A note on keats' generalization of the rasch model

An alternative derivation is given for a simple test model which incorporates anability parameter for the subject anddifficulty level andguessing parameters for the problem. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components.     

Multicomponent theory of perception

Summary In a complete identification experiment the three sides of an equilateral triangle were briefly presented as stimuli either singly or in pairs. The resulting 6×6 confusion matrices obtained with three subjects were analyzed according to Rumelhart's (1970, 1971) multicomponent theory of perception (MCTP) in order to test assumptions about feature extraction and decision processes. In agreement with MCTP the detection of a line segment occurring within a pair was stochastically independent of the detection of the other line segment. Two predictions of MCTP were however not confirmed: different line segments are not detected with equal probability, and the probability of detecting a line segment depends on the presence or absence of others. Several decision assumptions of MCTP were tested. The results are the following: If at most one line segment has been detected, then several responses (the candidate set) are compatible with this sensory state. It was argued that response selection from the candidate set is better described by the choice model (Luce, 1959) than by the matching Bayesian rule assumed by MCTP. For a given sensory state the size of the candidate set appears to vary over trials, whereas MCTP assumes it to be constant. In general, the confusion matrices could be predicted quite accurately by MCTP modified according to the above assumptions. However, more accurate predictions were achieved by assuming holistic perceptual processes as well as single feature extraction.This study was supported by a grant from the Universität Konstanz, Forschungsprojekt 32/72 Visuelle Reize, and the experiment to this study was performed in the laboratory of the Arbeitseinheit Mathematische Psychologie im Fachbereich Psychologie/Soziologie der Universität Konstanz.     

Response to instruction, English language learners and disproportionate representation: the role of assessment

Response to Intervention (RtI), a cyclical process that incorporates assessment and instruction, is both an approach to prevent learning difficulties and to establish student eligibility for special education. Assessment results are used to determine students' initial knowledge and skill, their need for successively more intensive levels of instruction, and to gauge their response to the intervention provided. Although this process is preferable to the IQ/achievement discrepancy model for determining the presence of specific learning disabilities, there are still a number of unresolved issues related to the assessment procedures in use. A pressing issue is the identification of measures and procedures that identify students with the greatest precision thus reducing inappropriate identification.     

Additive latency effects of selective and nonselective restricted priming types

The purpose of this investigation was to examine further the contention of Alain et al. (1988) that a third priming type exists, called nonselective restricted (NSR) and controlled by response probability, which is distinct from those types influenced by foreperiod duration (nonselective general priming) and prediction probability (selective priming). In a four-choice reaction time (RT) task, prediction probability (.5, .7, & .9, indicating the likelihood of a particular response) and response probability (.5, .9, denoting the likelihood that a response would be needed at all) exerted significant but noninteractive effects on RTs for prepared responses (most probable), suggesting that each of these probabilities influence different priming types (Sternberg, 1969; selective and NSR, respectively). This was further indicated by the fact that prediction probability, but not response probability, significantly altered RTs for the unprepared (lesser probable) responses. Finally, the hypothesized nonselective character of NSR priming (i.e., all outputs controlled by response probability are equally affected by its value changes) was supported when responses were equiprobable, and, while the null effect of response probability just mentioned seemingly argued against this property when selective priming took place, the interpretation provided herein negated this opposition.     

Effects of Response Probability on Response Force in Simple RT

Response force (RF) was measured in a simple reaction time (RT) experiment varying response uncertainty by cuing the probability of the response on each trial. In all cases, RF decreased as response probability increased. The dependence of RF on response probability was insensitive to foreperiod length and to the use of loud auditory response signals, although the dependence of RT on response probability was sensitive to both of these manipulations. In combination with previous findings, these results provide evidence that RT and RF can be dissociated. We describe an extension of Naatanen's readiness model that can account for the effects of response probability on RF and RT. According to this model, the distance between motor activation and a threshold for action is relatively large when subjects are unprepared, and a large increment is needed to exceed this threshold, resulting in slow but foreceful responses. A possible neurophysiological implementation of this model is suggested.     

