accumulator model. According to the "programming-in- teractions assumption," stimulus processing is tightly linked to response programming, so that both the ...
Psychological Research
Psychol Res (1987) 49:91-98
© Springer-Verlag 1987
Visual discrimination and response programming* Herbert Heuer Universit/it Bielefeld, Abteilung fiir Psychologie, Postfach 8640, D-4800 Bielefeld, Federal Republic of Germany
Summary. Choice reaction time (RT) depends on the relationship between responses, and these dependencies are usually interpreted in terms of the "advance-specification assumption." According to this assumption characteristics that are the same for the choice responses can be specified in advance of the response signal, thus allowing faster RTs. Since the advance-specification assumption is called into question by some of the available data, an alternative interpretation is suggested and formalized in terms of an accumulator model. According to the "programming-interactions assumption," stimulus processing is tightly linked to response programming, so that both the possible responses are programmed as long as there is uncertainty with regard to stimulus identity. This gives rise to interactions between simultaneous processes of motor programming. Predictions of this assumption for the joint effects of signal similarity and the relationship between responses are tested and confirmed. Information processing in a choice-reaction time task is often analyzed in terms of a sequence of processing stages. The time needed by each stage may depend on conditions, but its output, which is fed into the next stage of the chain, may not. In part, the predominance of the serial-stages framework is a result of the handy methodology that is available (see Sanders, 1980). Another convenient aspect of this framework is that it allows different stages to be studied independently of each other. For example, there exists a body of literature on signal discrimination without concern for the nature of the responses (for review see Vickers, 1979). Analogously, there is literature on response programming, with only little concern for the stimuli used (for a review see Marteniuk & MacKenzie, 1980; Rosenbaum, 1983, 1985). In this paper I want to argue that the assumption of nicely separable stages for stimulus processing and response programming may not always be correct; rather, stimulus processing and response programming seem to be intricately related to each other under some conditions.
The advance-specification assumption Consider a task in which a choice has to be made between responses with the left or the right hand. In one condition * This research was supported by grant no. He l 187/3-1 from the Deutsche Forschungsgemeinschaft
the movements assigned to the two hands are the same, but in another condition they differ with regard to their spatiotemporal pattern. The particular movements used have been labeled "tapping" and "alternating." Tapping is a simple up-and-down movement, alternating is mainly a horizontal movement with only a small vertical component. A reliable finding is that RT is longer if the movements are different (Heuer, 1984). This result can be easily interpreted within the general framework of independent serial stages. The particular assumption that is needed will be called the "advance-specification assumption," and is one of the basic assumptions of Rosenbaum's (1980) precuing method. It is postulated that if same responses are assigned to the two hands, then their spatio-temporal pattern can be preprogrammed in advance of the response signal, 1 while advance specification will not be possible if different movements are assigned to the two hands. Rather, in the latter case, specification of the spatio-temporal pattern of the movement finally executed would have to wait until after presentation of the response signal. The time needed for specification will contribute to the RT, which is not the case in the same-movements condition. By simple application of the subtraction logic, the time required for programming the spatio-temporal pattern, or any other response characteristic, can be estimated. The difference in mean RT is not the only reliable difference between conditions in which movements with same and different spatio-temporal characteristics are assigned to the two hands. In addition, with different movements RT variability is increased and the frequency of choice errors, that is, of confusions between the hands, is reduced (Heuer, 1984). This latter finding causes some problems for interpretation in terms of the advance-specification assumption. According to the advance-specification assumption the critical difference between conditions with same and dif1The term "preprogramming" is used in this paper to designate programming that occurs before presentation of the response signal, as is the term "advance specification." This is not a universally accepted meaning of the term; it is sometimes used also to designate programming that occurs before execution of the response. The distinction between preprogramming in advance of the response signal and programming after presentation of the response signal and before the start of the response is critical for the two hypotheses being contrasted
92 ferent movements assigned to the two hands is the point in time at which the spatio-temporal characteristics of the response are specified. They are specified either in advance of the response signal or after its presentation. Which hand to use for responding has to be specified after presentation of the response signal in both conditions. A high accuracy in specifying the hand could be due to high accuracy of stimulus identification, of response selection, or of programming the appropriate set of muscles on the left or the right side of the body. It is difficult to give a stringent reason why the accuracy of any of these processes should depend on whether the spatio-temporal pattern of the movement has to be specified in addition to the hand to be used (as in different-movements conditions) or not (as in samemovements conditions). It seems somewhat plausible, though, that in the choice between same movements of the two hands selection of the wrong hand is more likely than in the choice between different movements (as reported by Heuer, 1984). A simple way to solve this difficulty for the advancespecification assumption would be to explain the simultaneous differences in mean RT and error frequency in terms of different speed-accuracy criteria. Such an interpretation, however, can be excluded: By varying the speed-accuracy criteria it is possible to obtain the same accuracy levels in conditions with same and different responses, but the RT difference is not eliminated by this manipulation (Heuer, 1983). Thus, it seems that the relation between the two responses affects mean RT as well as accuracy. The advance-specification assumption runs into more serious difficulties when an attempt is made to prevent or at least impair advance specification even when the same movements are assigned to the two hands, for example, by introducing a high proportion of catch trials in which a warning signal, but no response signal is presented. If catch trials indeed succeed in impairing advance specification one would expect that with higher catch-trial frequency the advantage of same-movement conditions is lost. But the effect of this manipulation is exactly the opposite: With higher catch trial frequency the RT difference between conditions increases (Heuer, 1986b). This result seems to be inconsistent with the advance-specification assumption. Therefore, exploration of an alternative hypothesis appears justified.
