J. E. Keith Smith

Temporal properties of human information processing: Tests of discrete versus continuous models,

Abstract Cognitive psychologists have characterized the temporal properties of human information processing in terms of discrete and continuous models. Discrete models postulate that component mental processes transmit a finite number of intermittent outputs (quanta) of information over time, whereas continuous models postulate that information is transmitted in a gradual fashion. These postulates may be tested by using an adaptive response-priming procedure and analysis of reaction-time mixture distributions. Three experiments based on this procedure and analysis are reported. The experiments involved varying the temporal interval between the onsets of a prime stimulus and a subsequent test stimulus to which a response had to be made. Reaction time was measured as a function of the duration of the priming interval and the type of prime stimulus. Discrete models predict that manipulations of the priming interval should yield a family of reaction-time mixture distributions formed from a finite number of underlying basis distributions, corresponding to distinct preparatory states. Continuous models make a different prediction. Goodness-of-fit tests between these predictions and the data supported either the discrete or the continuous models, depending on the nature of the stimuli and responses being used. When there were only two alternative responses and the stimulus-response mapping was a compatible one, discrete models with two or three states of preparation fit the results best. For larger response sets with an incompatible stimulus-response mapping, a continuous model fit some of the data better. These results are relevant to the interpretation of reaction-time data in a variety of contexts and to the analysis of speed-accuracy trade-offs in mental processes.

Analyses of Multinomial Mixture Distributions: New Tests for Stochastic Models of Cognition and Action

Mixture distributions are formed from a weighted linear combination of 2 or more underlying basis distributions [g(x) = sigma j alpha j fj(x); sigma alpha j = 1]. They arise frequently in stochastic models of perception, cognition, and action in which a finite number of discrete internal states are entered probabilistically over a series of trials. This article reviews various distributional properties that have been examined to test for the presence of mixture distributions. A new multinomial maximum likelihood mixture (MMLM) analysis is discussed for estimating the mixing probabilities alpha j and the basis distributions fj(x) of a hypothesized mixture distribution. The analysis also generates a maximum likelihood goodness-of-fit statistic for testing various mixture hypotheses. Stochastic computer simulations characterize the statistical power of such tests under representative conditions. Two empirical studies of mental processes hypothesized to involve mixture distributions are summarized to illustrate applications of the MMLM analysis.

Data transformations in analysis of variance

Abstract A number of reasons for transforming dependent variable measures for use in analysis of variance is discussed, including nonnormality, heteroscedasticity, and scale-induced interactions. It is pointed out that nonlinear transformations change the interpretation of interactions, and that, depending on the theoretical framework, this may or may not be desirable. Finally, a method for reducing heteroscedasticity due to mean-variance correlation is described and examples given.

Recognition models evaluated: A commentary on Keren and Baggen

In a recent paper (1981), Keren and Baggen proposed two new models for alphanumeric confusion data, based on Tversky’s (1977) feature model of similarity, and compared them with Luce’s (1963) biased choice model. On the basis of their data, they concluded that, although the choice model fit slightly better, their models were to be preferred on grounds of parsimony and interpretability. It is shown here that both of these models are special cases of the Luce model, so that the general Luce model will necessarily fit better. This leads to considerable reinterpretation of Keren and Baggen’s conclusions. Finally, better methods of estimating parameters and evaluating goodness-of-fit are suggested, taking advantage of this relation between the models.

Similarity, identification, and categorization: Comment on Ashby and Lee (1991).

Ashby and Lee (1991) tested various models derived from the general recognition theory (GRT; Ashby & Perrin, 1988; Ashby & Townsend, 1986) on their ability to predict and interrelate similarity, categorization, and identification performance. This commentary (a) argues that contrary to Ashby and Lees suggestion, the likelihood-based GRT cannot generally predict categorization from identification without incorporating selective attention, (b) argues that the categorization rule in the likelihood-based GRT is extremely close in spirit to Nosofskys (1986) exemplar-based similarity model, (c) reports new model-based analyses that call into question Ashby and Lees interpretation of their identification-confusion data, (d) raises questions about the identification and similarity models tested by Ashby and Lee, and (e) criticizes Ashby and Lees methods of fitting and evaluating the various models.

An analysis of confusion errors in naming letters under speed stress

Three subjects named six visually presented letters under two levels of speed stress. The obtained confusion matrices for each stress condition were fit by Luce’s choice theory, which provided measures of stimulus similarity and response bias. Speed stress produced proportional increases in pairwise similarity measures but had no systematic effect on response biases. In Experiment 2, the same three subjects named the same letters under two levels of stimulus quality and a constant response-time deadline. As with speed stress, degrading the stimulus produced proportional increases in pairwise similarity measures but had no systematic effect on response biases. In Experiment 3, two of the subjects participating in Experiments 1 and 2 named the six letters under conditions where the probabilities of the letters were unequal. The letters toward which the subject had been most biased in Experiments 1 and 2 were assigned low probabilities, and the letters toward which he was least biased were assigned high probabilities. The result of this manipulation was to completely reverse the ordering of the response bias parameters of the Luce choice model. It is suggested that the present methodology provides a means of validating as psychological constructs the parameters of various mathematical models of stimulus recognition.