The Momentum of Compliance by John Nevin (1996) PDF

JOURNAL OF APPLIED BEHAVIOR ANALYSIS 1996, 29, 535–547 NUMBER 4 (WINTER 1996) THE MOMENTUM OF COMPLIANCE JOHN A. NEVIN UNIVERSITY OF NEW HAMPSHIRE...

JOURNAL OF APPLIED BEHAVIOR ANALYSIS 1996, 29, 535–547 NUMBER 4 (WINTER 1996) THE MOMENTUM OF COMPLIANCE JOHN A. NEVIN UNIVERSITY OF NEW HAMPSHIRE Compliance with demanding requests that are normally ineffective may be increased by presenting a series of easy or high-probability (high-p) requests before the more demand- ing requests. Mace and his colleagues have discussed the effectiveness of the high-p pro- cedure in relation to behavioral momentum—the tendency for behavior, once initiated and reinforced, to persist in the face of a challenge. The high-p procedure differs in several ways from that employed in laboratory research on momentum, and the methods and findings of basic research may not be relevant to applied work on compliance. This article reviews some laboratory procedures used in research on behavioral momentum, summarizes the major findings of that research, and discusses its relevance to the high-p procedure and its outcomes. Increased compliance with demanding requests following the high-p procedure can be understood in relation to the procedures and findings of basic research, but some questions arise in the process of translating research into appli- cation via the metaphor of momentum. These questions suggest some new directions for both experimental and applied behavior analysis. DESCRIPTORS: behavioral momentum, response rate, resistance to change, com- pliance, high-p procedure The metaphor of behavioral momentum that influence response rate and its persis- gives us a way to talk about two independent tence when those conditions are altered. dimensions of behavior that are of immedi- The goals of applied behavior analysis in- ate concern to applied behavior analysis: the clude the establishment of desirable, adap- rate of responding that is established and tive behavior through interventions that also maintained by the contingencies of rein- insure the persistence of that behavior when forcement, and its resistance to change when the intervention ends. Persistence requires responding is challenged or disrupted in that the behavior in question be sufficiently some way. The metaphor identifies these two resistant to change so that it continues dur- aspects of behavior with the velocity and ing the transition from treatment contingen- mass of a moving body, respectively. The cies to the natural contingencies of everyday product of the velocity-like and mass-like di- life. In terms of the momentum metaphor, mensions of behavior is behavioral momen- a successful intervention endows the behav- tum, a compound dependent variable that ior in question with a high level of momen- captures the outcome of training conditions tum. For example, an intervention designed to establish compliance with requests is suc- This paper was prepared while the author was an cessful if compliance occurs rapidly and re- Erskine Visiting Professor at the University of Canter- bury. I thank the University of Canterbury for its hos- liably during training (high velocity) and pitality and support, and especially Anthony McLean persists effectively, after explicit training has of the Psychology Department for many stimulating been discontinued, in the classroom, work- discussions and comments on a draft of this paper. place, and other social settings in which The treatment of differential reinforcement of low rate in relation to resistance to change and the character- compliance is appropriate (high mass). ization of the velocity of noncompliance are based in However, if compliance deteriorated rapidly part on his insights. when the intervention ended (low mass), we Address correspondence to John A. Nevin, RR#2, Box 162, Vineyard Haven, Massachusetts 02568 would not be fully satisfied with the out- (E-mail: [email protected]). come regardless of the rate of compliance 535 536 JOHN A. NEVIN during the intervention. Conversely, if com- amount of prefeeding or duration of extinc- pliance occurred only infrequently during tion sessions), research has concentrated on intervention (low velocity), we would not re- resistance to change in a given stimulus sit- gard it as firmly established in the person’s uation relative to that in one or more other repertoire even if that low rate also occurred situations involving different reinforcement outside the intervention conditions. This lat- contingencies. ter observation might suggest that noncom- A particularly convenient experimental pliance was highly resistant to change, per- paradigm for evaluating the resistance to haps because of an extensive history of re- change of one discriminated operant relative inforcement by escape from task demands. to another is a multiple schedule of rein- The therapist’s problem is to overcome that forcement, in which the experimenter pre- history with interventions that establish a sents two (or more) distinctive stimuli suc- high rate of compliance during treatment cessively, in regular or irregular alternation, and that make compliance likely to persist for predetermined durations. Different con- when treatment ends—in brief, to maximize tingencies or schedules of reinforcement for the momentum of compliance. a designated response (or responses) are ar- This article begins by reviewing some lab- ranged in the presence of these stimuli to oratory research on behavioral momentum, define two (or more) discriminated operants, conducted for the most part with pigeons as commonly termed the components of the subjects, and summarizes its main findings, multiple schedule. The components may be including their generality to people. It then separated by time-out periods to minimize discusses a procedure for establishing com- interaction between them. The component pliance in clinical settings that was devel- performances are trained until response rates oped by Mace et al. (1988), based in part appear to be stable to establish a reliable on an extension of the momentum meta- baseline, and then their relative resistance is phor. Known as the high-probability (high- evaluated by disrupting asymptotic perfor- p) procedure, it differs from basic research mance in some way that applies equally to on momentum in several ways, but its effec- both components—for example, by prefeed- tiveness can be understood within the con- ing (giving access to food in the home cage text of that research. shortly before an experimental session). The disrupter is usually arranged for a brief pe- riod (one or a few sessions) to minimize A RESEARCH REVIEW long-term effects of interaction between the Methods and Measures disrupter and the baseline conditions of re- First, it is important to understand that inforcement. Resistance to change is mea- momentum is a property of a discriminated sured most directly by comparing response operant—a three-term unit comprised of an rate under disruption with the immediately antecedent or current stimulus situation, a preceding baseline response rate, separately specified response class, and the contingen- for each component. Equivalently, it may be cies of reinforcement in that situation (Skin- estimated from the slope of a function relat- ner, 1969). Interest focuses on the asymp- ing response rate under disruption, on a log- totic response rate and the resistance to arithmic scale, to the value of the disrupter. change of that response rate within that The component performance that exhibits stimulus situation. Because the absolute val- the smaller change relative to baseline, or the ue of resistance to change depends on the shallower slope, is judged to be the more nature and value of the disrupter (e.g., resistant to change. Because comparisons are  THE MOMENTUM OF COMPLIANCE 537 made within subjects and sessions, they are usually quite reliable. An Experimental Example Nevin, Tota, Torquato, and Shull (1990, Experiment 2) arranged a three-component multiple schedule that illustrates several of the major findings of research on behavioral momentum. They employed food-deprived pigeons as subjects in a two-key chamber. In one component (designated Component C in their article and signaled by lighting both keys white), a standard variable-interval (VI) 60-s schedule provided 60 food reinforcers per hour of time in that component for right-key pecks; left-key pecks were not re- inforced. A second component (B, both keys lighted red) provided 15 reinforcers per hour for right-key pecks; again, left-key pecks were not reinforced. Thus, comparisons of baseline response rate and resistance to change for responding on the right key in Components B and C would evaluate the effects of different reinforcer rates for that response. A third component (A, both keys Figure 1. The three-component multiple-schedule lighted green) arranged concurrent VI VI paradigm employed in Experiment 2 of Nevin et al. schedules that provided 15 reinforcers per (1990). hour for right-key pecks as in Component B and 45 reinforcers per hour for left-key pecks, providing a total of 60 reinforcers per before a session, and by extinction (i.e., ter- hour as in Component C. Thus, compari- mination of all reinforcers), with baseline re- sons of baseline response rate and resistance covery between disruptions. For all 3 sub- to change for responding on the right key in jects, right-key response rates in baseline Components A and B would evaluate the were high in Component C, slightly lower effects of alternative reinforcement for the in Component B, and substantially lower in competing left-key response in Component Component A, reflecting the ordering of ab- A, and similar comparisons for Components solute reinforcer rate (60 per hour in C vs. A and C would evaluate the effects of the 15 per hour in B) and relative reinforcer rate distribution of reinforcers across keys with a (1.0 in B vs..25 in A) within components. constant total. Components alternated irreg- However, right-key responding in Compo- ularly with a time-out period between them. nent A was substantially more resistant to The paradigm is illustrated in Figure 1. change than in Component B. Likewise, After response rates had stabilized, base- right-key responding in Component C was line performances were disrupted by allow- more resistant than in Component B and ing satiation in a long continuous session, was similar to that in Component A. These by prefeeding in the home cage immediately results are illustrated for extinction in Figure 538 JOHN A. NEVIN 2. Note especially that right-key response rate in Component B started above that in Component A and fell below it as extinction progressed. This pattern of results held for all birds and all three resistance tests. The C-B comparison shows that resis- tance to change of right-key responding was directly related to the reinforcer rate for that response signaled by the component stimuli, consistent with a number of previous studies (see Nevin, 1992b, for review). However, the B-A and C-A comparisons suggest that re- sistance to change was directly related to the total reinforcer rate signaled by the compo- nent stimuli, independently of whether all reinforcers were contingent on the right-key response and independently of its baseline rate. Similar results were reported by Nevin et al. (1990, Experiment 1) using additional noncontingent reinforcers in one component rather than reinforcers that were explicitly contingent on a second alternative response as in Component A of Experiment 2. Nevin et al. (1990) concluded that the stimulus– reinforcer relation was the critical determiner of resistance to change. An important im- plication for applied work is that although alternative reinforcers (e.g., left-key reinforc- ers in Component A) reduce the rate of a target response, they also increase the resis- tance to change of that response rate because they are presented in the same stimulus sit- uation (see discussion by Mace et al., 1990). The Relativity of the Stimulus–Reinforcer Relation The specification of the stimulus–rein- forcer relation was refined by Nevin (1992a) in an experiment that arranged a constant reinforcer rate in one component of a two- component multiple schedule while the re- inforcer rate in the alternated component Figure 2. The course of responding on the right was varied across successive conditions, with key in each of the three components of Experiment 2 pigeons as subjects. Resistance to prefeeding of Nevin et al. (1990) during consecutive 1-hr blocks of extinction. Right-key response rates in the baseline and resistance to extinction in the constant session immediately preceding extinction are shown component were inversely related to rein- over 0, and the response-rate scale is logarithmic. Adapted from Nevin et al. (1990).  