Behavioural momentum theory (BMT) looks at how persistent a behaviour is in relation to its reinforcement history. The theory states that reinforcers increase the persistence of behaviour in the face of disrupters, distraction or discontinuation of reinforcement. The persistence of a target response is increased by alternative reinforcers that are presented in that situation regardless of whether they are contingent on that behaviour or, an alternative response. Nevin & Shahan (2011) base their equation and its derivatives on Newton’s second law of motion.
Newton’s 2nd Law states
When an external force is applied to an object in motion, the change in velocity is related directly to the magnitude of force and is related inversely to the object’s inertial mass. So, when a disrupter (x) is applied to an ongoing behaviour the decrease (or change in response rate ΔB) is directly related to the magnitude of the disrupter and inversely to the behavioural equivalent of mass (m).
Inertial mass is related inversely to the behavioural equivalent of mass. Just as inertial mass is independent of the velocity of a physical body in motion, the behavioural mass is independent of response rate. Here we outline the variables that affect the resistance to change. The metaphor of behavioural momentum in behavioural terms is derived from Newton’s following equation.
Newton's 2nd Law
F (force) = m (mass) x a (acceleration)
in its differential form, gives us the following (qualitative assertion of the resistance to change).
Where BMT can be represented by
ΔB response rate (this is the difference between the response rate in baseline compared to response rate during disruption)
x represents the value of the current disrupter (this is a negative sign to indicate disruptions decrease response rate)
m represents behavioural mass determined by the history of reinforcement (in steady state baseline and is assigned an r0.5 value).
Therefore, proportion of baseline response rate during disruption is an increasing function of r and a decreasing function of x and is represented as:
Which illustrates the effects of varying the magnitude of the disrupter (x) for the values of reinforcement rate in simple proportions to baseline.
The equation is from the Nevin & Shahan paper (2011). We have left out the use of logarithms which we felt complicated Newton’s 2nd law. We could not see the justification of using a logarithmic outcome to express a more linear relationship. There is a relationship between the quantity of the attempt to change behaviour and the predicted outcome and the mass equivalence is the counter effect of the resistance to change (mass equivalent).
In Graph Form
The slope depends on the rate of reinforcement and is steep when the rate of reinforcement is low and less so when the reinforcer rate is higher. The rate of decrease is greatest when r is small and least when r is large and this is the prediction of BMT.
The decrease in response, that is produced by a disrupter, is a function of the magnitude of the disrupter x and inversely functional to the reinforcement rate r prior to its disruption.
We can therefore predict that bigger disrupters decrease behaviour more but these are lessened by higher rates of reinforcement.
Alternative & Non-contingent Reinforcement (NCR) + Extinction
Strategies are often used when problem behaviour cannot be reduced by extinction. The case often being, that the behaviour could become worse or it is somehow impossible to withhold a reinforcer. In these cases, we will arrange an alternative reinforcement such as differential reinforcement of an alternative behaviour (DRA) and/or Non-contingent Reinforcement (NCR). NCR is technically an incorrect term which is used. However, it is popular and we are stuck with it. NCR as a term is technically incorrect because it implies that a reinforcer is delivered independent of a response & not contingent upon a response which is contradicting itself because it is independent of a contingency. A more correct term would be a Response Independent Schedule (RIS).
Some studies show that NCR has been linked with superstitious behaviour in humans. This, is defined as behaviour produced by Response Independent Schedules of reinforcement delivery, in which only an accidental relation exists between responses and delivery of reinforcers. However, if you are still providing an opportunity for an organism to access his reinforcer but it is not dependent on the original behaviour he is still being differentially reinforced. It was found that using Differential Reinforcement of Other behaviour (DRO) actually increased the strength of the target behaviour (the one put on reduction) due to an alternative other behaviour being reinforced (it strengthened the target behaviour as a by-product which made it more resistant to extinction). This forms the basis of the Premack Principle, which is beyond our scope in this article but forms the relational principle of reinforcement and is another application of momentum theory in which this law applies.
When using NCR & the reinforcement is happening at a high rate and not contingent upon the behaviour then you are in effect offering a DRO which will make the behaviour more resistant to extinction. The organism still has behavioural momentum. You might start to see behaviour chains, shaping or superstitious behaviours, develop in these cases but more importantly, you will have resistance to extinction.
Studies using NCR on a thick schedule and then going to a lean/extinction schedule predict that NCR provides an abolishing operation. Using a thick NCR then moving to an Extinction Schedule (EXT) gives much better results to decrease problem behaviour. This emerged when a schedule that went from lean to EXT rather than using EXT first and then NCR. The abolishing operation was found to be the factor to reduce the behaviour (Hagopian, Fisher 1994 & Iwata 2012).
