Authors: Joseph M. Lambert, Maria A. Osina, Bailey A. Copeland
Categories: Article, adults, behavioral economics, developmental disabilities, extinction burst, translational research
Source: Journal of Applied Behavior Analysis
Doi: 10.1002/jaba.1088
Extinction bursts, or temporary increases in rates and intensities of behavior during extinction, can preclude the inclusion of extinction in intervention packages meant to suppress severe challenging behavior. To identify underlying behavioral mechanisms responsible for response persistence and bursting, 69 adults with developmental disabilities completed a low-stakes translational investigation employing a 2×2 factorial, crossed, and randomized matched blocks design, with batched randomization logic. In each of the four test groups, we made distinct antecedent manipulations with two value parameters commonly studied through behavioral economics (i.e., demand intensity, Pmax) and evaluated the extent to which each of these manipulations influenced target responding during extinction. Although we found statistically significant differences attributable to both parameters, variations in reinforcer consumption relative to demand intensity were most influential across all dependent variables. This outcome implicates consumption relative to demand intensity as both a mitigating and exacerbating preextinction factor that influences the prevalence of adverse collateral extinction effects (e.g., bursts).
Keywords: adults, behavioral economics, developmental disabilities, extinction burst, translational research
Extinction describes the discontinuation of reinforcement that results in decreases in a measurable dimension of behavior (e.g., frequency, duration; Cooper et al., 2020). Bursts are reportedly a common collateral effect of extinction (Alessandri et al., 1990; although see Lattal et al., 2020) and are characterized by a temporary increase in behavior relative to baseline (Lerman & Iwata, 1995). Although precise definitions of bursting are utilitarian and fluctuate according to the questions asked by various researchers (Katz & Lattal, 2021), once defined, the general prevalence of bursts can be estimated (e.g., Lerman & Iwata; 1995; Lerman et al., 1999). However, likely due to poor understanding of the underlying behavioral mechanisms responsible for their manifestation (Fisher et al., 2023), no method currently exists to control their occurrence.
Notwithstanding, control is valuable. Treatments of challenging behavior are often less effective when they do not include extinction (Fisher et al., 1993; Hagopian et al., 1998). However, when challenging behavior is dangerous, practitioners may not risk increasing its rate or intensity. If we understood why bursts occurred, we could proactively work to mitigate their occurrence, thereby making extinction a more palatable treatment option in more settings.
Available evidence suggests baseline reinforcement parameters influence responding during extinction (Nevin & Grace, 2000; Shahan, 2022). For example, basic research has demonstrated that response persistence (i.e., resistance to changes in baseline response patterns in the face of disruptors such as extinction) can fluctuate as a function of deprivation. Specifically, levels of preextinction reinforcer consumption are inversely related to persistence during extinction (e.g., Marx, 1963, 1971; Mueller & Davenport, 1970; Reynolds et al., 1952).
Somewhat paradoxically, we also know that responding during extinction is both negatively and positively related to baseline reinforcer rates. Specifically, when considered in absolute terms, thinner schedules of reinforcement (particularly those that leverage ratio schedules; Boren, 1961) lead to higher rates of responding during extinction than denser schedules (although this relation is not linear; see discussion of behavioral economics below). However, when extinction data are transformed into proportion-of-baseline measures and the slope of change is considered on a logarithmic scale, it is the denser schedules that typically lead to greater persistence (Nevin et al., 1990) and more bursting (Katz & Lattal, 2020; Nist & Shahan, 2021). A probable explanation for the former is that transitions from thin schedules to extinction are harder to discriminate than transitions from dense schedules (Baum, 2012; Shull & Grimes, 2006; Thrailkill, 2023). Competing explanations for the latter have included appeals to Pavlovian processes described by behavioral momentum theory (Nevin & Grace, 2000) and choice behavior described by the temporally weighted matching law (Shahan, 2022).
Concerning the latter, contemporary theory proposes that baseline conditions in single-operant paradigms support at least two distinct classes of behavior that tend to compete for response (1) behavior that produces reinforcement (i.e., the target response) and (2) behavior that facilitates reinforcer engagement (e.g., approach responses, consumption). When Option 1 contacts extinction, the opportunity to engage in Option 2 is eliminated and a larger percentage of total responding is thus allocated to Option 1—functionally (and temporarily) increasing relative rates of responding. As Option 1 continues to contact extinction, its value quickly depletes and responding is reallocated to performances not relevant to acquiring the target reinforcer (Shahan, 2022).
Importantly, the reinforcing effects of stimuli can be relative and volatile (Herrnstein, 1961, 1970; Laraway et al., 2003). Simply put, different reinforcers support different magnitudes and qualities of responding (e.g., Hodos, 1961), and this support is likely to fluctuate in accordance with fluctuations in relevant contextual variables such as response effort and schedule requirements (e.g., DeLeon et al., 1997; Roane et al., 2001). Thus, although someone may be willing to share a thought for a penny, they are unlikely to build a house for one. This “not all reinforcers are created equal” epiphany has inspired scientists to account for (e.g., Shahan, 2022; Shahan & Craig, 2017) and even study (e.g., Iwata et al., 2000; Michael, 1988) “value” (i.e., variables that alter the degree to which specified consequences support specified outputs). As bursts are likely a product of baseline reinforcement parameters, consideration of value is essential to understanding the phenomenon.
