A clarification of self-terminating versus exhaustive variances in serial and parallel models

A recent study published in Perception & Psychophysics (Donnelly, Found, & Miller, 1999) employs response time (RT) variances (in the form of standard deviations) in addition to mean RTs. Variances can contribute greatly to model testing. However, there is a danger of perpetuating the kinds of logical and methodological errors that have long attended research employing mean RTs alone. This commentary clarifies the theoretical and methodological issues, points out some new results concerning variability in search processes, and indicates how to resolve the global and specific challenges associated with identifying psychological mechanisms.     

Implications of search accuracy for serial self-terminating models of search

In two experiments, the data from a total of 35 participants was compared to predictions from two competing serial search models, one with perfect memory and one with no memory. Reaction times were collected from an unlimited exposure duration, 4-alternative, target identification search task with array sizes of 8, 12, or 16 items. From the linear function relating RT to number of distractors a hypothetical “inspection time/item” was computed under the assumption of SSTS. Target identification accuracy was obtained from the same participants using the same displays, but with pre- and post-masks used to limit total inspection time (to 120, 180, 300, and 540 ms). Neither the memoryful nor memoryless model provided a good enough fit to the data to support the assumption that serial inspection is the primary process determining search time. Despite direct evidence for serial allocation of attention in visual search, these results suggest that scholars should seriously consider the possibility of hybrid search models in which serial and parallel strategies operate jointly.     

A test of parallel versus serial processing applied to memory retrieval

Townsend has identified necessary and sufficient conditions that reaction time distributions meet if they are produced by two underlying processes that are parallel and within-stage independent. This paper describes an attempt to use one of these conditions to assess the assumption of independent parallel memory retrieval in Anderson's ACT theory. In the experimental test, subjects studied profession-location pairs, with each profession and location included in two pairs. One pair had a high frequency of presentation and the other had low. When cued with a profession (or location), subjects responded with the first of the two studied locations (or professions) that came to mind. The reaction times to these responses were used to test the ACT assumption of independent parallel search. The problems encountered in trying to apply Townsend's abstract test to a concrete situation included the need to consider mixtures and convolutions of distributions and empirical, rather than theoretical, distributions. These difficulties are discussed at length and some formal analyses concerning their effect on the test are given. Despite these problems, we were able to use Townsend's test and the results of the experiment support the within-stage independent parallel assumption of ACT.     

Neuroimaging the serial position curve. A test of single-store versus dual-store models

Neuroimaging data could help clarify the long-standing dispute between dual-store and single-store models of the serial position curve. Dual-store models assume that retrieval from late positions is dependent on short-term memory (STM), whereas retrieval from early positions is dependent on long-term memory (LTM). Single-store models, however, assume that retrieval processes for early and late items are similar, but that early items are more difficult to discriminate than late items. The present study used functional magnetic resonance imaging to examine this question. Ten young adults were scanned while they recognized items from early or late serial positions. Recognition of early items uniquely activated brain areas traditionally associated with LTM, namely, regions within the hippocampal memory system. None of these areas was activated for retrieval of late items. These results indicate differential use of LTM retrieval processes, and therefore support dual-store models over single-store models.     

A clarification of some current multiplicative confusion models

Four recently proposed models of confusion are examined within a classification of major types of multiplicative models. It is shown that all four are equivalent within a single confusion matrix but are open to mutual testing across experiments producing two or more confusion matrices. Generalization of these models is considered.     

A clarification of Multisystem-Multimethod assessment: reductionism versus wholism

A clarification and response to a critique of the Multisystem-Multimethod (MS-MM) family assessment is provided in this paper. This approach consists of a logic for integrating family assessment, systems thinking, and clinical interventions. In contrast to the wholistic, or systemic, focus of MS-MM family assessment, the critique of these procedures recommends a more reductionistic approach that contradicts basic elements of systems theory. The critique advocates the isolation and measurement of a few family phenomena, whereas MS-MM assessment recognizes the interdependence among the levels of organization and components of family systems.     

A note on the identifiability of parallel and serial processes

Due to the significant research effort devoted to discovering whether certain psychological processes are serial or parallel, it seems important to establish the degree to which such processes are identifiable and to investigate possible ways in which such knowledge can improve our experiments. General definitions of parallel and serial systems are given, followed by a qualitative summary of identifiability results obtained with special classes of exponential systems. Some of these results are applied to a current experimental paradigm, and possible     

Reaction times for comparisons of successively presented visual patterns: Evidence for serial self-terminating search

Two-choice classification RTs were collected for eight conditions designed to vary the number of comparisons necessary between one or two visual patterns in perception and one or two in short-term memory (STM). Overall RT data supported both a serial self-terminating and parallel self-terminating model with distributed search times, while rejecting corresponding exhaustive models. Precise predictions for the parallel model proved difficult to derive; however, the serial model predicted the fine detail of the data surprisingly well. RTs suggested that Ss searched through all stimuli in memory first and that stimuli in both memory and perception were searched from right to left. Comparison times between identical stimuli were estimated to be longer than comparison times between different stimuli. Error rates increased with the number of hypothesized comparisons; predicted error rates, based on independence of rates within stages, also increased but failed to predict the empirical error rates very well.     

