Roger Ratcliff

A Theory of Memory Retrieval

A theory of memory retrieval is developed and is shown to apply over a range of experimental paradigms. Access to memory traces is viewed in terms of a resonance metaphor. The probe item evokes the search set on the basis of probe-memory item relatedness, just as a ringing tuning fork evokes sympathetic vibrations in other tuning forks. Evidence is accumulated in parallel from each probe-memory item comparison, and each comparison is modeled by a continuous random walk process. In item recognition, the decision process is self-terminating on matching comparisons and exhaustive on nonmatching comparisons. The mathematical model produces predictions about accuracy, mean reaction time, error latency, and reaction time distributions that are in good accord with experimental data. The theory is applied to four item recognition paradigms (Sternberg, prememorized list, study-test, and continuous) and to speed-accuracy paradigms; results are found to provide a basis for comparison of these paradigms. It is noted that neural network models can be interfaced to the retrieval theory with little difficulty and that semantic memory models may benefit from such a retrieval scheme.

Methods for dealing with reaction time outliers.

The effect of outliers on reaction time analyses is evaluated. The first section assesses the power of different methods of minimizing the effect of outliers on analysis of variance (ANOVA) and makes recommendations about the use of transformations and cutoffs. The second section examines the effect of outliers and cutoffs on different measures of location, spread, and shape and concludes using quantitative examples that robust measures are much less affected by outliers and cutoffs than measures based on moments. The third section examines fitting explicit distribution functions as a way of recovering means and standard deviations and concludes that unless fitting the distribution function is used as a model of distribution shape, the method is probably not worth routine use.

The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks

The diffusion decision model allows detailed explanations of behavior in two-choice discrimination tasks. In this article, the model is reviewed to show how it translates behavioral dataaccuracy, mean response times, and response time distributionsinto components of cognitive processing. Three experiments are used to illustrate experimental manipulations of three components: stimulus difficulty affects the quality of information on which a decision is based; instructions emphasizing either speed or accuracy affect the criterial amounts of information that a subject requires before initiating a response; and the relative proportions of the two stimuli affect biases in drift rate and starting point. The experiments also illustrate the strong constraints that ensure the model is empirically testable and potentially falsifiable. The broad range of applications of the model is also reviewed, including research in the domains of aging and neurophysiology.

Modeling Response Times for Two-Choice Decisions:

The diffusion model for two-choice real-time decisions is applied to four psychophysical tasks. The model reveals how stimulus information guides decisions and shows how the information is processed through time to yield sometimes correct and sometimes incorrect decisions. Rapid two-choice decisions yield multiple empirical measures: response times for correct and error responses, the probabilities of correct and error responses, and a variety of interactions between accuracy and response time that depend on instructions and task difficulty. The diffusion model can explain all these aspects of the data for the four experiments we present. The model correctly accounts for error response times, something previous models have failed to do. Variability within the decision process explains how errors are made, and variability across trials correctly predicts when errors are faster than correct responses and when they are slower.

Psychology and neurobiology of simple decisions

Patterns of neural firing linked to eye movement decisions show that behavioral decisions are predicted by the differential firing rates of cells coding selected and nonselected stimulus alternatives. These results can be interpreted using models developed in mathematical psychology to model behavioral decisions. Current models assume that decisions are made by accumulating noisy stimulus information until sufficient information for a response is obtained. Here, the models, and the techniques used to test them against response-time distribution and accuracy data, are described. Such models provide a quantitative link between the time-course of behavioral decisions and the growth of stimulus information in neural firing data.

Group reaction time distributions and an analysis of distribution statistics.