Shape constancy and a perceptual bias towards symmetry

In attempting to judge whether a briefly presented rotated figure was symmetrical (circle or square) or asymmetrical (ellipse or rectangle), a bias towards perceiving symmetry was evident. This bias appears to be perceptual rather than judgmental in origin in that it was affected neither by variations in the probability of occurrence of symmetrical figures nor by familiarization with the stimuli. A characterization of the stimulus similarity space based on the shape-slant invariance hypothesis is presented, and a model which incorporates both the similarity space and the symmetry bias is proposed. The model can account for our paradoxical finding that the more asymmetrical some projected images, the more likely they will be perceived as symmetrical. This model can also account for Massaro’s (1973, 1975) results on shape constancy. However, Massaro’s theory was not supported in that extension in depth did not account for increased difficulty of shape judgments.     

Component probability and component reinforcer rate as biasers of free-operant detection

Six pigeons were trained on multiple schedules whose components were concurrent variable-interval extinction and concurrent extinction variable-interval schedules. In Experiments 1a and 1b the stimuli signaling the components were two different light intensities, and in Experiments 2a and 2b they were two identical intensities. The components of the multiple schedule changed probabilistically after each reinforcer. In Experiments 1a and 2a, the probability of presenting the components was varied over five conditions and a replication. In Experiments 1b and 2b, the component probability was .5 and the component reinforcer rates were varied systematically over five conditions and a replication. The data, analyzed according to the Davison-Tustin behavioral detection model, confirmed that the discriminability of the stimuli signaling the components was high when the stimuli were different, and low when the stimuli were the same. Discriminability, measured by log d, was unaffected by component probability variation and by component reinforcer-rate variation. When discriminability was high, bias, or the response allocation between the two keys, was more strongly affected by variation of reinforcer rate within components than by variation of component probability, but the reverse was found when discriminability was low. The results suggest that free-operant detection performance is controlled by the rates of reinforcers in periods of time in which stimuli signal differential contingencies. These periods comprise the components when the component stimuli are discriminable, and comprise the total session when the components are indiscriminable. An extension of the Davison-Tustin behavioral detection model that incorporates these results is presented.     

Modeling the effects of choice-set size on the processing of letters and words

Letters and words are better identified when there are fewer available choices. How do readers use choice-set restrictions? By analyzing new experimental data and previously reported data, the author shows that Bayes theorem-based models overestimate readers' use of choice-set restrictions. This result is discordant with choice-similarity models such as R. D. Luce's (1963a) similarity choice model, G. Keren and S. Baggen's (1981) letter recognition model, and D. W. Massaro and G. C. Oden's (1979) fuzzy logical model of perception. Other models posit that choice restrictions affect accuracy only by improving guessing (e.g., J. L. McClelland & D. E. Rumelhart's, 1981, interactive activation model). It is shown that these models underestimate readers' use of choice-set restrictions. Restriction of choice set does improve perception of letters and words, but not optimally. Decision models that may be able to explain this phenomenon are discussed.     

Risky decision: Attention and path dependency as a function of response mode

It was previously shown and was here replicated that the amount of money required to induce a subject to exchange one gamble for a second and then the second for a third depends on the second (intermediate) gamble. This path dependency cannot be explained by any of the algebraic models (including SEU), nor can it be explained as a simple attention effect. A model was put forward which explains the effect in terms of differential masking depending on a kind of stimulus—response compatibility. The effect of response mode on path dependency was examined in this study; similarity judgements showed no consistent path dependency nor did difference in rated attractiveness of gambles presented in pairs, but rated attractiveness was different for gambles presented singly. Since it might be that monetary response emphasises the monetary aspects, that is, the winning amount of the gamble, it was thought that a probability response would emphasise the probability of winning. However, when subjects were asked to set the probability of winning $ 12 which would induce them to exchange one gamble for another, not only was no path dependency observed, but the subjects' responses seemed to depend only on the difference in expected value of the gambles. This suggests the possibility of developing response-display modes which would eliminate or at least attenuate the inconsistencies observed in risky decision processes.     