The programming-interactions assumption According to serial-stage models, when programming of a response begins after presentation of the response signal, there is already full information on which of the alternative responses to perform available. Thus, only one of the potential responses will be programmed, and the possibility of interactions between simultaneous processes of programming two responses is excluded. For this reason a difference in programming times has to be attributed to a difference in the amount of programming required for the particular response that has been selected in advance. This difference is assumed to come about by different amounts of preprogramming (or advance specification) in conditions with same and different movements assigned to the two hands. The situation becomes more complicated if continuous models of information processing are taken into consider-
ation. According to these models (e.g., McClelland, 1979) any evidence on stimulus identity that is available is fed into further stages more or less immediately. Two types of models can be distinguished according to how the relationship between signal identification and response programming is conceived of. In the first type of model the relationship is described as some kind of sequential feature mapping. This type of model was introduced by Miller (1982) and elaborated by Hoffmann and Ziel31er (1986). It gave rise to an extended controversy over whether the data presented by Miller as support for the model are appropriate or not (Reeve & Proctor, 1984; Miller, 1985; Reeve & Proctor, 1985). The essential characteristics of this first type of model are the assumption that information on signal identity is fed into programming stages in discrete steps and is of a categorial nature (e.g., lower case vs. upper case letter). Programming proceeds in step with the availability of partial information about the stimulus which is no longer uncertain, provided the information can be mapped on features that discriminate responses (e.g., left hand vs. right hand). Thus, the time needed until completion of programming after presentation of the response signal does not only depend on the amount of programming that is required, but also on the sequence of outputs of the stimulus identification stage and how these map onto response features. In the second type of model of continuous information processing, signal identification is represented as a continuous process with the odds in favor of one or the other signal available as output at any point in time. Instead of being conceived of in terms of odds, the output can be thought of as any other variable or set of variables which indicates the current evidence in favor of one or the other signal being presented. Various kinds of models, such as the recruitment model of LaBerge (1962), the random-walk model (Laming, 1968; Edwards, 1965) or the accumulatormodel of Vickers (1979), treat signal identification in this way. The important consequence of this kind of model is that it permits simultaneous programming of both the alternative responses as long as there is some uncertainty with regard to signal identity. When the alternative responses are programmed simultaneously, there is an opportunity for interactions between simultaneous processes of programming to take place. For example, if the spatio-temporal characteristics of responses assigned to the two hands are the same, interactions are likely to be facilitative: Programming of the response finally performed may profit from the partial programming of the same response for the other hand. In contrast, when the spatio-temporal patterns of the two responses are different, interactions are likely to be inhibitory. According to the hypothesis of programming interactions, which is an addition to the second type of models of continuous information processing, the differences between conditions with same and different movements assigned to the two hands come about by facilitative a n d / o r inhibitory interactions between simultaneous processes of programming. This hypothesis presupposes a tight and continuous linkage between signal identification and response programming in that it is assumed that programming of the alternative responses proceeds in line with the present evidence on signal identity. As long as the evidence in favor of one or the other signal is balanced, pro-
93 gramming of the !two responses will proceed about equally; the progressiv~ imbalance of the evidence in the course of signal identification will be accompanied by a progressive imbalance in programming, so that finally programming will be completed for the response executed but stop short of complet!on for the alternative response not executed. Which of:the two responses will be performed depends on which of the two simultaneous processes of programming is completed first. An implicatio!n of this hypothesis is an interaction between signal discriminability and the relationship between the alternative responses. If the discriminability of stimuli is reduced, there should be more uncertainty about the identity of the signal that is presented in any single trial. As a consequence, partial programming of the response that is not executed in the end should proceed further than in the case of better discriminable signals. This, in turn, should cause stronger programming interactions and a larger difference between conditions with same and different movements assigned to the two hands. The exact ,expectations based on the programming-interactions hypothesis with regard to mean RT, RT variability, and choice accuracy are hard to determine as long as this hypothesis is stated only qualitatively. Therefore, I shall consider a specific formalized variant, which, of course, is not the only one possible. The formalization is based on an available model that has been changed as little as possible.
