Speed-accuracy trade-off and item recognition: A reply to Gronlund and Ratcliff

IOURNAL

OF MATHEMATICAL

PSYCHOLOGY

36,

461467 ( 1992)

Theoretical

Note

Speed-Accuracy Trade-Off and Item Recognition: A Reply to Gronlund and Ratcliff E. HOCKLEY

WILLIAM Wirfrid

Laker

University

AND BENNET B. MURDOCK University

of Toronto

Gronlund and Ratcliff (1991, Journal of Mathematical Psychology, 35, 319-344) compared the ability of the decision model proposed by Ho&fey and Murdock (1987, Psychological Review, 94, 341-358) and Ratcliff’s (1978, Psychological Review, 85, 59-108; 1988, Psychological Review, 95, 238-255) diffusion model to account for speed-accuracy trade-off in item recognition. They argued that the decision model does not adequately account for speedaccuracy trade-off because it does not accumulate information during the decision process. We show that a version of the decision model appropriate for the tasks can describe the relationship between speed and accuracy in item recognition without assuming that information accumulates, and conclude that the decision model remains a viable alternative to Ratcliff’s resonance theory. cl 1992 Academic Press. Inc.

The model proposed by Hockley and Murdock (1987; see also Hockley, 1991, and Murdock & Hockley, 1989) was developed to provide an account of the decision processes underlying item recognition that would be compatible with a distributed view of memory (e.g., Murdock, 1982). This decision model, or Memory Interrogation Model (MIM), also provides an alternative to Ratcliff’s (1978) Resonance Retrieval Theory (RRT) of recognition memory. Both of these models have been applied to a variety of aspects of item recognition performance and both models have strengths and weaknesses. This work was supported by Research Grants APA 146 to B. B. Murdock and OGO012 to W. E. Hockley from the Natural Sciences and Engineering Research Council of Canada. We thank Scott Gronlund for sending us the observed results presented in Fig. 1 and Table 2, and Richard Shiffrin and the reviewers for their constructive comments on an earlier version of this paper. Correspondence may be addressed to W. E. Hockley, Department of Psychology, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada, or 8. B. Murdock, Department of Psychology, University of Toronto, Toronto, Ontario M5S lA1, Canada.

461 0022-2496192 $5.00 Copyright C 1992 by Academx Press, Inc All righls of reproductmn in any i6m1 reserved.

HOCKLEYAND

462

MURDOCK

One very important theoretical difference between these models concerns the question of whether or not there is an accumulation of information during the retrieval/decision process. In RRT, a diffusion process is used to represent the accumulation of evidence that drives the process towards a match or nonmatch boundary. In MIM there is no accumulation of informaton-the input to the decision system represents the match between the probe and information stored in memory and response latency is determined by the dynamics of the decision process. Gronlund and Ratcliff (1991) compared the ability of MIM and RRT to fit speed-accuracy trade-off (SAT) functions in item recognition. They argued that MIM does not provide an adequate description of SAT because there is no accumulation of information during the decision process, whereas RRT provides a better account of SAT because evidence is assumed to grow over time. In this reply we show that MIM can provide a reasonable account of SAT for the tasks in question and consequently it is not necessary to assume that information accrues during the decision process.

SPEED-ACCURACY

TRADE-OFF

Ratcliff (1978) distinguished between two different classes of procedures for examining the relationship between speed of responding and accuracy. Procedures that require subjects to respond according to experimenter-controlled deadlines are termed time-controlled processing tasks. Procedures that use instructions or payoffs to differentially emphasize speed or accuracy are termed information-controlled processing tasks. Time-Controlled Processing

Reed (1973, 1976) used a response signal procedure and showed that recognition accuracy increases monotonically as a function of processing time. Kounios, Osman, and Meyer (1987), and Meyer, Irwin, Osman, and Kounios (1988) assumed that response signal trials are a probability mixture of fast-finishing regular responses and guesses. These investigators developed a decomposition technique to estimate the accuracy of guesses by factoring out the contribution of fast-finishing regular responses on signal trials. Ratcliff (1988) used this technique in a study-test recognition task and found that the accuracy of guesses was above chance and increased slowly with processing time. Hockley and Murdock (1987) demonstrated that MIM can account for this pattern of results if it is assumed that guesses result from a probability mixture of random guesses and decisions based on a single criterion, and it is assumed that the probability of a decision based on a single criterion increases as the upper and lower criteria converge in the course of the normal decision process, The first assumption results in guesses with above-chance accuracy, and the second assumption produces an increase in guessing accuracy over time.

