Tests of the ratio rule in categorization.

Many theories of learning and memory (e.g., connectionist, associative, rational, exemplar based) produce psychological magnitude terms as output (i.e., numbers representing the momentary level of some subjective property). Many theories assume that these numbers may be translated into choice probabilities via the ratio rule, also known as the choice axiom (Luce, 1959) or the constant-ratio rule (Clarke, 1957). We present two categorization experiments employing artificial, visual, prototype-structured stimuli constructed from 12 symbols positioned on a grid. The ratio rule is shown to be incorrect for these experiments, given the assumption that the magnitude terms for each category are univariate functions of the number of category-appropriate symbols contained in the presented stimulus. A connectionist winner-take-all model of categorical decision (Wills & McLaren, 1997) is shown to account for our data given the same assumption. The central feature underlying the success of this model is the assumption that categorical decisions are based on a Thurstonian choice process (Thurstone, 1927, Case V) whose noise distribution is not double exponential in form.     

Effects of race on responses and response latencies in the weapon identification task: a test of six models

The authors consider six models of underlying process in the weapon identification task: The first two are response-time extensions of signal detection models; the last four, of the process dissociation model. Predictions for accuracy data, correct response latencies, and false response latencies are used to discriminate between models. In the present study, racial bias in responses and correct response latency was replicated. New findings were that the direction of bias was reversed in error latency and that errors were faster than correct responses. These findings rule out four models, in particular, the idea that race biases early perception and interpretation of targets. Implications for reducing errors in the weapon identification task and possibilities of discriminating between the remaining two models are discussed.     

Shuttling Between Depictive Models and Abstract Rules: Induction and Fallback

A productive way to think about imagistic mental models of physical systems is as though they were sources of quasi-empirical evidence. People depict or imagine events at those points in time when they would experiment with the world if possible. Moreover, just as they would do when observing the world, people induce patterns of behavior from the results depicted in their imaginations. These resulting patterns of behavior can then be cast into symbolic rules to simplify thinking about future problems and to reveal higher order relationships. Using simple gear problems, three experiments explored the occasions of use for, and the inductive transitions between, depictive models and number-based rules. The first two experiments used the convergent evidence of problem-solving latencies, hand motions, referential language and error data to document the initial use of a model, the induction of rules from the modeling results, and the fallback to a model when a rule fails. The third experiment explored the intermediate representations that facilitate the induction of rules from depictive models. The strengths and weaknesses of depictive modeling and more analytic systems of reasoning are delineated to motivate the reasons for these transitions.     

Optimal decision making in neural inhibition models

In their influential Psychological Review article, Bogacz, Brown, Moehlis, Holmes, and Cohen (2006) discussed optimal decision making as accomplished by the drift diffusion model (DDM). The authors showed that neural inhibition models, such as the leaky competing accumulator model (LCA) and the feedforward inhibition model (FFI), can mimic the DDM and accomplish optimal decision making. Here we show that these conclusions depend on how the models handle negative activation values and (for the LCA) across-trial variability in response conservativeness. Negative neural activations are undesirable for both neurophysiological and mathematical reasons. However, when negative activations are truncated to 0, the equivalence to the DDM is lost. Simulations show that this concern has practical ramifications: the DDM generally outperforms truncated versions of the LCA and the FFI, and the parameter estimates from the neural models can no longer be mapped onto those of the DDM in a simple fashion. We show that for both models, truncation may be avoided by assuming a baseline activity for each accumulator. This solution allows the LCA to approximate the DDM and the FFI to be identical to the DDM.     

Motor activation with and without inhibition: evidence for a threshold mechanism in motor control

Masked primes presented prior to a target can trigger response activation processes that may later be subject to inhibition. Evidence for response inhibition has previously been obtained with primes presented at fixation, but not with primes presented in the periphery of the visual field. It is argued that this central-peripheral asymmetry reflects a threshold mechanism in motor control. Foveal masked primes give rise to stronger perceptual representations than do peripheral primes, resulting in stronger response activations. Strong response activations are actively inhibited, whereas weaker activations remain below a hypothetical inhibition threshold. Evidence in favor of this hypothesis is obtained in four experiments that manipulated the perceptual strength of foveal and peripheral primes. Experiments 1 and 2 demonstrate that when the perceptual strength of peripheral primes is gradually increased by delaying mask onset, positive prime-target compatibility effects (reflecting the absence of response inhibition) turn into negative effects (indicating the presence of response inhibition). Experiments 3 and 4 demonstrate that when the perceptual strength of foveal primes is gradually decreased by degradation, negative compatibility effects turn into positive effects. The results are discussed in terms of a simple functional model of early motor control.     

