We reinforced problem behavior and appropriate behavior on concurrent schedules of reinforcement and analyzed the results using the GME. For all evaluations, the relative rate of responding was influenced by the relative rate of reinforcement. Bias was observed for all participants, with two analyses indicating a bias towards problem behavior (Greg [escape] and Alice) and two indicating a bias towards appropriate behavior (Greg [tangible] and Amy). Finally, DRA and extinction were successful in reducing problem behavior and increasing appropriate behavior to clinically significant levels.
One notable difficulty in such analyses involves defining a “reinforced response.” It is not always clear how responses are reinforced, even with a schedule of reinforcement in place. In concurrent schedule arrangements, the response for which a reinforcer is delivered is controlled by the experimenters. However, it is not clear whether, or to what extent, that reinforcer influences other responses. While not presented here, different results would have been obtained by changing the definition of a reinforced response. Future researchers should evaluate sequential relations between a response and a known reinforcer (i.e., the last response prior to reinforcer delivery counts as “reinforced”) or temporal relations between a response and a known reinforcer (i.e., all responses occurring within a set period of time prior to reinforcer delivery count as “reinforced”).
In addition to reducing problem behavior, one of the goals of this investigation was to further demonstrate the generality of the GME (Baum, 1974
). Although a lengthy analysis of concurrent schedules of reinforcement would not likely be necessary from a purely clinical standpoint, useful information can be gathered from such matching analyses. In addition to providing further support for the generality of the GME, in an experimental application with severe problem behavior, there are important applied considerations to this investigation. It is important to note that merely reinforcing appropriate behavior more than problem behavior did not decrease problem behavior to a clinically significant level. It is likely that during naturally occurring interactions between caregivers and children, concurrent schedules of reinforcement are in place. That is, sometimes a caregiver reinforces problem behavior (more than likely on a variable schedule), and sometimes reinforces appropriate behavior. As previous research on treatment integrity has suggested, this could affect the long term success of interventions to reduce problem behavior (Vollmer, Roane et al., 1999
; Wilder et al., 2006
; Worsdell et al., 2000
The present experiment suggests several areas for future research in which similar analyses may be conducted using concurrent-schedule arrangements based on naturalistic observations. For example, descriptive analyses (Bijou, Peterson, & Ault, 1968
) could be conducted with careproviders and the results could be analyzed using reinforcers identified in a functional analysis (Iwata et al. 1982/1994
) with procedures similar to those described by Borrero and Vollmer (2002)
. For example, if descriptive analysis data showed that problem behavior was reinforced approximately every 20 s, and appropriate behavior was reinforced every 40 s, experimental analyses could be designed to represent naturally occurring reinforcement rates in an experimental context. Concurrent schedules of reinforcement could be based on the derived schedules of reinforcement observed during naturally occurring situations, and a subsequent matching analysis could be conducted. The extent to which relative response allocation is similar under both descriptive and experimental arrangements may provide greater support for the generality of the matching relation. It is often difficult and perhaps unrealistic to train parents to refrain from providing reinforcement following problem behavior. Matching analyses may suggest the lower limit of caregiver reinforcement that may be provided while maintaining clinically acceptable levels of appropriate behavior (Vollmer, Roane, Ringdahl, & Marcus, 1999
An additional area of future research may include analyses of various parameters of reinforcement. Previous research (e.g., Borrero, Vollmer, Borrero, & Bourret, 2005
; Mace et al., 1994
; see Stromer, McComas, & Rehfeldt, 2000
for a comprehensive review) has suggested that duration of reinforcement (e.g., Fisher, Piazza, & Chiang, 1996
) delay to reinforcement (e.g., Neef et al., 1994
; Vollmer, Borrero, Lalli, & Daniel, 1999
), quality of reinforcement (e.g., Francisco, Borrero, & Sy, 2008
; Mace, Neef, Shade, & Mauro, 1996
), response effort (e.g., Cuvo, Lerch, Leurquin, Gaffaney, & Poppen, 1998
; Zhou, Goff, & Iwata, 2000
) and magnitude of reinforcement (e.g., Lerman, Kelley, Vorndran, Kuhn, & LaRue, 2002
; Volkert, Lerman, & Vorndran, 2005
) are important variables for evaluating response allocation, in addition to relative rate of reinforcement. Similar investigations could be conducted with different parameters of reinforcement by holding constant rate of reinforcement. In addition, the implications for the treatment of severe problem behavior may be significant. Often, problem behavior is so severe (e.g., head-banging on hard surfaces) that it is not possible to withhold reinforcement (i.e., extinction). That is, especially in the case of behavior reinforced by attention, it is not possible to ignore the behavior and some attention (e.g., blocking the response) will likely be necessary to ensure the safety of the individuals in the situation. However, it may be possible to manipulate other reinforcement parameters such as duration or quality of reinforcement (Athens & Vollmer, in press
One limitation of these experiments may be the small number of concurrent-schedule values. For Greg and Alice, we only manipulated two values for the concurrent schedules. For Amy, we manipulated three values; however, we did not conduct a thorough analysis of the third value (i.e., VI 60-s VI 20-s), nor did we conduct a reversal to that phase. Future research may also include parametric schedule-value evaluations. For example, the schedules could initially start with VI 20-s for problem behavior and VI 60-s for appropriate behavior, and then values in between (e.g., VI 25-s VI 55-s) until the schedules are reversed (i.e., VI 60-s VI 20-s). Such evaluations may be useful in quantifying reinforcer value by identifying indifference points (i.e., schedule values that produce comparable response allocation). Using the above example, it is possible that when the schedules are VI 35-s for problem behavior and VI 40-s for appropriate behavior, responding would be allocated similarly.