A method of obtaining an average reaction time distribution for a group of subjects is described. The method is particularly useful for cases in which data from many subjects are available but there are only 10-20 reaction time observations per subject cell. Essentially, reaction times for each subject are organized in ascending order, and quantiles are calculated. The quantiles are then averaged over subjects to give group quantiles (cf. Vincent learning curves). From the group quantiles, a group reaction time distribution can be constructed. It is shown that this method of averaging is exact for certain distributions (i.e., the resulting distribution belongs to the same family as the individual distributions). Furthermore, Monte Carlo studies and application of the method to the combined data from three large experiments provide evidence that properties derived from the group reaction time distribution are much the same as average properties derived from the data of individual subjects. This article also examines how to quantitatively describe the shape of reaction time distributions. The use of moments and cumulants as sources of information about distribution shape is evaluated and rejected because of extreme dependence on long, outlier reaction times. As an alternative, the use of explicit distribution functions as approximations to reaction time distributions is considered.

A Comparison of Sequential Sampling Models for Two-Choice Reaction Time.

The authors evaluated 4 sequential sampling models for 2-choice decisions--the Wiener diffusion, Ornstein-Uhlenbeck (OU) diffusion, accumulator, and Poisson counter models--by fitting them to the response time (RT) distributions and accuracy data from 3 experiments. Each of the models was augmented with assumptions of variability across trials in the rate of accumulation of evidence from stimuli, the values of response criteria, and the value of base RT across trials. Although there was substantial model mimicry, empirical conditions were identified under which the models make discriminably different predictions. The best accounts of the data were provided by the Wiener diffusion model, the OU model with small-to-moderate decay, and the accumulator model with long-tailed (exponential) distributions of criteria, although the last was unable to produce error RTs shorter than correct RTs. The relationship between these models and 3 recent, neurally inspired models was also examined.

Estimating parameters of the diffusion model: Approaches to dealing with contaminant reaction times and parameter variability

Three methods for fitting the diffusion model (Ratcliff, 1978) to experimental data are examined. Sets of simulated data were generated with known parameter values, and from fits of the model, we found that the maximum likelihood method was better than the chi-square and weighted least squares methods by criteria of bias in the parameters relative to the parameter values used to generate the data and standard deviations in the parameter estimates. The standard deviations in the parameter values can be used as measures of the variability in parameter estimates from fits to experimental data. We introduced contaminant reaction times and variability into the other components of processing besides the decision process and found that the maximum likelihood and chi-square methods failed, sometimes dramatically. But the weighted least squares method was robust to these two factors. We then present results from modifications of the maximum likelihood and chi-square methods, in which these factors are explicitly modeled, and show that the parameter values of the diffusion model are recovered well. We argue that explicit modeling is an important method for addressing contaminants and variability in nondecision processes and that it can be applied in any theoretical approach to modeling reaction time.

Connectionist models of recognition memory: constraints imposed by learning and forgetting functions

Multilayer connectionist models of memory based on the encoder model using the backpropagation learning rule are evaluated. The models are applied to standard recognition memory procedures in which items are studied sequentially and then tested for retention. Sequential learning in these models leads to 2 major problems. First, well-learned information is forgotten rapidly as new information is learned. Second, discrimination between studied items and new items either decreases or is nonmonotonic as a function of learning. To address these problems, manipulations of the network within the multilayer model and several variants of the multilayer model were examined, including a model with prelearned memory and a context model, but none solved the problems. The problems discussed provide limitations on connectionist models applied to human memory and in tasks where information to be learned is not all available during learning.

Inferences about predictable events.

If someone falls off of a 14th story roof, very predictably death will result. The conditions under which readers appear to infer such predictable outcomes were examined with three different retrieval paradigms: immediate recognition test, cued recall, and priming in word recognition. On immediate test, responses to a word representing the implicit outcome (e.g., dead) were slow, but on delayed test these responses were slow or inaccurate only when primed by an explicitly stated word. However, the word expressing the predictable outcome did function as an effective recall cue. Results suggest that readers encode these inferences into memory only minimally, but that they can make use of a cue word that represents the inference (e.g., dead) both at the time of an immediate test and in delayed cued recall.