A REPLY

Information-Controlled

TO GRONLUND

AND

RATCLIFF

463

Processing

Hockley and Murdock (1987) argued that MIM could account for speedaccuracy trade-off, when instructions or payoffs are manipulated, by appropriate changes in the initial locations of the upper and the lower criteria and in the rate at which the criteria converge over decision cycles after indeterminate outcomes. Within limits, the greater the distance between the starting positions of the criteria, and the slower the convergence rate, the slower but the more accurate the response will be. Gronlund and Ratcliff conducted an experiment in which three levels of speed-accuracy trade-off were manipulated using instructions. Subjects studied 16 words and were tested on the 16 study words and 16 distracters. Speed-accuracy trade-off instructions were blocked over trials. For speed instructions subjects were told to respond in less than 500 ms and were given only reaction time feedback. For normal instructions subjects were told to keep their response time between 500 and 700 ms and they received reaction time feedback after every trial and feedback after every error. In the accuracy condition subjects were told to be as accurate as possible and feedback after every error was provided. The obtained results are presented as solid lines in the top panel of Fig. 1. Gronlund and Ratcliff showed that MIM could not fit the observed pattern of results when only the starting positions of the criteria and the convergence rate were varied. The best lit of the decision model is also shown in the top panel Fig. 1. When only the criteria and convergence rate are free to vary, the lit of the decision model overestimates accuracy and underestimates latency in the speed condition. Also, the predicted response latency distribution for this condition is normally distributed, whereas the observed distribution is positively skewed. Gronlund and Ratcliff found that when guessing is incorporated in the speed condition, the decision model can generate a lit that is a good approximation to the observed results. In this version of the model, if on cycle 1 the signal-plus-noise did not go outside the criteria there was a 20% chance a guess would be made. The probability of a guess after an indeterminate outcome increased from 40% on cycle 2 to 100% on cycle 5. The addition of a guessing assumption in this application of MIM is consistent with the assumption that a proportion of the responses in the time-controlled SAT procedure are guesses. Gronlund and Ratcliff argue correctly that the incorporation of fast guesses is a less-than-optimal response strategy in this task from the point of view of the decision model. However, one could well argue that subjects do not act optimally in such tasks. In this note, we explore an alternative response to that criticism, the hypothesis that subjects do not encode the test probe in the same way when speed is emphasized as when accuracy is emphasized. Ratcliff (1978) and Reed (1976) have noted that subjects who have prior knowledge of the SAT condition (as in information-controlled SAT tasks) can change their decision criteria between conditions. Prior knowledge also allows the subject to encode the test probe differently in different conditions.

464

HOCKLEY

.a5

-

.a0

-

AND

MURDOCK

.75 0 HITS (06.5)

.70 g 0

0 HITS (MIM)

mCRs (ms)

651

0 0%

T

00

500

600

700

MEAN RESPONSE TIME

(MIM)

I

a00

(ms)

FIG. 1. Top Pane/: Observed and predicted (tit 1) hit and correct rejection rates as a function of mean hit and correct rejection response latency for the speed-accuracy trade-off experiment reported by Gronlund and Ratcliff (1991). MIM parameter values: means and variances of old and new item distributions are 2 and 1 and 0 and 1, respectively; means and variances of distributions representing time for other stages were 425 and 70 ms (old items) and 460 and 70 ms (new items); the starting values of the lower and upper criteria and the criteria convergence rate were 0.850, 0.850, and 0 (speed condition); - 1.55, 3.45 and 0.12 (normal condition); and - 1.78, 3.68, and 0.07 (accuracy condition). Bottom panel: Observed and predicted (lit 2) speed-accuracy trade-off functions. The parameters values for this fit are given in Table 1.

Most models of the memory comparison process account for the increase in memory performance with study time by assuming that more information is encoded when study items are presented for a longer duration. Most models also assume that the test probe is encoded and represented in the same fashion as the study items. Thus when accuracy is emphasized subjects can take time to encode the probe in sufficient detail. However, when speed is emphasized subjects may not take the same amount of time to encode fully the information represented in the probe. If the encoded representation of the probe differs between accuracy and speed conditions, then the resulting match between the information in memory and the information contained in the probe representation will differ and result in a poorer match in the speed condition. In Murdock’s (1982) distributed memory model this variation is captured by probabilistic encoding where components of the item vectors are encoded with probability p or not encoded with probability 1 -p; see Murdock (1989) or Murdock and Lamon (1988) for details.

A REPLY

TO GRONLUND

AND

465

RATCLIFF

The bottom panel of Fig. 1 presents a new lit of MIM to the experimental results of Gronlund and Ratcliff. This lit assumes that the mean of the distribution representing time for other stages varies with the experimental conditions representing different encoding times of the test probe. The fit also assumes that the mean of the input to the decision systems varies with experimental conditions reflecting the differences in the match between the different encoded representations of the probe and the contents of memory. Finally, the fit assumes that subjects differentially adjust their decision criteria for the different response conditions. The fixed and free parameter values for this tit are presented in Table 1. Given the above assumptions the decision model can provide an excellent lit to the changes in accuracy with response latency. MIM also closely mimics the changes in the parameters that describe the underlying response latency distributions in each condition. The observed and predicted distribution parameter estimates derived from the convolution of normal and exponential distributions (Ratcliff & Murdock, 1976) are presented in Table 2. One should not be overly impressed with the goodness of this lit because the fit utilizes live free parameters for each response condition. We report this fit only to demonstrate two important points. First, the decision model can provide a description of SAT for information-controlled processing that is consistent with the characteristics of the task. Second, this fit demonstrates that the informationcontrolled SAT procedure may not be the most informative procedure for TABLE Values

of the Fixed

Fixed

parameters

Mean

(new

and Free Parameters Used in the Fit of the Decision in the Bottom Panel of Fig. 1 and in Table 2

item distribution)