THE MOMENTUM OF COMPLIANCE 539 forcer rate in the alternated component. of reinforcement obtained by the target re- Nevin concluded that resistance to change sponse class. depended on the relative rather than the ab- 2. The resistance to change of a discrim- solute reinforcer rate in the presence of a inated operant maintained by a given rate of stimulus, and Nevin (1992b) showed that a reinforcement increases if additional rein- contingency ratio characterizing the reinforcer forcers are allocated to an alternative con- rate in a component relative to the overall current response, or are provided indepen- average reinforcer rate in the experimental dently of responding. context accounted well for all of the resis- 3. The resistance to change of a discrim- tance data obtained in his laboratory. For inated operant maintained by a given rate of applied work, the implication is that resis- reinforcement is inversely related to the rate tance to change in the therapy setting de- of reinforcement obtained by other, succes- pends on the reinforcer rate outside that set- sive discriminated operants. ting as well as within it. These three conclusions are consistent with determination of resistance to change Generality to Other Species by stimulus–reinforcer relations. Evidence Pigeons are notorious for pecking at light- reviewed by Nevin (1992b) suggests that ed keys that are paired with food regardless these conclusions hold for reinforcer mag- of the response–reinforcer contingency, as nitude as well as reinforcer rate. His review shown in research on autoshaping (see also suggests that: 4. The resistance to change of a discrim- Schwartz & Gamzu, 1977, for review). inated operant is independent of the steady- Thus, it is important both for interpretation state baseline rate of the target response. and for applied analysis that pigeon data be Taken together, these four conclusions replicable with humans who are engaged in comprise what has come to be known as be- arbitrary tasks. Experiment 1 by Nevin et al. havioral momentum theory. In fact, they are (1990) has been replicated by Mace et al. not theoretical statements but are generali- (1990) with adults with mental retardation zations from experimental data, and as such in a group home engaged in a sorting task, are perpetually open to revision. Applied re- and by Cohen (1996) with college students searchers may predict or interpret the effects engaged in a typing task. Experiment 2 has of various interventions in relation to these been replicated with rats by Mauro and conclusions, but should be careful to equate Mace (1996), with visual but not with au- the relevant variables in applied settings with ditory stimuli. It has not yet been repeated those that have been identified in basic re- with humans, to my knowledge, but the search. A more rigorous and quantitative ex- present status of cross-species replication pression of these conclusions in relation to suggests that the results reported by Nevin the metaphor of behavioral momentum is et al. (1990) do not depend on a species- presented in the Appendix. specific propensity to direct responses at sig- nals paired with reinforcers. Some Qualifications Harper and McLean (1992) challenged Summary and Conclusions the generality of the foregoing conclusions The following conclusions appear to be in an experiment that varied the reinforcer quite general: rate equally in two multiple-schedule com- 1. The resistance to change of a discrim- ponents with different reinforcer magni- inated operant depends directly on the rate tudes. They found that variations in rein- 540 JOHN A. NEVIN forcer rate produced equal proportional ing (not between) components (an internal changes relative to baseline in the two com- disrupter) there was no systematic difference ponents, a result that contrasted with their in the resistance of component performances own finding (and several others; e.g., Nevin, with different reinforcer rates. These find- 1974, Experiment 3) that responding was ings, which held for both rats and pigeons, more resistant to change in the component suggest that the relation between resistance with the larger reinforcer when free food was to change and baseline reinforcer rate may given during time-out periods between com- depend on the use of two or more signaled ponents. Accordingly, they distinguished be- schedules that alternate within sessions. tween external disrupters such as intercom- However, some single-schedule results exhib- ponent food or prefeeding that leave the it a positive relation between resistance to component contingencies intact, and inter- change and reinforcer rate (for review, see nal disrupters such as schedule changes that Nevin, 1979, 1988), and the critical factors alter those contingencies, where the latter that distinguish single-schedule studies that may not reliably confirm Conclusion 1. confirm and disconfirm the positive relation However, a change in the schedule for a remain to be identified. large reinforcer may be a greater disrupter Finally, different contingencies between than a comparable change for a small rein- responding and reinforcement in two com- forcer, as shown by Harper (1996). This dif- ponents that establish different response ference might counteract the expected dif- rates may influence resistance to change even ference in resistance to change. Moreover, when stimulus–reinforcer relations are the the usual effects of extinction (an internal same. For example, Lattal (1989) arranged a disrupter) on multiple-schedule perfor- tandem FR VI schedule in one component mances are entirely in accord with those of and a tandem differential-reinforcement-of- external disruptors (e.g., Shettleworth & low-rate (DRL) VI schedule in a second Nevin, 1965). Complete characterization and scaling of effective disrupters remain to component with pigeons as subjects. He be achieved. found that the low-rate tandem DRL per- Cohen, Riley, and Weigle (1993) also formance was more resistant to disruption challenged the generality of the foregoing by free food between components than was conclusions by showing that resistance to the high-rate tandem FR performance, rela- change does not depend on the reinforcer tive to their baselines, even though reinforcer rate for single-schedule performances that rates were equated. Lattal’s findings suggest were trained and maintained for a number that different sorts of contingencies may es- of consecutive sessions. For example, they tablish behavioral classes that are differen- found that resistance to prefeeding on fixed- tially susceptible to disruption. For example, ratio (FR) 40 did not differ from that on FR disruption of DRL performance may lower 160, regardless of the order of exposure to the tendency to refrain from responding im- these single schedules. This result is contrary mediately after a response as well as the over- to the expectation that resistance to change all tendency to engage in the DRL perfor- is positively related to reinforcer rate, which mance itself, resulting in a smaller net re- was higher for the FR 40 performance. duction in responding. However, when com- When they arranged the same schedules as parable response classes are established in components of a multiple schedule, however, both components, as in multiple VI VI they confirmed Conclusion 1, with one ex- schedules, there is no correlation between re- ception: When free food was provided dur- sponse rate and resistance to change.  THE MOMENTUM OF COMPLIANCE 541 THE HIGH-P PROCEDURE AND compliance using this procedure with chil- COMPLIANCE WITH REQUESTS dren who engaged in self-injurious behavior (SIB) unless it was coupled with extinction An Example of the Procedure and Results of SIB, possibly because SIB disrupted com- Mace et al. (1988) invoked the metaphor pliance during the high-p sequence. Con- of behavioral momentum in relation to a versely, the high-p procedure may not be method for increasing compliance with re- necessary to enhance compliance. Carr, quests in adults with mental retardation who Newsom, and Binkoff (1976) observed a lived in a group home. Their procedure was substantial improvement in compliance (and designed to enhance compliance with re- a reduction of SIB, which was their principal quests such as ‘‘clear the table’’ or ‘‘take a concern) when they told amusing stories to shower,’’ which were termed low-p requests a child with mental retardation in the com- because the clients rarely complied with pliance-request setting. However, the high-p them. To enhance low-p compliance, Mace procedure has been used successfully with et al. presented a series of three high-p re- different clients in a variety of settings (e.g., quests with which the clients readily com- Davis, Brady, Hamilton, McEvoy, & Wil- plied and appeared to enjoy doing, such as liams, 1994; Davis, Brady, Williams, & ‘‘give me five’’ or ‘‘show me your pipe,’’ and Hamilton, 1992; Ducharme & Worling, then presented a low-p request. When the 1994), and it is unquestionably a valuable low-p request followed shortly after the high- addition to the repertoire of behavioral in- p series, there was a striking increase in the terventions for addressing problems of non- probability of or a decrease in the latency to compliance. The issue here is the interpre- low-p compliance. tation of the high-p procedure in relation to Compliance is a discriminated operant, in behavioral momentum. which the immediate stimulus is a request, the response class is an action that conforms Some Procedural Issues to the request, and the consequence is at The high-p procedure differs in a number least intermittent social reinforcement, of ways from the procedures that are em- which is correlated with the overall stimulus ployed in basic research. First, although situation in which compliance occurs. Ac- there is a well-defined stimulus situation— cordingly, the findings of research on the the physical setting and the presence of the momentum of discriminated operant behav- therapist—there is no well-defined alternat- ior should be relevant. In the terms of the ed situation with different conditions of re- momentum metaphor, the high-p series may inforcement that is analogous to an alter- be viewed as establishing a high velocity of nated component of a multiple schedule. the response class ‘‘compliance.’’ At the same Second, there is no steady-state baseline re- time, reinforcers for compliance during the sponse rate against which to evaluate the ef- high-p sequence, whether explicit or implic- fect of a disrupter, for two reasons: (a) The it, increase the mass-like aspect of compli- compliance response class is not a free op- ance. The resulting momentum serves to erant, but is prompted by a discrete request make compliance more resistant to the chal- and indeed is defined by correspondence be- lenge of a low-p request. tween the request and the action; and (b) The high-p procedure may not always be the high-p sequence is too brief to establish sufficient to enhance compliance. For ex- a reliable baseline. Third, the disrupter in- ample, Zarcone, Iwata, Mazaleski, and volves the presentation of a more demanding Smith (1994) failed to obtain enhanced request rather than an orthogonal variable 542 JOHN A. NEVIN that is independent of the contingencies that response rate in each component of a mul- maintain compliance. Collectively, these dif- tiple schedule and found similar changes in ferences may seem to rule out the applica- these measures when responding was dis- tion of principles based on the disruption of rupted. Elsmore (1971) showed that the free-operant behavior in multiple schedules. probability of completing a fixed ratio with- I will consider these differences in order. in a brief trial period decreased to a lesser The single-stimulus situation. As noted pre- extent on trials that signaled a high proba- viously, Cohen et al. (1993) showed