Concepts in consumer demand theory (e.g., Bickel et al., 2000) may be helpful to this analysis. Specifically, a behavioral-economic framework (Hursh 1980, 1984) integrates concepts from microeconomics and operant psychology to understand how contextual variables influence value and choice across a wide range of socially important domains (e.g., Aston & Cassidy, 2019; Best et al., 2012; Bickel & Vuchinich, 2000; Collins et al., 2014; Epstein & Saelens, 2000; Foxall et al., 2007; Henley et al., 2016; Kaplan et al., 2018; Pickover et al., 2016).
Drawing analogies between currency and behavior, commodities and reinforcers, and supply constraints and schedules of reinforcement, behavioral economists view contingencies arranged in an experimental analysis as a functional market and interpret results under the premise that unidimensional choice rules (e.g., the matching law) cannot accurately account for all choice because choices vary as a dynamic function of context (Hursh & Silberberg, 2008). Specifically, choices are determined by qualitative differences in stimulus properties (e.g., essential/nonessential), unit prices, demand elasticity (defined below), and the availability and relative nature (e.g., complements, substitutes) of alternative reinforcers both within and outside of the system under analysis (Hursh, 1980).
In this paradigm, overall consumption of reinforcement (denoted by the letter Q in quantitative models) represents an equilibrium between supply and demand and has been used as one metric for quantifying value. As displayed in the left column of Figure 1, Q varies as a nonlinear function of changes in unit price, and demand is a term that describes the slope of changes in Q as a function of changes in unit price (the product of this scaling is known as the commodity’s essential value; Gilroy, 2023). The ratio of the relative change in Q to the relative change in unit price is referred to as elasticity (Gilroy, 2020). Elasticity varies across both individuals and commodities. It is relevant to an analysis of economic markets because it moderates reinforcer value in predictable ways, thus helping suppliers establish the economic conditions needed to maximize profit.
All else being equal, consumers will consume the most reinforcers when they are freely available (i.e., QFree). The level of consumption at QFree is sometimes referred to as bliss-point consumption (e.g., Gilroy et al., 2021) or demand intensity (e.g., Hursh, 1984). As price increases, consumers can only minimize reductions in bliss-point consumption by increasing response output (see top left panel of Figure 1). When the ratio of the change to consumption is less than the ratio of the change to unit price (i.e., when price increases lead to increases in overall responding), demand is considered inelastic. For example, motorists are unlikely to purchase less gas if the price increases by 5.00. The break point-1 (BP1) describes the largest unit price for which at least one unit of the commodity was obtained, and BP0 represents the first unit price at which the commodity was not obtained. The “inverted U” shape of responding displayed in the left column of Figure 1 has been reliably produced across species and commodities (Gilroy et al., 2018; Hursh & Silberberg, 2008).
Notably, the shift in demand from inelastic to elastic is a point of interest because it quantifies a dimension of the reinforcement process that moderates commodity value (i.e., elasticity) and helps identify optimal prices. The optimal price, or Pmax, is the price that supports maximum consumer spending, or Omax. Prices below Pmax are suboptimal because consumers would spend more if required. Similarly, prices above Pmax are also suboptimal because these price points decrease the value of the commodity and consumers will not spend as much to obtain it as they would if pricing had been more reasonable.
If it is only possible to consume a reinforcer within the system of contingencies under analysis (e.g., it is impossible to drink Coke outside of an experiment), the economy is said to be closed. In contrast, in an open economy there is an asymmetry between daily consumption and the equilibrium points in a demand curve (e.g., participants drink Coke both during and after the experiment). Without changing anything else, changing the economy from closed to open is one reliable way to diminish the intensity of demand, equilibrium points, and Pmax (e.g., Gilroy et al., 2018; Kodak et al., 2007; Roane et al., 2005).
Relatedly, diminishing marginal utility stipulates that reinforcers lose value as they are consumed more (Madden et al., 2024; although see Seward, 1956). That is, equilibrium points can be used to quantify temporary shifts in value at a specified price because the value of additional consumption is decreased as consumption approximates them. Individuals stop “paying” for reinforcers after consumption has crossed the equilibrium threshold. Laraway et al. (2003) account for this effect by distinguishing antecedent events (e.g., deprivation) that temporarily increase the value of consequences (e.g., access to food, an establishing operation [EO]) from other antecedent events (e.g., satiation) that work in the opposite direction and deplete value (i.e., an abolishing operation [AO]). Using these terms, one might say the value of additional consumption is abolished (decreased) the closer consumption gets to equilibrium. In contrast, the value of additional consumption is established (increased) when little or no consumption has occurred. The bottom right panel of Figure 1 illustrates how value can be quantified as consumption relative to equilibrium.
Generally, demand intensity and Pmax have not been considered in published treatments of bursts. However, as bursts are likely a product of baseline reinforcement conditions and because value can fluctuate according to molar (i.e., unit price) and molecular (i.e., satiation/deprivation) variables (see right column of Figure 1), consumer demand theory may provide a helpful framework from which to formulate and test hypotheses relevant to bursts. For example, bursts may be a product of baseline schedules of reinforcement (i.e., “unit prices”) relative to Pmax (Gilroy et al., 2019, 2021). Specifically, if baseline prices (i.e., number of responses required to obtain a reinforcer) fall within the inelastic range of a demand curve, consumers may be more inclined to increase output to a value that approximates Omax during extinction—a pattern typified by bursts (Nist & Shahan, 2021). Likewise, if baseline prices fall within the elastic range, then output has already been diminished and bursts may be less likely (Hodos, 1961; Tustin, 1994). It is also possible that bursts are a product of consumption before extinction. Specifically, if, prior to extinction, consumption has approximated QFree (thereby abolishing additional consumption as a reinforcer), responding during extinction may be less than if little to no consumption had occurred prior to extinction (Marx, 1963, 1971; Reynolds et al., 1952). Finally, it is possible that price (relative to Pmax) and consumption (relative to demand intensity) interact. Thus, the purpose of this study was to test these hypotheses and facilitate strategic extensions toward discovery for treatments of challenging behavior.