Best not to bet on the horserace: A comment on Forrin and MacLeod (2017) and a relevant stimulus-response compatibility view of colour-word contingency learning asymmetries

One powerfully robust method for the study of human contingency learning is the colour-word contingency learning paradigm. In this task, participants respond to the print colour of neutral words, each of which is presented most often in one colour. The contingencies between words and colours are learned, as indicated by faster and more accurate responses when words are presented in their expected colour relative to an unexpected colour. In a recent report, Forrin and MacLeod (2017b, Memory & Cognition) asked to what extent this performance (i.e., response time) measure of learning might depend on the relative speed of processing of the word and the colour. With keypress responses, learning effects were comparable when responding to the word and to the colour (contrary to predictions). However, an asymmetry appeared in a second experiment with vocal responses, with a contingency effect only present for colour identification. In a third experiment, the colour was preexposed, and contingency effects were again roughly symmetrical. In their report, they suggested that a simple speed-of-processing (or “horserace”) model might explain when contingency effects are observed in colour and word identification. In the present report, an alternative view is presented. In particular, it is argued that the results are best explained by appealing to the notion of relevant stimulus–response compatibility, which also resolves discrepancies between horserace model predictions and participant results. The article presents simulations with the Parallel Episodic Processing model to demonstrate this case.     

Simulating individual word identification thresholds and errors in the fragmentation task

This article presents a large-scale study that collected word identification thresholds and errors in the fragmentation task for all four-letter French words. In the first part of this article, we identify some of the variables (e.g., word frequency, neighborhood size, letter confusability) that affect performance in the fragmentation task. In the second part, we analyze individual response performance and identify different response strategies. We demonstrate that the interactive activation model can account for individual response strategies by adapting two of its original parameters: word-letter feedback and letter-word inhibition. In the third part, we demonstrate that the adaptation of the interactive activation model to the fragmentation task makes it possible to successfully simulate a facilitatory frequency effect on identification thresholds, an inhibitory neighborhood size effect on error rates, and an inhibitory letter confusability effect on identification thresholds. When the task-specific processes of the fragmentation task are specified and individual response strategies are considered, the interactive activation model provides a parsimonious architecture for modeling the task-independent processes involved in word perception.     

Testing a Poisson counter model for visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks

The authors propose and test a simple model of the time course of visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks. The model implies that during stimulus analysis, tentative categorizations that stimulus i belongs to category j are made at a constant Poisson rate, v(i, j). The analysis is continued until the stimulus disappears, and the overt response is based on the categorization made the greatest number of times. The model was evaluated by Monte Carlo tests of goodness of fit against observed probability distributions of responses in two extensive experiments and also by quantifications of the information loss of the model compared with the observed data by use of information theoretic measures. The model provided a close fit to individual data on identification of digits and an apparently perfect fit to data on identification of Landolt rings.     

After-effects of responding and of withholding responses in C.RT tasks

The effects of response repetition on choice RT were compared in b-reaction and in c-reaction tasks [Experiments I(a) and I(b)]. The difference in RTs for repeated and for non-repeated responses was found to be less for c-reaction than for b-reaction tasks. This seemed to be because in c-reaction tasks subjects can prepare themselves to make the same response on every trial, so that there is little further RT reduction consequent on immediate response repetition. In b-reaction tasks subjects cannot always prepare to make the same response, so that the difference between response repetition RT and responce alteration RT is greater. Experiment II examined transitions between events in a serial, self-paced C.RT task in which subjects made a different response to each of two signals but withheld any response to the onset of a third. In this task responses were faster when they followed other, different responses than when they followed “no go” trials. The results of these experiments allow us to reject, even for very elementary tasks, a simple “S--R connection network” model for the processes involved in the identification of signals and the production of responses to them.     

Response latency and accuracy in visual word recogniton

In a single visual word recognition experiment, the effects of (1) eccentricity of presentation, (2) word length, and (3) word frequency were investigated. The stimuli used were Dutch nouns in two frequency classes of about 15 and 150.10^-6; word length varied from 1 to 10; eccentricity varied from ?4 to +4 deg. The response quality and response latency of 11 subjects were measured. For the correct responses, recognition scores decreased and response latencies increased with eccentricity; both showed asymmetrical curves in the visual field. It is argued that word length proper affects neither the probability of correct responses nor latency. A clear word frequency effect was established. The eccentricity of presentation is considered as the determinant of the amount of available information, thus directly influencing accuracy and latency. The linear relationship between accuracy and latency is a major finding. A word recognition scheme is offered which incorporates (1) activation, (2) decision, and (3) speech. The time relations between incoming retinal information and response decision, leading to an extra 400 msec for incorrect as compared with correct responses, are discussed. Word recognition in reading is examined, together with the impact of the present experimental results on information flow in successive eye fixations, eye movement control, and eye-voice span.     