The frequency effect for pseudowords in the lexical decision task

Four experiments were designed to investigate whether the frequency of words used to create pseudowords plays an important role in lexical decision. Computational models of the lexical decision task (e.g., the dual route cascaded model and the multiple read-out model) predict that latencies to low-frequency pseudowords should be faster than latencies to high-frequency pseudowords. Consistent with this prediction, results showed that when the pseudowords were created by replacing one internal letter of the base word (Experiments 1 and 3), high-frequency pseudowords yielded slower latencies than low-frequency pseudowords. However, this effect occurred only in the leading edge of the response time (RT) distributions. When the pseudowords were created by transposing two adjacent internal letters (Experiment 2), high-frequency pseudowords produced slower latencies in the leading edge and in the bulk of the RT distributions. These results suggest that transposed-letter pseudowords may be more similar to their base words than replacement-letter pseudowords. Finally, when participants performed a go/no-go lexical decision task with one-letter different pseudowords (Experiment 4), high-frequency pseudowords yielded substantially faster latencies than low-frequency pseudowords, which suggests that the lexical entries of high-frequency words can be verified earlier than the lexical entries of low-frequency words. The implications of these results for models of word recognition and lexical decision are discussed.     

MODELING PROBABIUSTIC CATEGORIZATION DATA:

Abstract— In probabilistic categorization tasks, the correct category is determined only probabilistically by the stimulus pattern Data from such experiments have been successfully accounted for by a simple network model, but have posed difficulties for exemplar models In the present article, we consider an exemplar model, CLEM (concept learning by exemplar memorization), which differs from previously tested exemplar models in that exemplar traces are assumed to be stored only when the subject has guessed or made a classification error Fits of CLEM to both learning and test data were comparable to those of the network model, and better than those obtained for a version of CLEM in which encoding was independent of the subject's response The implications of these results for the processes underlying classification decisions are discussed.     

Associative sequence learning in humans

In a series of experiments using the serial reaction time paradigm, the authors compared the predictions of a powerful associative model of sequence learning (the simple recurrent network; J. L. Elman, 1990) with human performance on the problem devised by A. Maskara and W. Noetzel (1993). Even though the predictions made by the simple recurrent network for variants of this problem are often counterintuitive, they matched human performance closely, suggesting that performance was associatively based rather than rule based. Simple associative chaining models of sequence learning, however, have difficulty in accommodating these results. The authors' conclusion is that, under the conditions of the experiments, human sequence learning is associatively driven, as long as this is understood to mean that a sufficiently powerful means of extracting the statistical regularities in the sequences is in play.     

Patterns of Response Times and Response Choices to Science Questions: The Influence of Relative Processing Time

We report on five experiments investigating response choices and response times to simple science questions that evoke student “misconceptions,” and we construct a simple model to explain the patterns of response choices. Physics students were asked to compare a physical quantity represented by the slope, such as speed, on simple physics graphs. We found that response times of incorrect answers, resulting from comparing heights, were faster than response times of correct answers comparing slopes. This result alone might be explained by the fact that height was typically processed faster than slope for this kind of task, which we confirmed in a separate experiment. However, we hypothesize that the difference in response time is an indicator of the cause (rather than the result) of the response choice. To support this, we found that imposing a 3‐s delay in responding increased the number of students comparing slopes (answering correctly) on the task. Additionally a significant proportion of students recognized the correct written rule (compare slope), but on the graph task they incorrectly compared heights. Finally, training either with repetitive examples or providing a general rule both improved scores, but only repetitive examples had a large effect on response times, thus providing evidence of dual paths or processes to a solution. Considering models of heuristics, information accumulation models, and models relevant to the Stroop effect, we construct a simple relative processing time model that could be viewed as a kind of fluency heuristic. The results suggest that misconception‐like patterns of answers to some science questions commonly found on tests may be explained in part by automatic processes that involve the relative processing time of considered dimensions and a priority to answer quickly.     

Processing of English inflectional morphology

The present paper explores the representation of inflectional morphology in the English lexicon. There has been a long-standing debate about how these inflectional relationships might be involved during on-line processing. Inflected forms may be derived from an uninflected base form by rule application; by contrast, both regular and irregular inflection may be treated in the same way, with morphological patterns emerging from mappings between base and inflected forms. The present series of experiments investigated these issues using a lexical decision task. The first experiment showed that response latencies to nouns were significantly shorter than those to verbs. A possible explanation for these results can be found in differences in inflectional structure between English nouns and verbs. Namely, the relative frequency of uninflected compared with inflected forms is greater for nouns than for verbs. Two additional experiments compared noun stimuli with different inflectional structures. In all cases, differences in response latencies were predicted by the frequency of the surface form, whether uninflected or inflected. The pattern of results lends support for a unitary associative system for processing regular inflection of nouns in English and argues against the view that regular inflected plurals are derived by rule from a single, uninflected lexical entry.     