Across a 2-year period, we recruited 86 adults with disabilities to participate in this study and obtained consent. Inclusion criteria called for participants to (a) be older than 18 years of age, (b) have a diagnosis that qualified as a disability under the Individuals with Disabilities Education Act (IDEA, 2004), (c) correctly manipulate all study items, and (d) consent prior to and throughout the study. If participants could not legally consent, we obtained consent from guardians and assessed assent throughout the study (i.e., at the beginning of every session). We did not anticipate biological variables (e.g., sex) would affect the study outcomes, so we did not set criteria for such variables.
Of the 86 participants enrolled, 69 completed the study. Seventeen participants dropped out prior to study completion. Specifically, 11 participants were removed due to persistent scheduling conflicts, two were removed due to serious health concerns unrelated to the study, and two indicated that they no longer wished to participate. Two participants were also removed due to fidelity errors (i.e., research assistants implemented the wrong extinction protocol for these participants).
Participant demographic information is displayed in Supporting Information A. Of those who completed the study, 56.52% (39 of 69) identified (or were identified) as cisgender men, 40.58% (28 of 69) identified (or were identified) as cisgender women, 1.45% (1 of 69) identified as a transgender man, and 1.45% (1 of 69) identified as a transgender woman. Verbal reports indicated that 88.41% (61 of 69) of participants were White, 7.25% (5 of 69) participants were Black, 2.90% (2 of 69) of participants were South Asian (Indian), and 1.45% (1 of 69) of participants were American Indian/Alaska Native.
The mean participant age was 42.5 years (range: 18–78 years), with a median of 39 years. Using the IDEA classification system, caregivers reported that 59 participants had an intellectual disability, 12 participants were autistic, 10 had other health impairments, two had ortho-pedic impairments, two had traumatic brain injuries, two had speech or language impairments, and two had visual impairments. Through informal and subjective assessments of each participant’s expressive language, we estimated that 57 participants had proficient expressive verbal repertoires, 11 communicated most often through one- to two-word utterances, and one participant displayed no expressive language.
Recruitment materials were distributed through seven distinct organizations that served adults with disabilities, each in different capacities. Three of these organizations did not have clients who expressed interest in participation.
Of the remaining four, three specialized in providing residential and day-service programming for adults with disabilities and one specialized in providing inclusive post-secondary education experiences to adults with disabilities in a university setting.
All study appointments were conducted at a table with at least two chairs in physical areas that were visually accessible to stakeholders (e.g., staff, parents) in locations convenient to participants’ daily schedules. Although locations could vary, study appointments were primarily conducted in a day program, workshop, or university setting for 62.32% (43 of 69) of participants. Appointments were conducted in home settings for 37.68% (26 of 69) of participants. In all cases, we asked each organization to maintain business-as-usual staffing ratios and protocols, to monitor study appointments (when needed), and to maintain responsibility for all behavioral programming (when relevant).
All study sessions required a table with at least two chairs, manipulanda required to emit the target response (e.g., a die or a clothespin), plates to place edible reinforcers (when relevant), a sound system to play short (30-s) clips of preferred sounds (when relevant), and data collection hardware (i.e., handheld computers) and software (i.e., Countee). When secondary observers could not be present during appointments for which assessments of interobserver agreement were scheduled, sessions were recorded using video cameras and temporarily stored on a password-protected and encrypted Health Insurance Portability and Accountability Act-compliant cloud-based server (after interobserver agreement data were obtained, these videos were promptly deleted).
Participant-specific binders included relevant data collection (e.g., procedural-fidelity sheets) and summary materials for all study phases. It also included a sign-in sheet and punch card that researchers used at the end of each appointment to help participants track when they could expect to receive each $25 gift card (described below).
Trained observers collected continuous timed-event measures of the frequency of target responding and reinforcer delivery, latency from session onset to the delivery of programmed reinforcers, and overall session duration. During the progressive-ratio reinforcer analysis (PRA), we recorded the specific schedule value (e.g., fixed-ratio [FR] 1, FR 4, FR 7) that was satisfied prior to each reinforcer delivery. During the progressive fixed-ratio reinforcer analysis (PFRA), we recorded the specific schedule value (e.g., FR 1, FR 4, FR 7) that produced the highest response output (i.e., Omax).
Reinforcer delivery entailed placing an edible on a plate in front of participants (when relevant) or turning on a preferred sound for 30 s (when relevant). For 66 participants, target responding entailed die rolling (i.e., picking up a die and putting or dropping it back down). For three participants, target responding entailed manipulating a clothespin (i.e., picking up a clothespin, squeezing it, and putting it back down). For an explanation of how target responses were selected, see Response training (below).
