A statistical decision model for sensory discrimination which predicts Weber’s law and other sensory laws: Some results of a computer simulation

A model for visual intensity threshold discrimination is described. Simplified assumptions represent the main features of the visual afferent paths. Discriminative responses are selected centrally by a statistical decision procedure, limited by the noise level. Noise arises from the irreducible physical variability of light, from spontaneous firing, and from variations in transmission in the afferent paths, These variations will tend to be positively correlated. The model was simulated on a computer: it correctly predicts the form of the Weber function (the relation between difference threshold and background intensity) and the features of spatial and temporal “summation”. It also shows that the function relating the central effect of a stimulus to its physical intensity is unlikely to be logarithmic or a power function with a small exponent.     

A study of the near-miss involving Weber’s law and pure-tone intensity discrimination

A study of pure-tone intensity discrimination is presented in which amplitude changes are detected in 1000 Hz tone bursts 15–20 msec in duration. The masking function (log detectable increment vs log background intensity) is found to have a slope of 9/10 when calculations are carried out via energy measurements. This near-miss to Weber’s law is in agreement with other data reported in the literature. The masking slope proves to be essentially independent of stimulus duration between 15 msec and 1.5 sec. Our stable slope parameter is interpreted as a detectability restriction generated by “mass-flow” phenomena in the auditory channel. These phenomena are thought to be similar to the fluctuations accompanying a noisy or turbulent stream of events. Pure-tone intensity discrimination is then analyzed as a special case of energy detection.     

A computer simulation of children’s arithmetic word-problem solving

ARITHPRO is a computer simulation of children’s arithmetic word-problem solving behavior. It is an instantiation of a recently proposed cognitive model of the knowledge and procedures required to solve such problems. The program solves word problems by (1) comprehending the story text in which the problem is embedded, (2) comprehending numerical information as sets of objects, (3) building superstructures from these sets, thereby specifying their logical relations, and (4) using a counting procedure to derive the answer to the problem. This report describes ARITHPRO and its architecture and knowledge base. A few comparisons of ARITHPRO’s performance with that of children are also provided.     

Johannes Kepler’s computer simulation of the universe: Some remarks about theory in psychology

Computer simulation may be an overly seductive way of formulating theory in the social sciences. The capability of constructing complex computer simulation models may remove some of the incentive for finding simple laws. This point is illustrated via a fantasy in which the sixteenth century astronomical theorist, Johannes Kepler, uses Ms computer instead of his mind to account for extant data on stellar and planetary motion. Similarities between sixteenth century cosmology and twentieth century psychology are discussed.     

Reply to William R. Ferrell’s paper “A model for realism of confidence judgments: Implications for underconfidence in sensory discrimination”

Ferrell’s decision-variable partition model and our subjective distance model belong to the same family of Thurstonial models. The subjective distance model is limited to sensory discrimination with the method of constant stimuli and rooted in such notions as discriminal dispersion and sense distance. Ferrell’s model is intended to be wider in scope and to apply to both cognitive and sensory tasks. Both models need supplementary assumptions to predict calibration phenomena. The point of departure for us is the fact that the model predicts under-confidence under “guessing” and the empirical finding that people are about 100% correct when they report “absolutely certain.” Ferrell makes assumptions about cutoffs on the decision variable. The respondent is assumed to adjust or not adjust cutoffs according to “cues to difficulty.” We disagree with Ferrell’s claim that the hard-easy effect is explained by the respondent’s failure to adjust cutoffs sufficiently when there is a change in level of difficulty, and argue that this amounts to little more than a translation of the hard-easy effect into the lingua of Ferrell’s decision-variable partition model. Our argument is that the hard-easy effect is a consequence of the post hoc division of items according to solution probability. In addition, error variance may contribute to regression effects that enlarge the hard-easy effect. Finally, in contrast to Ferrell’s position, we regard inference (cognitive uncertainty) and discrimination (sensory uncertainty) as different psychological processes. An understanding of calibration in these two areas requires separate models.     

Bloch’s law and a Poisson counting model for simple reaction time to light

A series of three experiments was conducted with identical design as an earlier series (Hildreth, 1973). Its purpose was (1) to determine whether Bloch’s law holds for simple reaction time (RT) to still lower intensity visual stimuli, and (2) to provide data for testing a stochastic generalization of the temporal integration model (TI-ED) reported earlier. RT means were found to agree with Bloch’s law for durations below 48 msec. By a statistical test, Bloch’s law was shown to hold for both means and standard deviations below about 65 msec. Latency statistics—means and standard deviations—were predicted by a Poisson process counting model. This model assumes that a number of identical, parallel Poisson processes, activated by light, with pulse interarrival times decreasing with light intensity, trigger light detection when a critical number of pulses arrive at a counting center. For the intensities investigated, both the estimated number of Poisson processes and critical number of pulses required for detection range between 8 and 13. The model predicts the Broca-Sulzer effect for mean RTs which is observed in several of these experiments.     