A Connectionist Approach to Word Reading and Acquired Dyslexia: Extension to Sequential Processing

A connectionist approach to word reading, based on the principles of distributed representation, graded learning of statistical structure, and interactivity in processing, has led to the development of explicit computational models which account for a wide range of data on normal skilled reading and on patterns of reading impairment due to brain damage. There have, however, been recent empirical challenges to these models, and the approach in general, relating to the influence of orthographic length on the naming latencies of both normal and dyslexic readers. The current work presents a simulation which generates sequential phonological output in response to written input, and which can refixate the input when encountering difficulty. The normal model reads both words and nonwords accurately, and exhibits an effect of orthographic length and a frequency-by-consistency interaction in its naming latencies. When subject to peripheral damage, the model exhibits an increased length effect that interacts with word frequency, characteristic of letter-by-letter reading in pure alexia. Although the model is far from a fully adequate account of all the relevant phenomena, it suggests how connectionist models may be extended to provide deeper insight into sequential processes in reading.     

Response requirements as constraints on output

Two experiments studied how added response requirements affected fixed-interval schedule performance. Experiment 1 involved tandem fixed-interval fixed-ratio schedules, and Experiment 2 studied conjunctive fixed-interval fixed-ratio schedules. In both, pigeons' output, defined as overall response rate or as responses during the interval, first increased and then decreased as the ratio was raised. With small ratio requirements, the frequency of reinforcement in time either did not change or decreased slightly. With progressively larger ratios, reinforcement frequency decreased consistently. Alternative explanations were discussed. The first, a reinforcement theory account, was that response strength is an increasing monotonic function of both the response requirement and reinforcement frequency, and the bitonic output function represents interacting effects. Increases in the response requirement accompanied by small changes in reinforcement frequency enhance output, but further increases result in large enough decrements in reinforcement frequency so that output is lowered. The second explanation does not view reinforcement as a basic process but, instead, derives from concepts of economics and conservation. Organisms allocate their behavior among alternatives so as to maximize value, where value is a function of the responses that can occur in a given situation under the set of restrictions imposed by particular schedules. One form of this theory explicitly predicts that output is a bitonic function of ratio requirements in simple ratio schedules. However, it was not clear that this model could explain the present effects involving joint ratio and interval schedule restrictions.     

Testing Evidence Accrual Models by Manipulating Stimulus Onset

Many models of response time assume that subjects accrue stimulus "evidence" samples in time (e.g., random walk models, counter models). In this paper, the concept of one stimulus dominating another is used to construct a test of the whole class of evidence accrual models. For an example of dominance, consider stimuli that are presented either virtually instantaneously (stepped) or in a gradually increasing manner (ramped). Ramped stimuli are presented such that the ramped portion precedes the stepped onset of stepped stimuli. In this case ramped stimuli dominate stepped stimuli. In this paper the class of evidence accrual models is formalized. It is shown that under appropriate assumptions evidence accrual models do predict more accurate responses to dominating stimuli. However, this result does not hold for response latencies. There are anomalous cases where an evidence accrual model (the accumulator model of Vickers (1970, Ergonomics 13, 37-58)) predicts slower mean correct response latencies to dominating stimuli. It is shown through extensive computer simulation that these anomalous cases occur only when response criteria are so asymmetric that there are exceedingly extreme response biases. For experiments where response biases are not exceedingly extreme, random walk and accumulator models predict more accurate and quicker correct responses to dominating stimuli. In sum, manipulating the time course of stimuli in accordance with the concept of dominance can provide empirical tests of the class of evidence accrual models. Copyright 2001 Academic Press.     

A real-time criterion theory of duration discrimination

The common idea that a measure is taken of a duration stimulus over its temporal extent, and that the decision as to whether the stimulus is relatively long or short is based upon such a measure, is shown to be incorrect. Two experiments, which require speeded responding in duration discrimination and consider response latencies as well as response probabilities, demonstrate that the response that is made is determined by the outcome of a race between an internally timed interval, the criterion, and the presented stimulus. The onset of the stimulus triggers the criterion; if the criterion ends first, the response “long” is elicited. Duration discrimination is a matter of temporal order discrimination, and in the limit, “short” responses are simple reactions while “long” responses are time estimation responses. A specific model of the real-time criterion hypothesis is tested, and these initial tests generally confirm it. From this, it is concluded that errors in duration discrimination are due entirely to variability of the criterion and that afferent latencies are not necessarily variable. This adds additional evidence for the existence of deterministic afferent latencies.     