Derivative measures appropriate to each analysis described below served as our dependent variables and included break point-BP1 (i.e., the schedule of the last obtained reinforcer prior to response cessation [PRA]), equilibrium (i.e., the number of reinforcers obtained prior to response cessation at each schedule value [PFRA]), and observed Pmax (the schedule value at which the maximum response output was obtained [PFRA]). During baseline and extinction sessions of the extinction challenge, we calculated mean baseline response rate, peak response rate during extinction (i.e., the rate of responding during the session that displayed the single highest rate of responding during extinction), peak response rate during extinction depicted as a proportion of baseline (i.e., the peak response rate divided by mean baseline response rate, multiplied by 100), extinction burst (i.e., when the peak response rate fell two standard deviations [z scores] above the mean baseline response rate), total responses emitted during extinction, and latency to extinction (i.e., elapsed time from extinction-session onset to extinction-session offset [termination criteria are described below]).
To probe the potential influence of the discriminability of contingency disruption on performance during extinction (Ettenberg & Camp, 1986; Shahan, 2010, 2013), we also tracked reinforcers “missed” (e.g., 5) prior to achieving an extinction effect by dividing the total number of responses emitted in extinction (e.g., 20) by the baseline schedule value (e.g., FR4). That is, we quantified the number of times that participants should have expected to obtain a reinforcer but did not during extinction prior to desisting. This final variable was exploratory.
A second trained observer assessed interobserver agreement on all dependent variables for 98.55% (68 of 69) of participants during the PRA, for 98.55% (68 of 69) of participants during the PFRA, and for 97.10% (67 of 69) of participants during baseline and extinction conditions of the extinction challenge. Importantly, all participant data were exposed to interobserver agreement assessments (i.e., if interobserver agreement data were not assessed during one participant’s PRA, it was assessed for that participant’s PFRA and extinction challenge). Given the similarity of the measurement system across assessments and the volatility of our assessment-termination criteria, we determined that it was unnecessary (or prudent) to sample interobserver agreement across all assessments for all participants (although we often did).
We calculated interobserver agreement for each dependent variable by comparing frequency counts scored by primary and secondary observers and dividing the smaller count by the larger count and multiplying by 100. We then calculated a session agreement by aggregating scores for each relevant dependent variable. Across participants, mean interobserver agreement for PRAs was 99.3% (range: 93%–100%). Mean interobserver agreement for PFRAs was 99% (range: 84.6%–100%). The mean interobserver agreement for the extinction challenge was 99% (range: 89.1%–100%). Individual interobserver agreement scores are displayed in Supporting Information B.
We evaluated procedural fidelity for 100% of participants during the PRA, 100% of participants during the PFRA, and 98.55% (68 of 69) of participants during baseline and extinction conditions of the extinction challenge. Evaluations entailed responses to yes/no checklists that described critical elements of session implementation (see Supporting Information C). When a facilitator implemented a session element as described, observers scored a “yes.” When they did not, observers scored a “no.” Session fidelity was then calculated by dividing all yes responses by the sum of yes and no responses and multiplying by 100. Across participants, mean fidelity scores for PRAs were 99.5% (range: 93.8%–100%). Mean fidelity scores for PFRAs were 99.8% (range: 95.2%–100%). Mean fidelity scores for the extinction challenge were 99.8% (range: 96.6%–100%). Individual fidelity scores are displayed in Supporting Information B.
Following the completion of a small battery of intake assessments (described below), we evaluated between-groups differences in peak-response magnitudes during a single exposure to extinction using a 2 × 2 factorial, crossed, and randomized matched blocks design, employing batched randomization logic. Specifically, we recruited participants in batches of 10 and matched two tetrads according to similarity in break points produced through PRA assessments. That is, we sorted participants into two groups-of-four pairings that produced mean break points with the smallest range of variation (relative to alternative participant combinations within the relevant group of 10). We then used the randomization functions of Microsoft Excel to assign members of each tetrad to one of four experimental groups (i.e., inelastic EO, inelastic AO, elastic EO, elastic AO; described later). The two participants not assigned to a tetrad were then placed on hold after completing their PFRA until they could be matched with members of subsequently established tetrads (i.e., they did not advance to the extinction challenge until they were randomly assigned to an experimental group).
For the continuous and count dependent variables (all variables except extinction bursts) (a) the effect of relative consumption (i.e., the proximity of preextinction reinforcer consumption to Qfree), (b) the effect of relative price (i.e., inelastic or elastic, relative to Pmax), and (c) price-by-consumption interactions (whether the effects of consumption changed depending on price) were evaluated using the aligned rank transform analysis of variance (Wobbrock et al., 2011). This nonparametric alternative to factorial analysis of variance (ANOVA) was chosen because preliminary data investigation indicated significant violations of normality and homogeneity of variance assumptions. Descriptive and inferential statistics are displayed in Tables 1 and 2. All relevant calculations can be found in Supporting Information D. The frequencies of extinction bursts were too low to warrant any statistical analysis; raw counts are reported in Tables 1–3.
Several parameters are known or hypothesized to influence responding during extinction (e.g., reinforcer value, baseline schedule value, baseline response rate, obtained rates of baseline reinforcement; Fisher et al., 2023; Nevin & Grace, 2000; Perin 1942). As a result, we sought to control and evenly distribute variation in these parameters across test groups through our matching and randomization process. Thus, with one exception, we sought to ensure that between-group differences in these variables during the control phase were not statistically significant. However, as the inelastic/elastic dichotomy by definition should produce differences in baseline reinforcement schedules and obtained reinforcement rates, we expected to see statistically significant differences in these control variables for test groups for which baseline unit price was intentionally manipulated (i.e., inelastic vs. elastic). As interaction tests were irrelevant to control variables (i.e., price and consumption were not crossed until the extinction test), the difference in means for abolishing operation (AO) versus establishing operation (EO) and for inelastic versus elastic were assessed using Wilcoxon rank sum test (response variables were not normally distributed).