Bloch’s law and a temporal integration model for simple reaction time to light

In a series of experiments designed to determine whether Bloch’s law holds for simple RT to low-energy visual stimuli, mean RTs were found to agree with Bloch’s law to a close approximation only when a narrow range of stimulus intensities is used. However, they could be accounted for more generally by (1) assuming that detection depends on a “visual response function” (VRF) initiated and maintained by the light stimulus (when the time integral of the VRF reaches a criterion, S detects the light and initiates a response): and (2) the fact that VRF generated by a square-wave flash rises quickly to its maximum, remains at this value for the duration of the flash, and then decays exponentially to zero after flash offset. S continues to integrate the VRF throughout its lifetime, and consequently for a brief stimulus, detection will occur during the exponentially decaying portion of the response-the portion corresponding to “visual persistence.” Finally. when luminances used vary by more than a factor of four. Bloch’s law fails to hold, while the model succeeds, implying that the temporal integration model more generally accounts for RTs.     

A computer simulation model of rats’ place navigation in the Morris water maze

Rats rapidly learn to swim from a variety of starting locations, including novel ones, to a small invisible platform submerged in a pool of cool opaque liquid. A computer simulation based on a simple perceptual memory-matching model successfully mimics this ability. The model assumes that the rat, when it successfully reaches the platform, notes the distance to prominent extramaze landmarks and stores this perceptual information in memory. When placed in the pool on subsequent trials, the simulated rat attempts to match perceived distance between itself and the landmarks to the remembered distances from the platform to the landmark. The model accounts for many of the known facts about rats’ behavior in the swimming pool and makes some interesting predictions that could be easily tested experimentally. The model has the advantage, relative to other cognitive map models, of specifying how spatial information is represented in memory and how this information guides behavior.     

Generating correlation matrices with model error for simulation studies in factor analysis: A combination of the Tucker-Koopman-Linn model and Wijsman’s algorithm

Most simulation studies in factor analysis follow a process of constructing population correlation matrices from the common-factor model and generating sample correlation matrices from the population matrices. In the common-factor model, the population correlation matrix is perfectly fit by the model’s containing common and unique factors. However, since no mathematical model accounts exactly for the real-world phenomena that it is intended to represent, the Tucker-Koopman-Linn model (1969) is more realistic for generating correlation matrices than the conventional common-factor model because the former incorporates model error. In this paper, a procedure for generating population and sample correlation matrices with model error by combining the Tucker-Koopman-Linn model and Wijsman’s algorithm (1959) is presented. The SAS/ IML program for generating correlation matrices is described, and an example is also provided.     

Narrative responsibility and moral dilemma: A case study of a family’s decision about a brain-dead daughter

A brain death case is presented and reinterpreted using the narrative approach. In the case, two Japanese parents face a dilemma about whether to respect their daughter’s desire to donate organs even though, for them, it would mean literally killing their daughter. We argue that the ethical dilemma occurred because the parents were confronted with two conflicting narratives to which they felt a “narrative responsibility,” namely, the responsibility that drives us to tell, retell, and coauthor the (often unfinished) narratives of loved ones. We suggest that moral dilemmas arise not only from conflicts between moral justifications but also from conflicts between narratives and human relationships.     

In pursuit of a historical tradition: N. A. Rozhkov’s scientific laws of history

Despite all that has been written about Russian historiography and how it profoundly changed after the Bolsheviks seized power in 1917, very little is known about the historical tradition immediately before the Soviet era. This article attempts to begin to address this issue by examining the major forces that shaped the historical and sociological thought of Nikolai Alesandrovich Rozhkov (1868–1927). It argues that as Kliuchevskii’s successor and as the first professional historian to eventually present a Marxist analysis of Russian history, Rozhkov was not only the most important historian at that time but one whose work best represented the most significant transition in Russia’s historical tradition. The article concludes that an examination of Rozhkov’s historical methodology offers a new interpretation of the origins of Soviet historiography.

Using a computer simulation of three slot machines to investigate a gambler’s preference among varying densities of near-miss alternatives

The present article describes a software program in Visual Basic .NET designed to simulate three slot machines on a computer screen. This software is described in detail regarding utility, downloading, and usage; and data are presented illustrating the software’s potential for researchers interested in gambling behavior. A simulation of multiple slot machines such as this enables researchers to evaluate players’ preferences across various machines. In the highlighted experiment, 18 recreational slot machine players played the software for extra course credit and a chance at cash prizes. All participants played a version of the simulation in which every 5th response on average was a win, whereas the remaining trials were a loss. However, on those loss trials, a varying distribution of almost wins or near misses (i.e., two winning symbols on the payoff line and the final winning symbol directly above or below the payoff line) were presented in percentages of 15, 30, or 45. While no preferences across the three options could be predicted on the basis of reinforcement history alone, deviations from equal choices across the games were noted and appeared to be the result of the presentations of near-miss losing trials. Implications for a greater understanding of pathological gambling are presented.     