that al- bility of reinforcement than on trials that ternated exposure to two or more schedule signaled a low probability of reinforcement components that involve different schedules when the ratio value was abruptly increased. of reinforcement within a fairly short period, This result parallels the usual finding that such as an experimental session, may be nec- resistance to change is directly related to re- essary for demonstrating a positive relation inforcer rate in a component, suggesting that between resistance to change and rate of re- probability of responding in a discrete sig- inforcement. Thus, there may not be a pos- naled period may be functionally similar to itive relation between low-p compliance and response rate. Thus, there is no reason to the contingencies arranged by the high-p question the relevance of momentum re- procedure within the single-stimulus situa- search on the basis of the measures used in tion of a therapy session. However, it is sure- the high-p procedure. Moreover, Elsmore’s ly the case that a client experiences other disrupter (an abrupt increase in the response stimulus situations and their correlated re- requirement) may be analogous to a low-p inforcement contingencies for compliance, request. or noncompliance, or unrelated behavior, in The need for a stable baseline. Basic re- the course of daily life. These situations and search on behavioral momentum has rou- the uncontrolled or extraneous reinforcers tinely established stable baseline response available within them constitute the condi- rates before evaluating resistance to change. tions that alternate successively with therapy In this way, it combines the interest in sessions. The additional reinforcers arranged steady-state performance that characterizes during therapy sessions by the high-p pro- modern research on operant behavior with a cedure could be effective in differentially en- more traditional emphasis on behavior in hancing the persistence of compliance with- transition during acquisition or extinction. in that setting, construed as one component Although a steady-state baseline is necessary of a client’s life. for quantitative analyses (see the Appendix), Response measures. Because compliance is it is possible to make ordinal comparisons of by definition a response to a request, its rate resistance to change without a stable baseline of occurrence cannot exceed the rate of re- response rate. For example, Furomoto quests. Accordingly, its velocity-like aspect (1971) explored the effects of number of re- must be evaluated by its latency from the inforcers on resistance to extinction in a request, or its probability of occurrence parametric between-group experiment with within a brief period after a request. By con- pigeons as subjects. One of her groups re- trast, virtually all research on resistance to ceived a reinforcer after each of three con- change has employed the rate of a free op- secutive responses, and a pretraining control erant as its dependent variable. I am aware group received none. She found that the of only two published exceptions. Fath, three-reinforcer group made about seven Fields, Malott, and Grossett (1983) mea- times more responses than the zero-reinforc- sured both latency to the first response and er control group during a subsequent period  THE MOMENTUM OF COMPLIANCE 543 of extinction (actually, a continuation of about the separate determiners of the veloc- nonreinforcement for the control group). ity-like and mass-like aspects of behavior. This comparison did not require a stable First, if the high-p sequence increases the preextinction baseline, which in any case was mass of compliance, it presumably does so precluded by the brevity of training. Anal- through the correlation of reinforcers with ogously, the effects of prompting and rein- the stimulus situation. But as described pre- forcing compliance with three high-p re- viously, reinforcement for one class of be- quests on low-p compliance can be com- havior increases the mass of all behavior that pared with low-p compliance in the absence is maintained by the same reinforcer within of the high-p series without establishing a the situation, including competing responses stable high-p baseline. (as in Component A of Experiment 2 by The nature of the disrupter. The majority Nevin et al., 1990). Thus, paradoxically, re- of momentum research has employed dis- inforcing high-p compliance may also in- rupters such as prefeeding or free food dur- crease the mass of noncompliance—whatever ing periods between components that leave the client normally does in response to a the baseline contingencies unchanged. The low-p request in the same situation. At one high-p procedure differs in that its disrup- level, this is not a problem: Because the ter—a low-p request—is simply a more de- high-p sequence is structured to guarantee manding instance of compliance that has al- that noncompliance does not occur, its local ready been made probable by the high-p se- velocity within the high-p situation is zero, quence. In this sense, it may be more like and its momentum is therefore zero regard- Harper and McLean’s (1992) schedule less of its mass. However, if noncompliance change, which they characterized as an in- does occur in the therapy situation, there is ternal disrupter and, as noted previously, had a problem of interpretation. Let’s assume no differential effects on component perfor- that compliance is positively reinforced, mances maintained by different reinforcer whereas noncompliance is likely to be neg- magnitudes. However, as described above, atively reinforced (e.g., by escape from task Elsmore (1971) employed a demanding ratio demands). The question, then, is whether as an internal disrupter and obtained results positive reinforcement of one class of behav- ior also increases the mass of an incompati- that were entirely in accord with expecta- ble class that is maintained by negative re- tions based on momentum research with ex- inforcement. No research, to my knowledge, ternal disrupters. In summary, the proce- has addressed this question. If future re- dures and measures of momentum research search suggests that both