A coupled-accumulators model The model taken as a basis for formalizing the programming-interactions assumption is an accumulator model of visual discrimination that is extensively discussed by Vickers (1979). Formally, this model is supplemented by an additional parameter; further, it is reinterpreted to allow a reasonable mapping of parameters on experimental variables. A flow diagram of Vicker's model for a two-choice task is shown in Figure 1. During each time interval At an observation of a normally distributed random variable Xis drawn. For Monte-Carlo simulations the variance was set at 1.0. This arbitrary definition amounts to a scaling of the other parameters of the model. The observed value x is compared with a criterion value xo, which for simulations was set equal to zero. Depending on whether x is larger or smaller than xc, its absolute value is added to one or the other accumulator. This cycle is continued until one or the other threshold k is reached. Reaction time is treated as a linear function of the number of cycles n. So far the model is not at all concerned with motor programming. But it can easily be related to motor programming if the hypothetical process of accumulation is interpreted in a particular way. In fact, there seems to be much diversity in the meaning given to this concept. Often accumulation is defined in statistical terms, for example as continuous revision of posteriori odds (Edwards, 1965). Sometimes it is interpreted with regard to psychological theory like stimulus-sampling theory; in this context accumulation is conceived of as an increase in the number of stimulus elements that are conditioned to one or the other response (LaBerge, 1962). Finally, the analogy of the concept of accumulation to summation of excitation in the nervous system is obvious (see Vickers, 1979, pp. 97-99).
I n:O [ ai:O,i:1,2
1
4 n:n''
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o+ +no Fig. 1. Flow diagram of Vicker's (1979) model. The operations framed by broken lines are added
An interpretation of accumulation that allows motor variables to be included in the model is the following: The current state of the two accumulators is considered as reflecting the amount of programming done for each response so far. Thus, accumulation of evidence on signal identity is conceived of as programming the associated responses, and interactions during programming can be modelled by coupling the two accumulators. The choice of a particular kind of coupling has been governed by formal considerations, not by considerations of what the most "realistic" form of coupling could be. As is shown in Figure 1, the two accumulators are coupled in a very simple way: Any value x that is added to one of the accumulators, is subtracted from the other one after multiplication with a "coupling parameter" c that can vary between 0 and 1. This constrains interactions between accumulators (or processes of programming) to be inhibitory. But it has the formal advantage of providing a continuous transition between accumulator and randomwalk models, which usually are treated as discrete alternatives (e.g., Heath, 1984). If c = 0, then the two accumulators are independent, but if e = 1, then the two accumulators behave as mirror images of each other and are equivalent to one accumulator, for which a lower and a higher threshold are defined. The model has been simulated to gain some insight into its qualitative predictions of the effects of the relationship between responses and how these change when signal discriminability is varied. The relationship between responses is mapped onto t h e coupling parameter c ; c is small (e.g., zero) for conditions with same responses assigned to the two hands, and larger for conditions with different responses, where inhibitory interactions are to be expected. Signal similarity is mapped onto the mean Ix of the random variable X, which is sampled during each time interval At. Results are presented only for one value of the
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Fig. 2. Predictions of the formal model for choice accuracy (Pc), mean (-6) and variability [s(n)l of the number of cycles as a function of signal similarity (represented by Ix) and relationship between responses (represented by c). Threshold is k = 4.0 threshold k, but the main qualitative features are independent of k. Figure 2 shows that the model predicts the triad of effects that is typically observed (Heuer, 1984). For conditions with different responses assigned to the two hands (larger value of c) a higher accuracy, a larger mean RT, and a larger RT variability is predicted. (Mean RT and RT variability correspond to the mean number of cycles and their variability as shown in Figure 2.) Further, with increasing signal similarity, represented by decreasing values of IX, all three effects are predicted to increase; only for accuracy the increase should be followed by a decrease if a sufficiently low accuracy is reached. These predictions were tested in the following experiment.
Method
Subjects. Nine female and seven male subjects, aged 19-30 years, took part in the experiment for pay. According to the Edinburgh Handedness Inventory (Oldfield, 1971) 14 subjects were right-handed and two were lefthanded.