A second limitation of these experiments may be the brevity of the conditions. In a basic preparation, it is usually possible to conduct conditions until meeting a stability criterion. However, in applied settings it was not always possible to bring each condition to stability before exposing behavior to another condition. Therefore, the matching analyses conducted in these experiments may not be based on stable responding, and this could account for some of the variability observed. It is likely that the early sessions in each condition represent a transition state, during which the participant begins to discriminate between the concurrent schedules of reinforcement, and that stable responding occurs towards the end of each condition. While only the last five sessions of each condition were included in the matching analyses, comparisons of the session-by-session scatter plots and the mean scatter plots were also analyzed and suggested that closer approximations to matching were observed by calculating the mean of the last five sessions of each condition rather than calculating all sessions in each condition. This effect was observed for all participants. It is also possible that the history of reinforcement for problem behavior and appropriate behavior could have affected these results, or made problem behavior more likely. It is unknown whether the participants' histories of reinforcement favored problem or appropriate behavior.
A third potential limitation may be that the results were somewhat variable, and the rates of responding did not always correspond to the rates of reinforcement. Prior matching studies have programmed schedule-correlated stimuli (e.g., Neef et al., 1992
) to make the conditions more discriminable. It is possible that better correspondence would have been obtained had we included schedule-correlated stimuli. While this was not an investigation of responding during naturally occurring situations, it is not likely that schedule-correlated stimuli are programmed in natural environments. Our goal was simply to assess behavior under these conditions without additional schedule-correlated stimuli and to observe how responding was allocated. Similar procedural limitations may be noted in the absence of a COD for Alice and Amy. Although the COD is a common manipulation in matching research (e.g., Herrnstein, 1961
), a COD was implemented for Greg only to eliminate a chained response that was observed. It may be the case that a COD would not be programmed, or at least not implemented with high integrity, in natural environments. Again, given that the participants engaged in severe problem behavior, conditions were designed to be more similar to naturally occurring concurrent schedules. However, even though the conditions were designed in this manner, it is important to note that we observed undermatching in three of four data sets. As Baum (1974)
pointed out, undermatching could be related to poor discrimination between the schedules. It is possible that by incorporating a COD or schedule-correlated stimuli the GME could have better described responding. Davison and Jenkins (1985)
and Davison and Nevin (1999)
offered an alternative to the GME that would take into account the discriminability of available reinforcers in concurrent schedule arrangements. This “detection-theory model” may provide an alternative explanation of these data and should be considered in future studies.
The present experiment focused on evaluating the rate of reinforcement and the effects on problem and appropriate behavior to determine if the GME provided descriptions of response allocation on concurrent schedules of reinforcement. This preliminary experimental investigation is the first such demonstration with 3 individuals with developmental disabilities who engaged in severe problem behavior. While the results were variable, generally they indicated that the GME described response allocation. The limitations associated with this investigation suggest numerous areas of future research related to problem behavior and the matching law that could provide further support for this relation, and address some of the difficulties noted above. From a research standpoint, this investigation contributes to the empirical work supporting the generality of the matching law, although from a clinical standpoint, the contributions may not be as clear. However, there are clinical benefits in assessing response allocation by determining how responses may be reinforced on concurrent reinforcement schedules, particularly because concurrent schedules are likely to be in place in natural environments. It may be particularly difficult to determine how responses are reinforced (temporally, sequentially, or scheduled) in the natural environment, which is an important consideration when training caregivers or generalizing treatments to other settings (e.g., home protocols, schools). It is possible that there may be some discrepancy between what we as researchers define as a reinforced response, and what actually functions as a reinforcer.