positively and neg- can be interpreted as relevant to the effects atively reinforced response classes gain sim- of the high-p procedure on low-p compli- ilarly in mass when additional reinforcers are ance. given for the former, a momentum account would have to argue that compliance wins Some Conceptual Issues out over noncompliance when a low-p re- When low-p compliance occurs reliably quest is presented after a high-p sequence after the high-p sequence, is this the result because the high-p sequence selectively in- of the velocity of compliance, the mass of creases the velocity of compliance. Future compliance, or both (momentum)? This applications of the high-p sequence would may seem like a scholastic question concern- therefore concentrate on response–reinforcer ing angels on pinheads, but it is important contingencies that maximize the velocity of because of what we know (and don’t know) compliance. However, if it turns out that 544 JOHN A. NEVIN positive reinforcers have a selective effect on Third, Mace et al. (1988, Experiment 3) the mass of positively reinforced behavior, did not observe an enhancement in low-p low-p compliance would be construed as ev- compliance when the interval between the idence of the mass of compliance as well as high-p series and the low-p request was in- its velocity, and future applications would creased from 5 s to 20 s. How might a mo- emphasize situation–reinforcer relations. mentum account interpret this transience of Second, the high-p series may not be nec- low-p compliance? One approach is to con- essary for increasing low-p compliance. Al- ceptualize the delay between the high-p se- though Mace et al. (1988, Experiments 2 ries and the low-p request as an independent and 4) conducted attention controls that in- disrupter, in addition to the disruptive chal- cluded the presentation of pleasant com- lenge posed by the low-p request itself. Per- ments with no evidence of enhanced low-p haps the delay after the high-p series allows compliance, Carr et al. (1976) improved other competing behavior to intervene and compliance by telling amusing stories in the disrupt compliance; but whatever the inter- therapy setting, and Kennedy, Itkonen, and pretation of the delay effect, it should be Lindquist (1995) obtained comparable levels reduced by any procedure that increases the of low-p compliance by presenting the high- mass of compliance. For example, response- p series and by making pleasant comments independent positive reinforcers could be in separate conditions. These findings ap- provided in addition to the high-p series re- pear to be problematic for a momentum ac- inforcers. If the mass-like aspect of compli- count because there is no obvious source of ance is enhanced by such reinforcers, low-p velocity in the absence of the high-p se- compliance should be more resistant to dis- quence. However, they may be understood ruption and persist over longer delays. To in relation to the foregoing argument. If make more direct contact with the multiple- amusing stories and pleasant comments are schedule paradigm, this sort of analysis construed as response-independent positive might profitably be conducted in two phys- reinforcers, they should increase the mass of ically different settings with two different compliance in much the same way as the therapists, one providing response-indepen- high-p sequence reinforcers do. In both dent reinforcers in conjunction with the studies, compliance had a history of rein- high-p series and the other using the high-p forcement in the therapy setting before series alone. Resistance of low-p compliance amusing stories or pleasant comments were to delay after the high-p series could then be introduced. Therefore, the mass of compli- compared between settings. ance with low-p requests might be enhanced by response-independent positive reinforc- ers, leading to the observed result. (Note CONCLUSION that this interpretation works only if such In summary, the effectiveness of the high- reinforcers did not equally increase the mass p procedure and its variants can be under- of noncompliance, as argued above.) An op- stood and, perhaps, advanced within the timal method for enhancing low-p compli- framework of the momentum metaphor ance might present explicit response-contin- from which it developed. However, translat- gent positive reinforcers in the high-p series ing the terms of the metaphor into the high- to establish the velocity and mass of com- p procedure, or indeed any other applica- pliance, and also provide response-indepen- tion, encounters some uncertainties and en- dent reinforcers in the treatment situation to tails a fair amount of speculation; thus, al- enhance its mass. ternative accounts are surely possible. Basic  THE MOMENTUM OF COMPLIANCE 545 research can address these uncertainties, but the home. Journal of Applied Behavior Analysis, 27, 639–647. the direct application of laboratory findings Elsmore, T. F. (1971). Effects of response effort on to clinical work with people whose histories discrimination performance. Psychological Record, and environments are complex and uncon- 21, 17–24. trolled will always involve a certain amount Fath, S. J., Fields, L., Malott, M. K., & Grossett, D. (1983). Response rate, latency, and resistance to of faith. On the basis of research on resis- change. Journal of the Experimental Analysis of Be- tance to change, I have considerable faith in havior, 39, 267–274. the power of stimulus–reinforcer relations to Furomoto, L. (1971). Extinction in the pigeon after continuous reinforcement: Effect of number of re- influence the persistence of discriminated inforced responses. Psychological Reports, 28, 331– operant behavior in a wide variety of set- 338. tings. Harper, D. N. (1996). Response-independent food My faith is based to some extent on the delivery and behavioral resistance to change. Jour- nal of the Experimental Analysis of Behavior, 65, appeal of the metaphor of behavioral mo- 549–560. mentum, which continues to guide much of Harper, D. N., & McLean, A. P. (1992). Resistance my research. Metaphors can be dangerous if to change and the law of effect. Journal of the Experimental Analysis of Behavior, 