A markov model for discrimination learning

A theory for discrimination learning which incorporates the concept of an observing response is presented. The theory is developed in detail for experimental procedures in which two stimuli are employed and two responses are available to the subject. Applications of the model to cases involving probabilistic and nonprobabilistic schedules of reinforcement are considered; some predictions are derived and compared with experimental results.This research was supported by a grant from the National Science Foundation.     

A dual-task analysis of detection accuracy for the case of high target-distractor similarity: Further evidence for independent processing

Previous studies of visual detection performance indicate that perceptual span has a negligible effect on detection accuracy; hence, previous results suggest that individual characters within a multielement array are perceived independently. In this study, additional experimental factors were examined in order to determine whether conditions exist in which perceptual span influences detection performance: targets and distractors were chosen to be maximally similar, and detection accuracy was studied in relation to display size, target redundancy, and homogeneity of distractor characters. To test for perceptual span effects, a three-state model was proposed which incorporates the assumption that individual characters are perceived independently. The model may be applied to (a) both yes-no and forced-choice tasks, and (b) the case when effects of display characteristics differ for response alternatives. Predictions based on the three-state model agree satisfactorily with observed proportions. Moreover, interactions between display characteristics and response alternatives accord well with model predictions, and accuracy differences between subjects are consistent with individual differences in model parameters. The results provide further evidence for the independence assumption and illustrate additional conditions for which perceptual span has a negligible effect on detection accuracy.     

Dissociating speed and accuracy in absolute identification: the effect of unequal stimulus spacing

Identification accuracy for sets of perceptually discriminable stimuli ordered on a single dimension (e.g., line length) is remarkably low, indicating a fundamental limit on information processing capacity. This surprising limit has naturally led to a focus on measuring and modeling choice probability in absolute identification research. We show that choice response time (RT) results can enrich our understanding of absolute identification by investigating dissociation between RT and accuracy as a function of stimulus spacing. The dissociation is predicted by the SAMBA model of absolute identification (Brown, Marley, Dockin, & Heathcote, 2008), but cannot easily be accommodated by other theories. We show that SAMBA provides an accurate, parameter free, account of the dissociation that emerges from the architecture of the model and the physical attributes of the stimuli, rather than through numerical adjustment. This violation of the pervasive monotonic relationship between RT and accuracy has implications for model development, which are discussed.

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Beyond statistical inference: A decision theory for science

Traditional null hypothesis significance testing does not yield the probability of the null or its alternative and, therefore, cannot logically ground scientific decisions. The decision theory proposed here calculates the expected utility of an effect on the basis of (1) the probability of replicating it and (2) a utility function on its size. It takes significance tests—which place all value on the replicability of an effect and none on its magnitude—as a special case, one in which the cost of a false positive is revealed to be an order of magnitude greater than the value of a true positive. More realistic utility functions credit both replicability and effect size, integrating them for a single index of merit. The analysis incorporates opportunity cost and is consistent with alternate measures of effect size, such as r2 and information transmission, and with Bayesian model selection criteria. An alternate formulation is functionally equivalent to the formal theory, transparent, and easy to compute.     

On interpretation of interactions

The principle focus of this paper is on interpretation of interactions that are obtained when response probability is used as a dependent variable. It is argued that results obtained with probability [or any dependent variable) are only interesting insofar as they reflect something about a corresponding theoretical component. It follows that the functional mapping of response probability [which is measured) onto the state of a theoretical component (which is inferred) must be somehow specified if conclusions are to be meaningful. Depending on the nature of such a mapping, various types of results, particularly results involving interactions, may or may not be interpretable.     

The role of morphological constituents in reading Finnish compound words

The processing of transparent Finnish compound words was investigated in 2 experiments in which eye movements were recorded while sentences were read silently. The frequency of the second constituent had a large influence (95 ms) on gaze duration on the target words, but its influence was relatively late in processing: A clear effect only occurred on the probability of a third fixation. The frequency of the whole compound word had a similar influence on gaze duration (82 ms) and influenced eye movements at least as rapidly as did the frequency of the second constituent. These results, together with an earlier finding that the frequency of the first constituent affected the first fixation duration, indicate that the identification of these compound words involves parallel processing of both morphological constituents and whole-word representations.