During extinction, we predicted that the mean magnitude of peak responding for participants assigned to inelastic conditions would be higher than that for participants assigned to elastic conditions, holding consumption constant. Additionally, we predicted that the mean magnitude of peak responding would be higher for those participants assigned to EO than AO, holding the price constant. Further, we predicted a consumption-by-price interaction such that the difference in mean peak responding in inelastic and elastic conditions would be higher in EO relative to AO.
To avoid familywise Type I error inflation (due to the number of analyses in our plan), we adjusted p values for multiple testing using the false discovery rate procedure (Benjamini & Hochberg, 1995). Before making this adjustment, we determined that control and test variables should be considered different families of tests because hypotheses for each data set were unrelated. We hypothesized that, with the above-mentioned exceptions, between-group differences in means in control variables would not be statistically significant. For the test variables, we sought to evaluate the extent to which parametric manipulations of our independent variables influenced all relevant dependent variables during extinction.
Power analysis and sample size calculations were conducted using the R project for statistical computing (version 4.2.2; R Core Team, 2022). Given that our study represented a novel contribution, we could not rely on previous literature to estimate the expected population effect size. However, unpublished pilot data suggested that the effect size would not be small. Thus, we calculated the sample size based on a bench-mark value for Cohen’s f ^2^ of 0.15 that corresponded to a medium effect size (Cohen, 1988). To achieve 80% power in a linear model with three predictors (i.e., price, consumption, Price × Consumption) and α = .05, we projected that 77 participants would be required. With this sample, the power to find any of the three predicted effects (given medium effect size) was 88%. As we anticipated participants would be equally distributed across four groups, we budgeted effort for 80 participants.
It is important to note that although the original power analysis was done for a regression model, we applied an aligned rank transform ANOVA to the obtained data because of significant deviations from normality and nonconstant variance on the dependent variables. Both methods rely on the same statistical model, whereas the nonparametric analysis accommodates the violations of test assumptions.
In addition to programmed reinforcers, all participants were compensated with gift cards at a rate commensurate with minimum wage in Tennessee and Utah (i.e., 25 gift card and initiated a new punch card during the next appointment.
We note that facilitators aways rounded up. For example, a participant who terminated an appointment after a 60-s session would have earned one punch. A participant who terminated an appointment after 20 min and 60 s would have earned two punches. When participants could not manage their own money, gift cards were given to their conservators with the promise that the money would be spent to satisfy participants’ preferences and/or needs. Across this study, participants earned an average of 50–$75).
For each participant, we scheduled one to five appointments per day across 1–5 days per week. To the extent possible, we attempted to hold appointments at the same times each day and week. Similarly, we attempted to offer reinforcer options that were not typically available to participants (e.g., preferred snacks or activities not found in their homes). However, as it would have been a rights violation to ask caretakers to withhold preferred items or activities outside of formal study sessions, we never made this request. Thus, although we took steps to establish a closed economy, we could not guarantee it.
All participants completed the same (1) interview (i.e., informed consent, appointment scheduling, identification of programmed reinforcers and target responses), (2) target-response training, (3), Qfree, (3) PRA, (4) PFRA, and (5) extinction challenge.
All assessment-related activities were framed as a choice to minimize unintended coercive practice. Specifically, researchers initiated each appointment with a 5-min casual conversation. Before each session, researchers displayed the apparatus for the target response (e.g., a die) and a low-preferred alternative activity (e.g., a magazine or a toy). They paraphrased a script unique to each study condition (described below and in Supporting Information C). The specific language for each script was shaped by problem-solving efforts during pilot-study initiatives as an attempt to preempt the generation of inaccurate self-rules about prevailing contingencies and/or facilitator expectations (e.g., Lambert et al., 2020). All appointments terminated the moment a participant indicated they wanted it to end.
All target responses entailed a multistep manipulation and restoration. The final step of each response (i.e., restoration) automatically set up another opportunity to complete the task. Eligible responses needed to be easy to execute but unlikely to occur without contrived incentives. Response topographies were matched to participant skill set. Specific responses were disqualified if participants continually emitted them in the absence of programmed consequences during target response training. They were also disqualified if participants demonstrated (or expressed) difficulty emitting them.
During training, researchers modeled the correct response and instructed participants to replicate it. If they could not, researchers used a least-to-most prompting procedure to assist with initial responding and then delivered a nontargeted reinforcer (e.g., praise) contingent on each completion (Collins, 2022). If participants did not or could not independently emit a response after initial demonstration and practice, said response was disqualified and a new response was evaluated.