57, 317–337. they are extrapolated beyond the domain in Herrnstein, R. J. (1970). On the law of effect. Journal which their terms have unambigious refer- of the Experimental Analysis of Behavior, 13, 243– ents, but they can also be helpful in com- 266. municating scientific ideas. Most important, Kennedy, C. H., Itkonen, T., & Lindquist, K. (1995). Comparing interspersed requests and social com- they may foster innovation because they can ments as antecedents for increasing student com- interact unpredictably with the repertoires of pliance. Journal of Applied Behavior Analysis, 28, scientists, as exemplified by the development 97–98. Lattal, K. A. (1989). Contingencies on response rate of the high-p procedure. and resistance to change. Learning and Motivation, 20, 191–203. Mace, F. C., Hock, M. L., Lalli, J. S., West, B. J., REFERENCES Belfiore, P., Pinter, E., & Brown, D. K. (1988). Behavioral momentum in the treatment of non- Carr, E. G., Newsom, C. D., & Binkoff, J. A. (1976). Stimulus control of self-destructive behavior in a compliance. 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Behav- (Eds.), Advances in analysis of behaviour: Vol. 1. ioral momentum and stimulus fading in the ac- Reinforcement and the organization of behavior (pp. quisition and maintenance of child compliance in 117–158). Chichester, England: Wiley. 546 JOHN A. NEVIN Nevin, J. A. (1984). Pavlovian determiners of behav- Staddon (Eds.), Handbook of operant behavior (pp ioral momentum. Animal Learning & Behavior, 53–97). New York: Prentice Hall. 12, 363–370. Shettleworth, S., & Nevin, J. A. (1965). Relative rate Nevin, J. A. (1988). Behavioral momentum and the of response and relative magnitude of reinforce- partial reinforcement effect. Psychological Bulletin, ment in multiple schedules. Journal of the Exper- 103, 44–56. imental Analysis of Behavior, 8, 199–202. Nevin, J. A. (1992a). Behavioral contrast and behav- Skinner, B. F. (1969). Contingencies of reinforcement. ioral momentum. Journal of Experimental Psychol- New York: Appleton-Century-Crofts. ogy: Animal Behavior Processes, 18, 126–133. Tota-Faucette, M. (1991). Alternative reinforcement Nevin, J. A. (1992b). An integrative model for the and resistance to change. Unpublished doctoral dis- study of behavioral momentum. Journal of the Ex- sertation, University of North Carolina at Greens- perimental Analysis of Behavior, 57, 301–316. boro. Nevin, J. A., Mandell, C., & Atak, J. R. (1983). The Williams, B. A., & Wixted, J. T. (1986). An equation analysis of behavioral momentum. Journal of the for behavioral contrast. Journal of the Experimental Experimental Analysis of Behavior, 39, 49–59. Analysis of Behavior, 45, 47–62. Nevin, J. A., Smith, L. D., & Roberts, J. (1987). Zarcone, J. R., Iwata, B. A., Mazaleski, J. L., & Smith, Does contingent reinforcement strengthen oper- R. G. (1994). Momentum and extinction effects ant behavior? Journal of the Experimental Analysis on self-injurious escape behavior and noncompli- of Behavior, 48, 17–33. ance. Journal of Applied Behavior Analysis, 27, Nevin, J. A., Tota, M. E., Torquato, R. D., & Shull, 649–658. R. L. (1990). Alternative reinforcement increases resistance to change: Pavlovian or operant contin- Received April 29, 1996 gencies? Journal of the Experimental Analysis of Be- Initial editorial decision June 19, 1996 havior, 53, 359–379. Revision received July 10, 1996 Schwartz, B., & Gamzu, E. (1977). Pavlovian control Final acceptance July 17, 1996 of operant behavior. In W. K. Honig & J. E. R. Action Editor, David P. Wacker APPENDIX The momentum metaphor links behavioral mass to resistance to change by invoking Newton’s second law, which states that the change in velocity of a moving body is inversely related to its mass when a given external force is imposed. More formally, Dv 5 f /m, (1) where Dv is the change in velocity (i.e., acceleration) over the period of force application, f is the imposed force, and m is the inertial mass of the body. For behavioral applications, Nevin, Mandell, and Atak (1983) proposed that Dv be expressed as the logarithm (base 10) of response rate during disruption (BX) relative to baseline response rate (BO): log(BX/BO) 5 f /m, (2) where f is the value of the disrupter and m is behavioral mass. When a given disrupter ( f ) is applied equally to Components 1 and 2 of a multiple schedule, Equation 2 is written separately for each and the resulting expressions are divided, giving log(BX1/BO1)/log(BX2/BO2) 5 m2/m1. (3) That is, the ratio of behavioral masses is inversely proportional to the ratio of the logarithms of responding under disruption relative to baseline in the two components. This computation gives a point estimate of the mass ratio, which may be unreliable. If the disrupter value is varied systematically over a series of tests or is defined by a series of consecutive sessions with a given disrupter (e.g., extinction), the ratio of behavioral masses may be estimated more reliably by calculating the slopes of functions that relate response rates under disruption to the value of the disrupter, and quantifying the mass ratio by the inverse slope ratio. Nevin (1992b) used the inverse-slope analysis to summarize results from a wide variety of procedures employing two- component multiple schedules, multiple chain schedules, and serial schedules that differed in reinforcer rate, magnitude, and contingency between the target response and the reinforcer, with disrupters including free reinforcers between components, signaled concurrent reinforcement, prefeeding, and extinction. He found that the ratio of masses was a power function of a contingency ratio characterizing reinforcer rate or magnitude in one component relative to that in another component, where each was expressed relative to the overall average reinforcer rate or magnitude in the experimental session. In effect, the contingency ratio quantifies the stimulus–reinforcer relation, which has been shown above to be a powerful determiner of resistance to change. Its value can be altered experimentally by changing the reinforcer rate in a target component, the reinforcer rate in an alternated component, or the length of time-out periods between components (which affects the overall average reinforcer rate for a session). Nevin (1992a) showed that these different ways of changing the contingency ratio had similar effects on mass ratios.  