Multiplicatively interacting factors selectively influencing parameters in multiple response class processing and rate trees

Evidence in many experiments indicates that the processes involved in producing responses are arranged in a tree structure. Evidence often indicates further that an experimental factor, such as item similarity, changes a single parameter, leaving others invariant. In typical studies, a few tree structures are hypothesized a priori, and tested by goodness of fit. With the method of Tree Inference, a tree is constructed by examining the data to see if patterns occur that are predicted when two factors selectively influence different processes (Schweickert & Chen, 2008). The patterns can reveal, for example, whether selectively influenced processes are executed in order, and what the order is. If the patterns do not occur, one can conclude that no tree is possible in which the factors selectively influence processes. In earlier work, three restrictions were imposed on the trees considered: There were two classes of responses; parameters were probabilities, bounded above by 1; and factors were assumed to change parameters associated with children of a single vertex. More general results are derived here, removing these restrictions. Results on representation, uniqueness of parameters, uniqueness of tree structure, and mixtures of trees are presented.     

Metamorphosed characters in dreams: constraints of conceptual structure and amount of theory of mind

Dream reports from 21 dreamers in which a metamorphosis of a person-like entity or animal occurred were coded for characters and animals and for inner states attributed to them (Theory of Mind). In myths and fairy tales, Kelly and Keil (1985) found that conscious beings (people, gods) tend to be transformed into entities nearby in the conceptual structure of Keil (1979). This also occurred in dream reports, but perceptual nearness seemed more important than conceptual nearness. In dream reports, most inanimate objects involved in metamorphoses with person-like entities were objects such as statues that ordinarily resemble people physically, and moreover represent people. A metamorphosis of a person-like entity or animal did not lead to an increase in the amount of Theory of Mind attribution. We propose that a character-line starts when a character enters a dream; properties and Theory of Mind attributions tend to be preserved along the line, regardless of whether, metamorphoses occur on it.     

Mental architectures with selectively influenced but stochastically interdependent components

The way external factors influence distribution functions for the overall time required to perform a mental task (such as responding to a stimulus, or solving a problem) may be informative as to the underlying mental architecture, the hypothetical network of interconnected processes some of which are selectively influenced by some of the external factors. Under the assumption that all processes contributing to the overall performance time are stochastically independent, several basic results have been previously established. These results relate patterns of response time distribution functions produced by manipulating external factors to such questions as whether the hypothetical constituent processes in the mental architecture enter AND gates or OR gates, and whether pairs of processes are sequential or concurrent. The present study shows that all these results are also valid for stochastically interdependent component times, provided the selective dependence of these components upon external factors is understood within the framework of a recently proposed theory of selective influence. According to this theory each component is representable as a function of three arguments: the factor set selectively influencing it, a component-specific source of randomness, and a source of randomness shared by all the components.     

Tree inference with factors selectively influencing processes in a processing tree

We show how to systematically construct a processing tree using data from an experiment in which two experimental factors are intended to selectively influence two different processes. Only two arrangements are possible for the two selectively influenced processes: ordered and unordered. We show that there are only two standard trees that need be considered, one for each arrangement. Necessary and sufficient conditions are given for each tree to be applicable. If the conditions do not hold, no tree is possible. If the selectively influenced processes are ordered, their order is sometimes determined by the data. We consider two factors that selectively influence two processes in every tree in a set of trees, such that on a given trial, a tree is selected from the set at random. We show that if the influenced processes are ordered in every tree or unordered in every tree, then the mixture of trees is equivalent to one of the two standard trees. To illustrate the method, a tree is constructed from simulated data from a model of Batchelder and Riefer [Batchelder, W.H., Riefer, D.M. (1980). Separation of storage and retrieval factors in free recall of clusterable pairs. Psychological Review, 87, 375–397].     

Concurrent visual search and time reproduction with cross-talk

Previous experiments indicate that humans can reproduce a time interval while concurrently searching a visual display presented near the beginning of the reproduced interval (Fortin, C., Rousseau, R., Bourque, P. & Kirouac, E. (1993). Time estimation and concurrent nontemporal processing: Specific interference from short-term-memory demands. Perception & Psychophysics, 53, 536-548.). In the earlier experiments, reproduced intervals were either insensitive to or shortened with increasing duration of visual search, suggesting that reproduction and search proceeded concurrently but sometimes with cross-talk. Here we test concurrency of time reproduction and visual search using a different methodology than before. Assuming the underlying mental processes are in a critical path network, factors selectively influencing concurrent processes are predicted to produce certain patterns in response time means and, through recent developments, certain patterns in cumulative distribution functions. Processes in an experiment were influenced by manipulating four factors, the time interval to be produced, stimulus onset asynchrony, display size, and target presence/absence. Patterns in response times provide evidence for concurrent time reproduction and visual search. However, a prediction based on selective influence failed in a manner suggesting the presence of cross-talk produced by a filled interval illusion.     