This assessment was conducted once and served to establish consumption patterns when reinforcer supply was constraint free (i.e., we sought to establish Qfree). Before initiating this condition, a facilitator presented an array of potential reinforcers (informed by intake interview outcomes) and asked participants to pick one reinforcer to consume for the remainder of the study. Available options conformed to stated preferences, as well as dietary restrictions. For participants for whom free access to edible reinforcement was a concern, no-calorie edibles (e.g., small pickle pieces) and nonedible alternatives (e.g., music, simple crafts) were provided. After reinforcer selection, facilitators paraphrased the following
For participants with complex communication needs, contingency reviews were simplified and experience based (i.e., responses were prompted and consequated in conjunction with the delivery of instructions). At session onset, facilitators placed carefully measured and equalsized units of edible reinforcers on a plate in front of participants one at a time. Each time participants picked up a morsel to consume, another was placed on the plate. Participants also had access to low-preferred alternative activities intended to compete with reinforcer consumption as the value of consumption depleted. Likewise, facilitators did not speak to participants during sessions. If participants attempted to initiate a conversation while also consuming reinforcement, facilitators indicated that they could not talk while participants were eating/listening to music but that they could talk if participants decided to terminate the session. This was done to avoid conflating the value of a programmed reinforcer with the value of a programmed reinforcer paired with attention.
Sessions terminated when a participant refrained from consuming a reinforcer for 60 s (e.g., because they began to engage with the alternative activity), stated that they wished to terminate the session, touched a laminated “stop” card, or after 1 hr had elapsed (no assessment was ever terminated due to the passage of time). For participants with complex communication needs, we also accepted the act of walking away from the table as an indication of dissent/session termination.
For participants with dietary restrictions, programmed consequences were auditory and reinforcement procedures were adapted from Lambert et al. (2019). That is, facilitators began the session by playing the identified song on an iPhone. If the song finished before participants terminated a session, facilitators allowed the next song of the relevant album to begin. Thus, participants could listen to up to an hour of music from the same album containing the identified song. After session termination, we divided the session duration by 30 to determine the number of 30-s units each participant had consumed during the assessment. To avoid confounds associated with satiation, no additional sessions were conducted during the same appointment in which this condition was conducted.
Participants were exposed to three PRA sessions, each interspersed with control sessions. Controls occurred prior to PRAs. To avoid satiation, only one test condition was conducted per appointment. Control and test conditions of the PRA were set up similarly to the assessment of demand intensity, with the following modifications.
Facilitators placed the target-response apparatus (e.g., die) in front of participants and delivered a paraphrase of the following contingency
Facilitators then began a session by saying, “3, 2, 1, start” and looking down to avoid eye contact. If participants emitted a target response during a control session, facilitators interrupted additional responding and paraphrased the following
They then reset their timer and restarted the session. This procedure continued until facilitators obtained a 60-s sample of the absence of target responding or participants asked to stop the session (we determined that both cases represented a disinclination to continue to emit the response in the absence of programmed consequences and provided compelling evidence that responding that occurred during subsequently conducted test sessions was maintained by programmed consequences).
Target responding during test sessions was reinforced according to a basis 2 progressive-ratio (PR) 3 schedule (Jarmolowicz & Lattal, 2010; e.g., Reed et al., 2009). Specifically, after every other reinforcer delivery, price increased by three responses (i.e., FR 1, FR 4, FR 7). At the beginning of each session, facilitators paraphrased the following
Facilitators then began a session by saying, “3, 2, 1, start” and looking down to avoid eye contact. If participants asked how many responses were needed to earn the next reinforcer, the facilitator told them. For those who needed it, the facilitator also counted out loud the number of responses made each time a new response was made. This was typically faded after delivery of the first three to five reinforcers of a given session.
Approximately once every 5 min, facilitators reminded participants that they should not respond to make the facilitator happy; that they should only continue responding if they wanted the programmed reinforcer; and that they should stop the moment they were tired of responding, did not want the reinforcer, or simply wanted to quit. Sessions terminated when a participant refrained from emitting a target response for 60 s, stated that they wished to terminate the session, touched a laminated “stop” card, walked away from the table, or after 1 hr had elapsed (no session was ever terminated due to the passage of time).
The PFRA analysis was similar to the PRA, with a few exceptions. First, the PFRA did not include a control condition. Next, schedule values were fixed (held constant) for the entire session. That is, response requirements increased by three across sessions rather than across reinforcer deliveries (this modification allowed us to establish equilibrium points for programmed reinforcers at each schedule value). To control for satiation, we conducted one PRFA session per appointment (sessions ended following 1 min without responding or after 1 hr).
As was the case during the PRA, facilitators then began each session by saying, “3, 2, 1, start” and looking down to avoid eye contact after paraphrasing the following contingency review.
For participants who did not want to hear the entire contingency review, facilitators simply asked them if they remembered what to do. If so, they asked participants to explain the relevant contingencies to the facilitator. If, during a session, participants asked how many responses were needed to earn the next reinforcer, the facilitator told them. Likewise, facilitators counted out loud the number of responses emitted by participants who needed this support for the first few reinforcer deliveries of a given session. Approximately every 5 min, facilitators reminded participants that they could quit whenever they wanted to stop. Sessions terminated after 60 s elapsed without a target response, a participant stated that they wished to terminate the session, they touched a laminated “stop” card, they walked away from the table, or 1 hr had elapsed (no session was ever terminated due to the passage of time). The entire assessment ended after the aggregate response output for a current session fell below the output produced by the previous session (i.e., after Pmax had been empirically confirmed).
The purpose of the extinction challenge was to first establish a history with baseline contingencies of reinforcement. Baseline schedules were set according to PRA and PFRA results. Specifically, we compared the difference between each participant’s PFRA-identified Pmax and the mean of their PRA-identified break points (BP1).