Bias in exponential and power function fits due to noise: Comment on Myung,Kim, and Pitt

Myung, Kim, and Pitt (2000) demonstrated that simple power functions almost always provide a better fit to purely random data than do simple exponential functions. This result has important implications, because it suggests that high noise levels, which are common in psychological experiments, may cause a bias favoring power functions. We replicate their result and extend it by showing strong bias for more realistic sample sizes. We also show that biases occur for data that contain both random and systematic components, as may be expected in real data. We then demonstrate that these biases disappear for two- or three-parameter functions that include linear parameters (in at least one parameterization). Our results suggest that one should exercise caution when proposing simple power and exponential functions as models of learning. More generally, our results suggest that linear parameters should be estimated rather than fixed when one is comparing the fit of nonlinear models to noisy data.     

Facilitation in the abstract selection task: The effects of attentional and instructional factors

The present study examined performance on Wason's four-card abstract selection task. Baseline performance is very poor, usually less than 10% correct; and this task has a long record of resistance to facilitation. It was hypothesized that the two primary sources of difficulty are selective encoding of the problem information and the lack of satisfactory analytic processing. Three experiments were conducted to test this hypothesis. In Experiment 1, performance was improved by explicating the implication rule. The majority of subjects, however, still failed to make the correct selection. Subjects were required in Experiment 2 to provide reasons for their selection or non-selection of each of the cards. This response procedure, paired with an explicated rule, led to further improvements in performance (over 50% correct selections). In Experiment 3, the influence of the type of selection instruction (true-false vs. violation) was examined. Paired with an explicated rule and the reasons response format, violation instructions led to one of the highest correct selection rates ever observed for any version of the selection task: over 80% correct. Because of the importance of this result, it was replicated twice. The results of these three experiments are discussed in terms of Johnson-Laird and Byrne's mental models theory and Evans's two-stage model of reasoning.     

An amorphous model for morphological processing in visual comprehension based on naive discriminative learning

A 2-layer symbolic network model based on the equilibrium equations of the Rescorla-Wagner model (Danks, 2003) is proposed. The study first presents 2 experiments in Serbian, which reveal for sentential reading the inflectional paradigmatic effects previously observed by Milin, Filipovi? ?ur?evi?, and Moscoso del Prado Martín (2009) for unprimed lexical decision. The empirical results are successfully modeled without having to assume separate representations for inflections or data structures such as inflectional paradigms. In the next step, the same naive discriminative learning approach is pitted against a wide range of effects documented in the morphological processing literature. Frequency effects for complex words as well as for phrases (Arnon & Snider, 2010) emerge in the model without the presence of whole-word or whole-phrase representations. Family size effects (Moscoso del Prado Martín, Bertram, H?iki?, Schreuder, & Baayen, 2004; Schreuder & Baayen, 1997) emerge in the simulations across simple words, derived words, and compounds, without derived words or compounds being represented as such. It is shown that for pseudo-derived words no special morpho-orthographic segmentation mechanism, as posited by Rastle, Davis, and New (2004), is required. The model also replicates the finding of Plag and Baayen (2009) that, on average, words with more productive affixes elicit longer response latencies; at the same time, it predicts that productive affixes afford faster response latencies for new words. English phrasal paradigmatic effects modulating isolated word reading are reported and modeled, showing that the paradigmatic effects characterizing Serbian case inflection have crosslinguistic scope.     

Focal and nonfocal processing of color and form

Langley Porter Neuropychtatrte Institute, University of California, San Francisco. Californta 94122 Response latencies to color are usually shorter than those to form. but sometimes this difference is absent or reversed. Three experiments investigated whether these differences result from differential susceptibility of color and form to extra focal processing. Experiment I showed shorter same-difference latencies to color than to form when two stimuli were presented simultaneously. This difference disappeared or reversed when the two stimuh appeared sequentially. Experiment II. using a multistimulus matching task, found that differences between response latencies to form and color were minimal at the center of the display and increased peripherally. Experiment III showed that eye movements were more frequent in matching forms than colors. Tasks that produced many eye movements had long average latencies, but the relationship between eye movements and latency was not a simple one. There was evidence both for parallel and serial strategies tn the use of the eyes to gather information. The results of these experiments are considered in relation to a theory of distributed attention.     

The components of latency of response in two models for auditory detection with deadlines

Two models are described for the case of auditory detection with response time deadlines. These are the “timing” model, modified from Luce and Green (1972), and the “interval of uncertainty” (IU) model, modified from the “counting” model of McGill (1967). The two models are expressed in the form of additive component latencies, including a component which varies inversely with probability of response and a component for a longer response on the “nondeadline” response condition. An experiment is described, incorporating deadlines on both s and n trials separately, and the additive component latencies of the models are calculated. The “interval of uncertainty” model is seen to represent the data better than the “timing” model, even though different versions of the latter model are considered. Parameters are then fitted to give a representation of the IU model. The data from one subject of another study not employing deadlines can also be fitted to the model, and an interesting problem then arises concerning the exact locus of the speed-accuracy tradeoff. It is concluded that the IU model needs extending if it is to describe the data without the use of a component of latency which varies inversely with response probability.