or data artifacts such as outliers, unreliable measurement, or variance compression. The preponderance of evidence supports the hypothesis that the WPR holds for cognitive tasks high in g saturation but not for cognitive tasks low in g saturation. The paper ends with a call for research on the causes of the WPR and for research on the correlates of best performance.     

A parallel rule activation and rule synthesis model for generalization in category learning

This paper proposes a distinction between primary generalization (transfer from stored exemplars to perceived targets) and secondary generalization (transfer from inferred abstractions to perceived targets). This distinction is embodied in the parallel rule activation and rule synthesis (PRAS) model, a production model capable of exemplar-based and abstraction-based categorization. As an exemplar model, the PRAS model is related to the generalized context model (Nosofsky, 1984). Exemplars are stored in memory encoded as condition-action rules. Working as an exemplar-based model, rules are activated on the basis of their strength and their similarity to the current to-be-categorized instance. Similarity between a target and a stored exemplar is weighted for attention to the dimensions of the psychological space. Depending on the value of a special parameter, the PRAS model is also able to operate as an abstraction model. In the latter case, it attempts to construct generalizing productions, which are activated according to the same rules as the exemplar-specific rules. The model is described in detail. It is applied to a number of important observations described in the research literature, and an experiment is reported that tested the usefulness of the proposed secondary-generalization mechanism. Finally, the discussion elaborates on the implications of the present study for further research.     

A test of the distraction explanation of disfluency modification in stuttering

The distraction explanation of changes in stuttering rate was examined in the present experiment. Twelve stutterers were compared with 12 nonstutterers who were matched for age, sex, and level of education. Subjects were tested for disfluency production under conditions designed to reflect the dimension of distraction. These conditions were: (a) over attention to speech (counting speaking errors). (b) “normal” conditions (no additional task), and (c) distraction (pursuit tracking of an irregular target). The results showed no effect on stuttering rate that could be attributed to the distraction conditions. However, stutterers rated the difficulty of these conditions in concordance with the distraction theory. It was suggested that, while stutterers' perceptions may account for the popularity of the distraction explanation, evidence supporting the theory is lacking.     

A test of the spatial-frequency explanation of the Müller-Lyer illusion

Previous investigations have shown that the response of spatial-frequency-specific channels in the human visual system is differentially affected by adaptation to gratings of distinct spatial frequencies and/or orientations. A study is reported of the effects of adaptation to vertical or horizontal gratings of a high or a low spatial frequency on the extent of the Brentano form of the Müller-Lyer illusion in human observers. It is shown that the illusion decreases after adaptation to vertical gratings of low spatial frequency, but seems unaffected otherwise. These results are consistent with the notion of visual channels that are spatial-frequency and orientation specific, and support the argument that the Müller-Lyer illusion may be due primarily to lower-spatial-frequency components in the Fourier spectra of the image.     

A test of the peak-end rule with extended autobiographical events

Forty-nine students went on vacation for an average of 7 days and sent daily text messages about the happiness they had experienced over the previous 24 h. After their vacation, they were questioned on the overall happiness they had experienced and were asked to recall the daily record of their happiness. The duration of the vacation had no effect on the subsequent evaluations, and participants were not able to recall the detail of their day-to-day changes in happiness. A number of summary measures provided reasonable prediction of the recalled overall happiness of the vacation. The peak-end rule was not an outstandingly good predictor. Overall, the results indicate much reconstruction of the affective states.     

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.     

A diffusion model for discrimination of temporal numerosity

This paper presents a model for sequential discrimination between the temporal frequencies of two discrete events. The model results from adjoining a theory for continuous estimation of temporal numerosity to a mathematical representation of the response criterion. A simple set of assumptions is used to describe the time evolution of numerosity estimates by a stochastic diffusion process. The predictions of the model are extensively compared to a body of results presented in a previous report, with an emphasis on individual performances. It is shown that a number of response strategies, observed in actual experiments, can be predicted by generalizing the classical notion of a single-valued response threshold to a stochastic, time-varying process.     

A method for analysing performance in the rod-and-frame test

Abstract.— Scoring only the unsigned (absolute) errors in the Rod-and-Frame Test (RFT) is questioned because the method confounds a number of variables. Another way of scoring the RFT is proposed which differentiates between (1) the subject's constant error, (2) the effect of the tilted frame, and (3) the rod starting position effect. The method also allows estimation of the response consistency of the subject. What is more, the values for each subject of the constant error, of the frame tilt effect, and of the rod starting position effect may be tested for significance on the basis of the degree of response consistency observed for that particular subject, thus making the new method more person-oriented than the unsigned error method.     

A new processing model for predicting performance on Pascual-Leone's test of M-space

A new model is proposed for explaining children's performance on Pascual-Leone's test of M-space. The model differs from Pascual-Leone's in three regards. (1) It assumes that children do not stop sampling a compound stimulus until every simple stimulus in their field of attention has already been noticed and responded to. (2) It assumes that the probability of sampling different combinations of simple stimuli conforms to the laws of Maxwell-Boltzman statistics rather than Bose-Einstein statistics. (3) It assumes that children's ability to detect all the simple stimuli in a compound stimulus is highly dependent both on the relative saliencies of the simple stimuli and on the length of time for which the compound stimulus is exposed. Using the developmental values of M hypothesized by Pascual-Leone, and standard techniques of computer simulation, the new model is used to generate theoretical performance curves for children at four different age levels and seven different levels of stimulus complexity. It is shown that the predicted performance curves for an exposure time of 5 sec provide a reasonable fit to the data originally reported by Pascual-Leone (1970), and that the predicted performance curves for an exposure time of 10 sec provide a reasonable fit to data obtained more recently by Parkinson (1976). Finally, it is shown that the order of children's responses as well as the number of their responses can be predicted. Two conclusions are drawn. (1) The new processing model offers a viable alternative to the model originally proposed by Pascual-Leone. (2) Regardless of which processing model is employed, the M-values originally postulated by Pascual-Leone are valid.     