For participants assigned to elastic, we added half of the calculated difference between Pmax and BP1 to their Pmax value and then rounded up to the nearest whole number. For example, if Pmax was FR 4 and BP1 was FR 8, then half of the difference was two, which we added to Pmax to establish an elastic baseline of FR 6. Similarly, for participants assigned to the inelastic condition, we subtracted half of the Pmax − BP1 difference from pmax and rounded down to the nearest whole number (i.e., FR 2).
The default session duration for the baseline condition was 5 min. However, to ensure an opportunity to obtain no fewer than five reinforcers per session, we referenced latency to the first obtained reinforcer of the matched PFRA session (i.e., the PFRA session with a schedule value that most closely approximated the baseline schedule). For example, if the above-mentioned participant was assigned to the elastic baseline condition (i.e., FR 6), we would consider their performance during the matched PFRA (FR 7) session to predict the number of obtained reinforcers possible during a typical 5-min session. If, during the matched PFRA session, latency to the first obtained reinforcer was 56 s, we would conclude that it was physically possible for this participant to obtain at least five reinforcers at the default session duration of 5 min when the baseline reinforcement schedule was set at FR 6 and would thus not change schedule duration. However, if the latency to the first obtained reinforcer had been 90 s, we would have increased session duration to 7.5 min.
To set a maximum appointment duration (during which multiple consecutive baseline sessions could be conducted), we used the maximum duration of any previously recorded appointment as a proxy measure of AO (e.g., fatigue, satiation) and ensured appointment durations during the extinction challenge never exceeded that value by more than 5 min (i.e., the default duration of one baseline session). Similar considerations were made to ensure that appointment-reinforcer consumption never surpassed demand intensity (or the highest equilibrium point from the PFRA in cases in which Qfree did not yield the highest consumption levels). For example, suppose the participant mentioned above consumed a maximum of 55 reinforcers during the FR 1 session of his PFRA. At FR 6 (his assigned baseline schedule), we would project that it would require 11 sessions to consume 55 reinforcers, estimating (roughly) 60 s to earn each reinforcer (justified above). Thus, this participant could have completed all 10 baseline sessions during a single appointment. In contrast, if participants could consume the maximum number of reinforcers during a single 5-min session, then each of the 10 baseline sessions needed to be conducted across each of 10 distinct appointments. Notably, some participants completed more than one appointment per day. When this happened, facilitators always ended the first appointment by crediting participants for their work and completing all relevant aspects of the compensation system (described above), allowing appointments to be interspersed with non-study-related activities and obtaining new assent for the subsequent appointment.
Baseline sessions were similar to PFRA sessions. During the first five sessions, facilitators paraphrased the contingency review listed in the PFRA section (above) and reinforced target responding according to participant-specific baseline schedules (i.e., inelastic, elastic). When allowable (i.e., when more than one baseline session could be conducted during an appointment and participants had not yet indicated they wanted to stop), facilitators began new sessions immediately after previous sessions had terminated.
When participants terminated sessions early, we used the full 5-min session duration as our denominator when calculating response rates. This was done to reflect the fact that participants were given the opportunity to respond across the full session duration, without artificially inflating rates of responding for participants who consistently terminated sessions early. That is, this decision allowed us to standardize our unit of analysis without requiring participants to remain in the research area after they had indicated they would like to leave.
During extinction, target responses ceased to produce programmed consequences. For AO participants, we introduced extinction after appointment-reinforcer consumption fell one below the total number of reinforcers consumed during any single appointment or after a participant indicated they no longer wished to consume the reinforcer. Previous appointments were thus coordinated in such a way that extinction for the AO group was introduced toward the end of the relevant appointment (however, we did not cap appointment duration during extinction). If baseline sessions were completed before appointment-reinforcer consumption levels were achieved, facilitators delivered reinforcers one at a time and noncontingently to participants either until consumption fell one below demand intensity (or the highest equilibrium point from the PFRA, in cases in which Qfree did not yield the highest levels of consumption) or until participants indicated they wished to stop consuming reinforcers.
In contrast, we introduced extinction to the EO group as the first session of the relevant appointment, when consumption had been low. In both cases (i.e., AO/EO) and prior to initiating the extinction session, facilitators prompted participants to emit enough responses to earn a single reinforcer at the established baseline schedule value (e.g., FR 6) and then delivered a reinforcer. They then delivered the standard contingency review and reminded participants that they should stop when they got bored or did not want to consume more reinforcers.
Extinction continued until responding reduced to 10% (or less) of the mean of the final three baseline sessions across a duration equivalent to two consecutive sessions (i.e., 10 min) or until dissent. Importantly, to avoid disrupting the operation of extinction (or introducing other response-suppressive elements attributable to procedures for transitioning between sessions), we conducted a single extinction session that could last up to 1 hr. When the duration of extinction was greater than the duration of a single baseline session, we later segmented participant performance during extinction into intervals that matched baseline session duration (thus standardizing opportunity and allowing for direct comparisons between performances during baseline and extinction in graphical displays).
Of the 69 participants who completed this study, 15 were randomly assigned to the inelastic EO condition, 19 were randomly assigned to the inelastic AO condition, 18 were randomly assigned to the elastic EO condition, and 17 were randomly assigned to the elastic AO condition. Globally, 34 participants were assigned to an inelastic baseline condition and 35 were assigned to an elastic baseline condition. Similarly, 33 participants were assigned to an EO extinction challenge and 36 participants were assigned to an AO extinction challenge.