Experimental conditions. In two conditions same movements were assigned to the two hands (tapping-tapping, alternating-alternating), while in two other conditions the movements were different (tapping-alternating, alternating-tapping). These choice conditions were presented in separate blocks o f trials. Signal similarity was varied within blocks in an unpredictable manner so that speed-accuracy criteria could not be adjusted. Response signals were horizontal lines of 2 cm length; their midpoints were in distances of 0.3, 0.6, 1.0, and 1.5 cm from the display midline. The response to the left signal was with the left hand and to the right signal with the right hand.
Apparatus. Subjects grasped two horizontal handles which had a lateral separation o f 14.5 cm, stretched their index fingers and placed them on two contact plates (1 x l cm). The height of the handles could be adjusted to accommodate different hand sizes. For a tapping response the index finger had to be lifted by about 3 cm and lowered again. The height o f the movement was controlled b y a photoelectric make-and-break. In performing an alternating response, the finger had to be m o v e d across a barrier 1 cm in height to a second contact plate in a lateral distance of 3 cm, and back again. The initial direction o f the movement was away from the median plane. The warning signal was a tone (1000 Hz, 60 dBA) presented via loudspeaker. The horizontal lines 2 cm in length that were used as response signals were presented on an oscilloscope screen in front of which a mask was placed with a window of 6 cm width and 2 cm height. Behind the oscilloscope a video monitor was located that was used to instruct movements for each block of trials and to present knowledge o f results. Design and procedure. Each subject participated in a practice session and four test sessions. In each session four blocks of 104 trials were presented; the first eight trials were considered as warming-up trials. Breaks between blocks lasted about 3 min. The sequence of choice conditions was varied across subjects according to a digram-balanced latin square. For any single subject the sequence was the same in each session. At the start of a block of trials the movements assigned to the two hands were indicated on the video monitor and remained visible throughout the block. The sequence of response signals was r a n d o m with the restriction that each combination of signal similarity and hand was presented 12 times in the 96 test trials of a block. A single trial began when both index fingers were placed on the appropriate contact plates. After 1 s the auditory warning signal was presented for 1.5 s; it was replaced by one of the response signals. The response signal remained on until the correct response had been executed. A period of 1 s followed, during which KR was presented if one of the following errors had occurred, KR indicating the nature of the error: 1. Anticipatory response: A response was initiated before presentation of the response signal. These trials were repeated immediately. 2. Choice error: The response was initiated with the wrong hand. 3. Execution error: A tapping response was of insufficient height, or with an alternating response the second contact plate was not reached. Execution errors as well as choice errors had to be corrected before the sequence of trials was continued. 4. Errors o f coactivation: During execution of the correct movement a movement with the other hand was initiated.
Dependent variables. Means and standard deviations :of reaction times were computed for each subject separately for each combination o f signal similarity, relationship between responses, response (tapping or alternating), and hand. Trials on which an error occurred or on which RT exceeded 1500 ms or movement time 1200 ms were discarded.
95 Results
Errors. The propOrtions of trials discarded because of excessively long RTs and movement times were 0.13% and 0.17%, respectively. Errors of coactivation could not be analyzed due to their very low frequency of 0.05%. Execution errors are more frequent, and, as indicated by a Friedman test, X2(3) = 10.9, P < 0.05, their frequency increases with increasing signal similarity (0.91%, 1.06%, 1.17%, and 1.64%). Choice error frequencies as a function of signal similarity and the relationship between responses are presented in Table 1. For each subject, separately for conditions with same and different responses, an orthogonal polynomial of third order (Steel & Torrie, 1960, pp. 341-343) was fitted to the data. For both conditions the first-, second-, and third-order coefficients are significantly different from zero, as indicated by Wilcoxon signed-rank tests. Thus, the nonlinear increase of choice error frequency with signal similarity is reliable. Comparisons between conditions (Wilcoxon signed-rank tests) are significant for zero-order and first-order coefficients: In conditions with same responses, choice-error frequency is larger and it shows greater increases with signal similarity. Mean RT. Mean RT is presented in Figure 3 (left half). The data were analyzed by means of a four-way mixed effects ANOVA with the factors signal-similarity, relationship between responses, response (tapping or alternating), and hand. Signal similarity was treated as a random factor. As is evident from Figure 3, RT increases with increasing signal similarity, that is, with decreasing distance of the stimuli from the midline, F(3,45)= 129.1, P < 0.01, and RT is faster for conditions with same responses than for those with different responses, F' (1,8)=32.2, P