A test of the self-perception explanation of the effects of rewards on intrinsic interest

An experiment was conducted to test the proposition that rewards undermine or enhance intrinsic interest in a task to the extent that individuals interpret their behavior as being motivated by the reward. It was predicted that when subjects were denied the opportunity to develop and confirm this attribution, rewards would not produce an undermining effect, but rather would enhance dispositions and behavior. Subjects were recruited to evaluate a new sugar-free soft drink. Two levels of incentives (reward-no reward), two levels of examination (opportunity-no opportunity), and three levels of outcome (good-neutral-poor) were employed. The results support the prediction that an incentive's effect depends on the examination opportunity. In the examination condition, rewarded subjects attributed their behavior more to external factors than did unrewarded subjects, but gave more negative product evaluations only after tasting it. In the no examination condition, there were no differences in the attributions made by rewarded and unrewarded subjects, and rewarded subjects were more positively disposed toward the product both before and after tasting it. These results are explained as a consequence of two properties of rewards, enhancement through reinforcement and undermining through discounting, and of hypothesis-testing processes.     

A test of the deadline model for speed-accuracy tradeoffs

Two experiments were conducted to evaluate the deadline model for speed-accuracy tradeoffs. According to the deadline model, participants in speeded-response tasks terminate stimulus discrimination as soon as it has run to completion or as soon as a predetermined time deadline has arrived, whichever comes first. Speed is traded for accuracy by varying the time deadlines; short deadlines yield fast but sometimes inaccurate responses, whereas long deadlines allow for slow, accurate responses. A new prediction of this model, based on a comparison of reaction time distributions, was derived and tested in experiments involving the joint manipulation of speed stress and stimulus discriminability. Clear violations of this prediction were observed when participants made relative brightness judgments (Experiment 1) and when they made lexical decisions (Experiment 2), rejecting both the deadline model and the fast-guess model. Several alternative models for speed-accuracy tradeoffs, including random-walk and accumulator models, are compatible with the results.     

A goodness of fit test for the rasch model

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope,i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates. Based on the within scoregroup estimates and the over-all estimates of item difficulties a conditional likelihood ratio is formed. It is shown that—2 times the logarithm of this ratio isx ²-distributed when the Rasch model is true. The power of the proposed goodness of fit test is discussed for alternative models with logistic item characteristic curves, but unequal discriminating items from a scholastic aptitude test.     

A fast numerical algorithm for the estimation of diffusion model parameters

In this paper, we describe a new algorithmic approach for parameter estimation in Ratcliff's [(1978). A theory of memory retrieval. Psychological Review, 85 (2), 59-108] diffusion model. This problem, especially if inter-trial variabilities of parameters are included in the model, is computationally very expensive; the parameter estimation procedure often takes a long time even with today's high-speed computers. The algorithm described here makes the calculation of the cumulative distribution functions for predicted process durations computationally much less expensive. This improvement is achieved by solving the Kolmogorov backward equation numerically instead of employing the previously used closed form solution. Additionally, the algorithm can determine the optimum fit for one of the model parameters (the starting point z) directly, thereby reducing the dimension of the parameter search space by one. The resulting method is shown to be notably faster than the standard (closed-form solution) method for parameter estimation.     

A diffusion model decomposition of the practice effect

When people repeatedly perform the same cognitive task, their mean response times (RTs) invariably decrease. The mathematical function that best describes this decrease has been the subject of intense debate. Here, we seek a deeper understanding of the practice effect by simultaneously taking into account the changes in accuracy and in RT distributions with practice, both for correct and error responses. To this end, we used the Ratcliff diffusion model, a successful model of two-choice RTs that decomposes the effect of practice into its constituent psychological processes. Analyses of data from a 10,000-trial lexical decision task demonstrate that practice not only affects the speed of information processing, but also response caution, response bias, and peripheral processing time. We conclude that the practice effect consists of multiple subcomponents, and that it may be hazardous to abstract the interactive combination of these subcomponents in terms of a single output measure such as mean RT for correct responses. Supplemental materials may be downloaded from http://pbr .psychonomic-journals.org/content/supplemental.     

A response rule for positive and negative stimulus interaction in associative learning and performance

The present article presents a response rule developed to account for both positive and negative stimulus interaction. In the response rule proposed here, positive interaction phenomena (e.g., second-order conditioning) and negative interaction phenomena (e.g., Pavlovian conditioned inhibition) are presumed to occur during performance and acquisition, respectively. Also, in this rule the novelty of the test stimulus determines the expression of positive interaction on responding. As the stimulus loses its novelty over training, positive interaction effects will wane, which will allow negative interaction effects to emerge in responding elicited by the stimulus. It is proposed that this response rule can be adopted by acquisition-focused associative models (e.g., Rescorla & Wagner, 1972) in order to account for contrary associative phenomena in the literature. The simulation program used in this study is available for download from the author’s website and from the Psychonomic Society website at www.psychonomic.org/archive.