Numerical predictions for serial, parallel, and coactive logical rule-based models of categorization response time

Recent theoretical advances in theories of categorization response times have made it possible to differentiate mental architectures that specify how processes occurring over several information-processing channels are combined (e.g., in serial or in parallel). This article introduces the numerical computations necessary to generate predictions for a class of logical rule-based models that have recently been used to account for speeded perceptual categorization judgments (Fifi?, M., Little, D.R. & Nosofsky, R. M. . Psychological Review, 117:309–348, 2010).     

A faithful embedding of parallel computations in star-finite models

The purpose of this paper is to show that there exist star-finite tree-structured sets in which the computations of parallel programs can be faithfully embedded, and that the theory of star-finite sets and relations therefore provides a new tool for the analysis of non-deterministic computations.This research was carried out while the author held a Postdoctoral Fellowship from the Natural Sciences and Engineering Research Council of Canada. The author also gratefully acknowledges the support of the Centre inter-universitaire en études catégoriques de Montréal.     

Establishing the loci of serial and parallel effects in syntactic processing

Recent experimental work has demonstrated a robust effect of syntactic context on lexical decision times. Wright and Garrett (1984) report that targets belonging to syntactic categories required by the context produce faster RTs than either ungrammatical or optional continuations of the context string. The present study reports that structurally ambiguous contexts produced faster recognition times for syntactic categories required by only the putative nonpreferred reading of the ambiguities tested. These findings are argued to favor a parallel processing model in which syntactic representations are ranked according to structural criteria and shunted in a serial fashion to subsequent processors.     

Parameterizing inequality constraints on unique variances in linear structural models

Current computer programs for analyzing linear structural models will apparently handle only two types of constraints: fixed parameters, and equality of parameters. An important constraint not handled is inequality; this is particularly crucial for preventing negative variance estimates. In this paper, a method is described for imposing several kinds of inequality constraints in models, without the necessity for having computer programs which explicitly allow such constraints. The examples discussed include the prevention of Heywood cases, extension to inequalities of parameters to be greater than a specified value, and imposing ordered inequalities. Work on this project was aided by the City University of New York—Professional Staff Congress Research Award Program Grant Number 13631.     

Bounds on variances of estimators for multinomial processing tree models

When there are order constraints among the parameters of a binary, multinomial processing tree (MPT) model, methods have been developed for reparameterizing the constrained MPT into an equivalent unconstrained MPT. This note provides a theorem that is useful in computing bounds on the estimator variances for the parameters of the constrained model in terms of estimator variances of the parameters of the unconstrained model. In particular, we show that if X and Y are random variables taking values in [0,1], then Var[XY]?2(Var[X]+Var[Y]).     

Visual search time based on stochastic serial and parallel processings

Two stochastic latency models were developed in order to account for random fluctuations of the search time that the S consumed when he was asked to search for a single target number or one of two (or three) target numbers through the sets of small two-digit numbers randomly distributed on a white square. It was shown that the search time distribution for a single target number can be adequately described in terms of McGill’s two-step serial processing model. The parallel processing model whose structure is exponential was found to fit approximately the search time distributions for the first target number that the S detects among the two (or three) target numbers predesignated. This model, however, does not satisfactorily handle the long search times.     

Electrophysiological evidence for parallel and serial processing during visual search

Event-related potentials were recorded from young adults during a visual search task in order to evaluate parallel and serial models of visual processing in the context of Treisman's feature integration theory. Parallel and serial search strategies were produced by the use of feature-present and feature-absent targets, respectively. In the feature-absent condition, the slopes of the functions relating reaction time and latency of the P3 component to set size were essentially identical, indicating that the longer reaction times observed for larger set sizes can be accounted for solely by changes in stimulus identification and classification time, rather than changes in post-perceptual processing stages. In addition, the amplitude of the P3 wave on target-present trials in this condition increased with set size and was greater when the preceding trial contained a target, whereas P3 activity was minimal on target-absent trials. These effects are consistent with the serial self-terminating search model and appear to contradict parallel processing accounts of attention-demanding visual search performance, at least for a subset of search paradigms. Differences in ERP scalp distributions further suggested that different physiological processes are utilized for the detection of feature presence and absence.     

A test of engagement versus disengagement in catastrophe models

The present study explored the interactive effects of self‐efficacy and increasing/decreasing task difficulty upon engagement and disengagement within a cusp‐catastrophe model framework. Using a closed motor skill aiming task participants (N=60) were required to compete in conditions where task difficulty increased and then decreased (or vice versa) where they were rewarded for good performance but penalized for bad. Participants who reported low levels of self‐efficacy disengage at an earlier level of task difficulty than their high self‐efficacy counterparts. Furthermore, this group did not re‐engage with the task until task difficulty had significantly decreased. Although task disengagement occurred with high difficulty in the high self‐efficacy group, this group re‐engaged in a similar manner in which they disengaged. Findings support and extend those of previous tests of catastrophe models by directly allowing for task disengagement.     

Merging race models and adaptive networks: A parallel race network

This article presents a generalization of race models involving multiple channels. The major contribution of this article is the implementation of a learning rule that enables networks based on such a parallel race model to learn stimulus—response associations. This model is called aparallel race network. Surprisingly, with a two-layer architecture, a parallel race network learns the XOR problem without the benefit of hidden units. The model described here can be seen as a reduction-of-information system (Haider & Frensch, 1996). An emergent property of this model is seriality: In some conditions, responses are performed with a fixed order, although the system is parallel. The mere existence of this supervised network demonstrates that networks can perform cognitive processes without the weighted sum metric that characterizes strength-based networks.