A problem for Wegner and colleagues’ model of the sense of agency

The sense of agency, that is the sense that one is the agent of one’s bodily actions, is one component of our self-consciousness. Recently, Wegner and colleagues have developed a model of the causal history of this sense. Their model takes it that the sense of agency is elicited for an action when one infers that one or other of one’s mental states caused that action. In their terms, the sense of agency is elicited by the inference to apparent mental state causation. Here, I argue that this model is inconsistent with data from developmental psychology that suggests children can identify the agent behind an action without being capable of understanding the relationship between their intentions and actions. Furthermore, I argue that this model is inconsistent with the preserved sense of agency in autism. In general, the problem is that there are cases where subjects can experience themselves as the agent behind their actions despite lacking the resources to make the inference to apparent mental state causation.     

Metacognitive control of action: Preparation for aiming reflects knowledge of Fitts’s law

Metacognitive control has been studied in intellectual skills but has not yet been studied in perceptual-motor skills. To probe metacognitive control in a perceptual-motor context, we developed a task in which participants chose the position of a cursor relative to two targets. One of the two targets was randomly erased. Participants tried to move the cursor into the remaining target within a limited amount of time. The target widths were varied, making the difficulty of moving to either target dependent on the chosen cursor position. Predictions were based on the assumption that participants could use an analogue of Fitts’s law to choose optimal positions. The fit between observed and predicted positions was excellent, suggesting that participants used information about movement speed-accuracy trade-offs to guide movement preparation. The findings suggest that metacognition applies to both perceptual-motor skills and intellectual skills, and that these two domains are more similar than traditionally assumed.     

A comparison of two estimation algorithms for Samejima’s continuous IRT model

This study compares two algorithms, as implemented in two different computer softwares, that have appeared in the literature for estimating item parameters of Samejima’s continuous response model (CRM) in a simulation environment. In addition to the simulation study, a real-data illustration is provided, and CRM is used as a potential psychometric tool for analyzing measurement outcomes in the context of curriculum-based measurement (CBM) in the field of education. The results indicate that a simplified expectation-maximization (EM) algorithm is as effective and efficient as the traditional EM algorithm for estimating the CRM item parameters. The results also show promise for using this psychometric model to analyze CBM outcomes, although more research is needed in order to recommend CRM as a standard practice in the CBM context.     

A step at a time: Preliterate children’s simulation of narrative movement during story comprehension

A growing body of work suggests that narrative comprehension involves the simulation of the described events and actions (e.g., Barsalou, 2008, Matlock, 2004). Preliterate children’s ability to simulate a narrative character’s movements is explored here in three studies. Children’s simulations of a character’s movements were found to be constrained by their expectation of the duration of the described activities (i.e., walking vs. driving) and by their expectations about the motivating influence of certain psychological factors (i.e., character being eager or not eager to get to a location). These findings reveal an ability among preliterate children to create impressively rich and dynamic mental representations of narrative events and address, with a novel methodology, an identified need for greater exploration of precursors to narrative comprehension.     

Militant Islam and Weber’s Social closure: interrelated secular and religious codes of exclusion

Weber’s concept of social closure can help to illuminate the social processes that result in the development of militant Muslim groups. Adapting and applying the concept helps to establish the interrelationships between secular processes and Islamification that are designed by the militants to exclude others and usurp governments. These processes include the implementation of secularisation, conversely concessions to religion and the reinvigoration of Islamic concepts that are used as codes of closure to unite followers and ostracize other Muslims and religious denominations.

A Mother’s Death,a Daughter’s Birth: A 12-Year Journey of Healing and Self Discovery

This article describes a personal journey to understand the psychological meaning in an archetypal near-death experience at the time of my birth and describes its effect on the mother–child relationship before and after my mother's death. Part of that process involved researching the subject of birth trauma and its effect on personality and ultimately on one's fate. It also outlines treatment implications for patients with birth trauma, from a Jungian perspective, based on my own experience of coming to terms with my own birth trauma and the death of my mother.     

Jumping to conclusions: A network model predicts schizophrenic patients’ performance on a probabilistic reasoning task

This article extends computational models of schizophrenia that focus on the negative aspects of this syndrome to behavioral biases that are associated with a positive symptom of schizophrenia, namely delusions. The phenomenon studied is the “jump-to-conclusions” style of reasoning that is characterized by delusional patients—in comparison with controls—whereby they make less-informed decisions when an option to collect more decision-specific information is available. Simulations show that these differences can be mimicked by modulating the gain parameter—associated with variations in dopamine level—in a simple network model.