Properties of the organization of memory for people: Evidence from dream reports

Steyvers and Tenenbaum (2005) showed that semantic networks for words have three organizational properties: short average path lengths, high clustering, and power law degree distribution. If these are general properties of memory organization, they would apply to memory for other complex material, including people and relations between them. In addition, if during dreaming, characters are generated via knowledge in the dreamer’s memory, the three properties would be found in a relational network of characters in dreams. In dream reports from three individuals, two characters in the same dream were considered affiliated. Resulting social networks have the three properties, with the power law holding when low degrees are omitted. One network with a treelike outline is different from the other two. Results suggest associative memory has the three properties, and demonstrate that dream reports are a potentially valuable source for information about social networks.     

Effects of generation on immediate memory span and delayed unexpected free recall

We investigated the effects of generating words from fragments on pronunciation time, on immediate memory span, and on delayed free recall. Subjects read long words and short words aloud or generated them from strings with missing letters. Word-length and generation condition had multiplicative effects on speaking rate, as expected if each affected a separate process regulating the rate. We replicated the standard finding that span is smaller for longer words. Generation improved delayed free recall, indicating that relatively brief presentation times are adequate to produce a generation effect. Although generation improved long-term memory for the words, memory span was shorter for the words that were generated. The harmful effect of generation on span appears to be due to its slowing of speaking rate.     

Intensity and number of alternatives in hue identification: Piéron’s law and choice reaction time

Two experiments investigated the effects of intensity and the number of response alternatives in hue identification. Three questions were addressed. First, what is the relationship between these effects? If intensity and number of alternatives affect different processes in series, these factors would have additive effects on reaction time (RT). Other models predict a multiplicative interaction. These models assume that when a stimulus is presented, evidence accrues over time for each response alternative, and that when the evidence for a particular alternative exceeds its criterion, the response is made. A natural auxiliary assumption is that intensity affects the rate of evidence accrual, while the number of alternatives affects the criterion. The second question addressed is, how does choice RT change as a function of intensity? Piéron used a power function to describe the effect of intensity on simple RT. This paper considers three candidates for intensity’s effect on choice RT: the power, logistic, and Michaelis functions. Each candidate function was tested in an additive model and a multiplicative model. The best account was given by the power function in an additive model. The last question is, does each process produce an output that can be classified as correct or incorrect? Schweickert (1985) proposed that factors that selectively influenced such processes would have additive effects on log percent correct. Instead, an interaction was found. Perhaps the assumption that the process affected by intensity produces a single output is wrong.     

Synthesizing partial orders given comparability information: Partitive sets and slack in critical path networks

A problem which arises in the analysis of reaction times is considered. Suppose a task requires the completion of a set of mental activities which can be represented as a partially ordered set of arcs in a critical path network, but the network is unknown. If one knows for every pair of activities whether the pair is comparable (i.e., sequential) or incomparable (i.e., concurrent), then a partial order for the activities can be constructed with a procedure known as the transitive orientation algorithm. It is known that only two partial orders are possible, one the converse of the other, unless some proper nonsingleton partitive subset of the activities is not stable. Two main results are presented: First, a set of arcs generating a weakly connected subnetwork is partitive if and only if the subnetwork has a unique source, a unique sink, and no vertex of attachment other than these. Second, a simple relationship between partitive sets of activities and the slack between comparable activities is presented. These issues are important for the uniqueness problem in the synthesis of critical path networks representing cognitive tasks.     

A critical path generalization of the additive factor method: Analysis of a stroop task

Sternberg's additive factor method was generalized to apply to tasks involving both serial and concurrent processing. The generalization is based on the critical path method of scheduling. The effects on reaction time of factors prolonging separate processes in a task are discussed; in general these effects are interactions of a simple form. Reaction times can be used to deduce, in part, the schedule of the mental processes in a task, including their order of execution. Bounds on process durations can be derived. Often there are redundant equations so the method can be easily rejected if it does not apply. A dual task experiment by Greenwald was analyzed. In the task subjects were presented with two stimuli and made a response to each under high and low compatibility conditions. Two bottlenecks in processing were located: (a) Subjects make only one decision at a time, in accordance with single channel theory, although the high compatibility condition may be an exception; (b) there is a mental process which takes longer when the stimuli conflict. The decisions about the two stimuli probably change places in the schedula when compatibility is changed.