The behaviour change actually occurs when a thick schedule of NCR is offered first to reduce the motivation for the behaviour. This means that the reinforcement is offered on a high rate (disruption of momentum in a contingency independent manner relating to the target behaviour and never when it occurs) and when the extinction phase is introduced, it shows very promising results for its use as a scheduling strategy for reduction in particularly challenging behaviours. In fact, Iwata et al 1994 reported 80-90% decrease in behaviour using alternative schedules alone. However, research on basic operant behaviour has found that if alternative reinforcement is used to reduce problem behaviour, the rates of responding become more resistant to interventions that include extinction. This is distinct from whether the contingencies are independent or contingent on a defined alternative response DRA. This has been found in many animals such as pigeons, rats and humans (Cohen, 96; Grimes & Shull 2001: Harper 1999, Sakagami, 2004, Shahan 2011).
The rate of target response decreases in the NCR condition but the reinforcers in the discriminative stimulus context or DRA condition work to increase the resistance to extinction. When DRA is used as a concurrent reinforcement for a defined alternative response rather than NCR it is found that DRA decreased rates of target behaviour. However, these rates of target behaviour were much more resistant to extinction. This falls in line with the BMT application because the overall rate of reinforcement was increased. Nevin et al, looked at post DRA extinction. He found that it was substantially greater during an intervention which used DRA. Although, it did decreased rates of problem behaviour, it increased resistance to extinction.
Studies by Mace et al 1990 & Parry-Crywys et al (2011) looked at the effects of alternative reinforcement and found that they had the same effects as disruption, but the effects using reinforcement on a target response are likely to persist as long as those reinforcers are present.
When using a DRA as a baseline, then applying EXT, it is found that there is a reversal in the extinction phase. This appears with disrupters & extinction as response rates rather than related to proportions of baseline (Nevin et al 90).
When problems behaviours are reduced by alternative reinforcement and then extinguished, the rate might be higher than if alternative reinforcement had not been arranged before extinction. This is clear in the DRA data of Mace et al 2010. It appears in the NCR data of Mace as a resistance to disruption.
The general thought here is that interventions which provide alternative reinforcement to reduce problem behaviour, are counter therapeutic, especially when the behaviour is challenged in some way. When the DRA is discontinued there is resurgence & this is because the disruptor is reduced or no longer available. Therefore, a thick schedule DRA produces a higher rate of disruption of the target behaviour and therefore shows a greater decrease in response when it is present. However, we still have the increased effect when we add more reinforcement into the stimulus situation and this increases the strength of the target behaviour. This becomes evident during the reduction in DRA in the extinction condition.
EXT as a condition used alone, to reduce behaviour, also has the problem of resurgence and the appearance of a problem behaviour after the intervention has been discontinued. Leitenberg et al (1975) looked at the effect of duration on extinction and alternative reinforcement and found time to be a salient factor in extinction conditions. Resurgence is less likely to occur with increasing time in extinction. Wacker et al found resurgence of problem behaviour was reduced when using alternative reinforcement when longer periods of extinction were used and alternative behaviours successfully employed which form a functional effect when introduced earlier in the response class hierarchy (such as functional communication training FCT).
Behavioural momentum predicts that the baseline prior to extinction reinforcement rate is a factor because, if there are higher rates of reinforcement here, there would be greater resistance to the disruptive effects of DRA during EXT & less resurgence when the DRA is stopped. But, if higher than baseline rates of DRA are delivered then the resurgence is larger and this starts to obey Newton’s 3rd law (Whenever two bodies interact in the physical world, a force results & the interaction of two bodies results in two equal and opposite forces, one acting on each body involved in the interaction).
It is thought that this resurgence is because there is greater suppression of response and this means less resistance to extinction in this phase, which could also obey Hooke’s law ( linear relationship and the force required to stretch an object such as a spring is directly proportional to the extension of the spring).
If we are ignorant of the pre-treatment rates of reinforcement and then use high rates of DRA this might not have much effect on eliminating the response rate and the resurgence would have a higher than predicted magnitude especially with higher rates of alternative reinforcement. (Shahan & Sweeney 2011) This is counterproductive and a side effect of implementing a thick DRA schedule.
It is typically found that when using a response dependant schedule or independent schedule of reinforcement the response rate of the target behaviour decreases (Skinner, 1938; Zeiler, 1968 et al). This decrement is not as large as the shift to extinction (Herrnstein, 1966). Weisberg & Kennedy 1969 & Neuringer 1970 found that responding was maintained by NCR even when only a few response dependant reinforcers had been given.
The relationships between NCR and response dependant schedules are not equivalent. The arbitrary relationship in NCR produces a delay in responding, breaks the contingency relationship and this attenuates the effects of the reinforcers (Sizemore et al 1978).
As the response gains momentum (or frequency) the increase in response starts to become contiguous and this has an effect on subsequent behaviour. Organisms experience ambiguous environments in their everyday lives in which the contingencies are not known. The behaviour is affected by these events and their sequences in a contiguous way to their behaviour and even though these contingencies are response independent schedules, the behaviour is maintained because there often are not reinforcers that occur without responses but occur as a sequence of events which is somehow related to their behaviour. This is thought to be the reason why superstitious behaviour occurs and often a single contiguity is enough to give a frequency of responding enough momentum to continue, despite there being no actual contingency in place. Skinner (1953) called this the single response-reinforcer contiguity.
The foregoing are the conclusions of the author of this paper. Comments and feedback are invited to firstname.lastname@example.org
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