THE MOMENTUM OF COMPLIANCE 547 The foregoing material addresses the quantification and determiners of behavioral mass. We turn now to velocity, measured as baseline response rate in a multiple-schedule component. Baseline response rate in single schedules is de- scribed by Herrnstein’s (1970) well-known hyperbolic equa- tion: (4) B 5 kR/(R 1 RE), where B represents response rate, R represents reinforcer rate, RE represents the rate of extraneous reinforcers, and k rep- resents the asymptotic response rate as reinforcer rate increas- es indefinitely. Herrnstein (1970) modified the equation to account for interactions in multiple schedules: (5) BN 5 kRN/(RN 1 mRA 1 RE), where BN represents response rate in the target Component N, RN represents reinforcer rate in that component, and RA represents reinforcer rate in the alternated component; m, which ranges from 1.0 to 0, represents the degree of inter- action between components; and k and RE remain defined as above. Equation 5 provides an adequate account of re- sponse rate in many experiments, but it makes some incorrect predictions and has logical shortcomings. Williams and Wixt- ed (1986) proposed an equation that resolves these difficul- ties: (6) BN 5 sRN/(RN 1 pRN-1 1 f RN11)/(1 1 p 1 f ) 1 C, where BN is response rate and RN is reinforcer rate in the target Component N, RN-1 is the reinforcer rate in the pre- ceding component, and R is the reinforcer rate in the following component; p andN1f 1reflect the degree of interaction with the preceding and following components, respectively; C represents the inhibitory effects of all reinforcers in the situation; and s is a scaling constant. Equation 6 describes steady-state response rate in a variety of multiple-schedule procedures quite well. If f is greater than p, the equation also accounts for the fact that response rate is lower in the pres- ence of a component with a given reinforcer rate if it precedes a component with a richer schedule than if it precedes a component with a leaner schedule. Equations 4, 5, and 6 all predict that response rate main- tained by a rich schedule will be more resistant to change than that maintained by a lean schedule. This is because a given increase in RE or C, characterizing the disruptive effect of an external variable (force in the momentum metaphor), will have a relatively smaller impact on BN if RN is large than if it is small. This aspect of the equations for asymptotic response rate suggests that a single formulation, such as Equa- tion 6, may be able to describe resistance data as well as response rate, obviating the need for a separate formulation of the relation between behavioral mass and the stimulus– reinforcer contingency. However, these equations cannot han- dle some aspects of the Nevin et al. (1990) results (see their article for discussion), and they predict the opposite of some data on resistance to change. For example, Nevin (1992a) disconfirmed the predictions of Equations 4, 5, and 6 as extrapolated to resistance to change in a standard two-com- ponent multiple schedule when the reinforcer rate in the al- ternated component varied between conditions. In addition, Equation 6 predicts that both response rate and resistance to change will be greater in a target component with a given reinforcer rate that is preceded or followed by a leaner com- ponent schedule than in an identical target component that is preceded or followed by a richer component schedule. However, Nevin (1984) and Nevin, Smith, and Roberts (1987) found that resistance in a target component was great- er when it was followed by a richer component, and Tota- Faucette (1991) found that resistance was similarly enhanced regardless of whether the richer schedule preceded or fol- lowed the target component. The results of Nevin (1984), Nevin et al. (1987), and Tota-Faucette (1991) are consistent with the conclusion that behavioral mass depends directly on the stimulus–reinforcer contingency ratio, because their constant target components were embedded within a serial compound defined by a re- peating stimulus sequence that was correlated with a distinc- tive situational cue such as the location of a lighted key. Nevin (1992b; see also McLean, Campbell-Tie, & Nevin, 1996) argued that, for serial schedules, the contingency ratio is the joint product of the reinforcer rate in the target com- ponent, relative to the overall session average, and the rein- forcer rate in the serial compound within which the target component is embedded, again relative to the overall session average. Nevin (1992b) showed that when the resistance data of serial schedules were analyzed in this way, target-compo- nent mass ratios were related to contingency ratios by the same power function as for conventional two-component multiple schedules. Collectively, these analyses suggest that resistance to change in a target component is directly related to the rate of reinforcement obtained in a distinctive stimulus situation, regardless of whether those reinforcers are obtained during, before, or after the target component, and regardless of whether they are allocated to the target response, contin- gent on an alternative response, or noncontingent. The conclusion is that steady-state response rate is deter- mined by the rate of reinforcement for a target response, relative to all reinforcers in the experimental situation, as described by Equations 4, 5, 6, or related forms, whereas resistance to change is determined by the rate of reinforce- ment that is correlated with a target component, irrespective of its source and independent of response rate in that com- ponent, as described by a power function relating resistance to a contingency ratio that characterizes the stimulus–rein- forcer relation. The independence and separate determination of response rate and resistance to change parallel the inde- pendence and separate determination of velocity and mass in classical mechanics, which gave rise to the metaphor of be- havioral momentum.