Variance

(new

Variance

(old

item distribution)

Variance

(TOS

distributions)

Criteria

= 1

= 70 ms

Rate = 0.10

parameters

Speed

Mean (old item distribution) Lower Criterion (a) Upper

(b)

condition

Normal

Accuracy

1.35 - 0.90

1.95 - 1.30

2.15 - 1.63 3.12

2.00

3.10

TOS

(new)

445

490

515

TOS

(old)

410

455

480

Note:

Criterion

Presented

= 1

Response Free

Model

= 0

item distribution)

Convergence

I

TOS = mean

of distribution

for time for other

stages in ms.

466

HOCKLEYANDMURDOCK TABLE

2

Observed (Gronlund & Ratcliff, 1991) and Predicted Parameter Values from the Convolution Analysis of the Response Time Distributions for the Means Presented in the Bottom Pane1 of Fig. 1 Hits

Correct rejections

Mu

Sigma

Tau

MU

Sigma

Tau

408 411

47 65

109 88

430 452

55 67

117 84

Data MIM

465 453

34 64

129 136

500 490

48 67

134 140

Accuracy Data MIM

500 482

25 70

166 176

541 520

33 71

182 178

Speed Data MIM Normal

evaluating the effects of SAT on retrieval and/or decision processes: When SAT is varied through instructions or payoffs, subjects are not only free to vary their decision criteria in each condition, but they may also vary their encoding of the test probe.

SUMMARY

A version of the Hockley-Murdock decision model that takes into account the freedom allowed by information-controlled SAT tasks can provide an adequate account of the SAT data for item recognition reported by Gronlund and Ratcliff (1991). Thus MIM remains viable as a general model for decision processes in recognition memory. More generally it should be noted that our account does not assume there is an accumulation of information over time during retrieval. To date there is no direct or compelling evidence showing that the time for decision in recognition memory is taken up by an information accumulation process.

REFERENCES GRONLUND, S. D., & RATCLIFF, R. (1991). Analysis of the Hockley and Murdock decision model. Journal of Mathematical Psychology, 35, 319-344. HOCKLEY, W. E. (1991). Interrogating memory: A decision model for recognition and judgment of frequency. In W. C. Abraham, M. C. Corballis, & K. G. White (Eds.), Memory mechanisms: A tribute fo G. V. Goddard, (pp. 219-245). Hillsdale, NJ: Erlbaum.

A REPLY

TO GRONLUND

AND

RATCLIFF

467

HOCKLEY, W. E., & MURDOCK, B. B., JR. (1987). A decision model for accuracy and response latency in recognition memory. Psychological Review, 94, 341-358 KOUNIOS, J., OSMAN, A. M., & MEYER, D. E. (1987). Structure and process in semantic memory: New evidence based on speed-accuracy decomposition. Journal of Experimental Psychology: General, 116, 3-25.

MEYER, D. E., IRWIN, D. E., OSMAN, A. M., & KOUNIOS, J. (1988). The dynamics of cognition and action: Mental processes inferred from speed-accuracy decomposition. Psychological Review, 95, 183-237. MURDOCK, B. B., JR. (1982). A theory for the storage and retrieval of item and associative information. Psychological

Review,

89, 609-626.

MURDOCK, B. B., JR. (1989). Learning in a distributed memory model. In C. Izawa (Ed.), Currrenr issues in cognitive processes: The Tulane Flowerree symposium on cognition (pp. 69-106). Hillsdale, NJ: Erlbaum. MURDCICK,B. B., & HOCKLEY, W. E. (1989). Recognition in a distributed-memory model. In D. Vickers and P. L. Smith (Eds.), Human information processing: Measures, mechanisms, and models (pp. 395409). Amsterdam: North-Holland. MURDOCK, B. B., & LAMON, M. (1989). The replacement effect: Repeating some items while replacing others. Memory & Cognition, 16, 91-101. RATCLIFF, R. (1978). A theory of memory retrieval. Psychological Review, 85, 59-108. RATCLIFF, R. (1988). Continuous versus discrete information processing: Modelling accumulation of partial information. Psychological Review, 95 238-255. RATCLIFF, R., & MURDOCK, B. B. JR. (1976). Retrieval processes in recognition memory. Psychological Review, 83, 19G-214. REED, A. V. (1973). Speed-accuracy trade-off in recognition memory. Science, 181, 574-576. REED, A. V. (1976). List length and the time course of recognition in immediate memory. Memory & Cognirion, 4, 1630.