Most attrition occurred after randomization but before differential exposure to test conditions. Participants often dropped out during PRA or PFRA assessments and prior to the baseline condition of the extinction challenge. Thus, procedural differences across test conditions do not explain differential attrition rates across these groups (see Participants section for specific reasons). Notwithstanding, differences in participant numbers across test conditions led us to use an ANOVA with a Type-3 sum of squares that relies on unweighted means when assessing the significance of the main effects (described in the method section). This method controlled for different-sized experimental groups and provided sufficiently accurate and conservative estimates of the significance of study findings.
Participants spent a mean of 73.7 calendar days (range: 5–323 days) completing this study. Across this time frame, they completed a mean of 16 total appointments (range: 10–23 appointments). Appointments were held primarily in the mornings and afternoons, and the primary appointment structure for most participants was one appointment (range: one to five appointments) per day. The mean maximum number of appointments conducted during a week was 6.1 (range: two to 15 appointments).
Variance in time spent in the study was attributable to (a) facilitator–participant schedule compatibility and (b) proximity of research sites to the host university. For example, due to costs associated with room and board for a traveling researcher, out-of-state participants were served on a condensed timeline, which sometimes required more than one appointment per day. When more than one appointment was held per day, the amount of time and the number of activities that divided appointments was individualized according to stakeholder reports of participants’ fatigue and satiation profiles. That is, multiple appointments were only an option for participants likely to agree to participate multiple times per day and who were likely to consume comparable amounts of reinforcement across appointments. When this happened, subsequent appointments were only held after the full interappointment interval (specified by caregivers) had elapsed. There were no discernable differences in study outcomes across appointment structure (i.e., one per day vs. multiple per day).
Tables 1 and 2 and Figures 1 through 5 display study results. Individual graphs, a project data-summary workbook, and disaggregated (session-by-session) response and reinforcer data can be found in Supporting Information E, F, and G, respectivly. Across participants, the mean PRA-derived break point was a FR 16.8 (SD = 13.1, 1–58), with a median of FR 14. The mean PFRA-derived Pmax was FR 7.9 (SD = 4.3, 1–19) with a median of FR 7.
Figure 5 Interquartile Ranges and Means Comparisons for Total Number of “Missed” Reinforcers, Scaled to Include Ranges Introduced by OutliersNote. The box plots in the left column show the median (the dark line in the middle), interquartile range (the scores between 25% and 75% in the boxes), the min and the max scores (the whiskers) and the outliers. The line plots in the right column show the means and standard errors.
Tables 1 and 2 display within-groups means, standard deviations, ranges, and medians, as well as inferential F ratios, p values, and effect sizes (partial eta-squared) for test variables and the Wilcoxon rank sum test statistic and p values for control variables. Data in the “control” segment of Tables 1 and 2 are intended to evaluate the extent to which there were significant between-groups differences in parameter values across variables known, or hypothesized, to influence responding during extinction (e.g., reinforcer value, baseline schedule value, baseline response rates, obtained rates of baseline reinforcement), which we attempted to control and evenly distribute across test groups through our matching and randomization process. Data in the “test” segment of these tables are intended to demonstrate the extent to which differences in our preextinction baseline preparations (i.e., inelastic/elastic, EO/AO) differentially affected performance during each participant’s exposure to extinction.
Following randomization, and as intended, we did not find statistically significant (p < .05) between-groups differences in the break points (M = 16.7 [EO], 17 [AO], 15.8 [inelastic], 17.9 [elastic]), Pmax values (M = 8.3 [EO], 7.5 [AO], 7.5 [inelastic], 8.4 [elastic]), or aggregate rates of baseline responding (M = 14.7 [EO], 13.6 [AO], 10.5 [inelastic], 17.7 [elastic]).
In the EO versus AO comparison, there were also no significant differences in baseline reinforcement schedules (M = FR 9.0 [EO], FR 9.1 [AO]) or aggregates of obtained rates of baseline reinforcement (M = 2.8 [EO], 2.0 [AO]). In the inelastic versus elastic comparison, and as intended, there were statistically significant (p < .05) differences in baseline reinforcement schedules (M = FR 3.5 [inelastic], FR 14.6 [elastic]) and aggregates of obtained rates of baseline reinforcement (M = 3.6 [inelastic], 1.2 [elastic]). Thus, all values associated with identified preextinction parameters suggest that our experimental preparation was sufficiently controlled to consider the independent effects of value-parameter manipulations during our test.
As shown in Table 2 and Figures 2 through 5, we found a statistically significant Price × Consumption interaction with total responses emitted (M = 76.8 [inelastic EO], 44.2 [elastic AO], 279.2 [inelastic EO], 42.8 [elastic AO]). That is, as seen in the second row of Figure 2 and the bottom row of Figure 3, participants who were under conditions of acute reinforcer deprivation (EO) responded significantly more than participants who were under conditions of acute reinforcer satiation (AO) in both elastic and inelastic conditions. Further, an increase in ratio requirements amplified the effects of both deprivation and satiation such that the proportional differences in responding between EO and AO conditions were significantly greater in the elastic condition relative to the inelastic condition. Said differently, pairing an elastic (thin) schedule of reinforcement with an AO was the most effective way to decelerate response rates during extinction. Intriguingly, pairing an elastic (thin) schedule of reinforcement with an EO was the most effective way to accelerate response rates during extinction.
Figure 2 Individual Data Points and Means Comparisons Across Four Representative MeasuresNote. In addition to variables listed on the Y-axis, means, medians, and group sizes are displayed in the left-column graphs. The dotted horizontal line in top-panel graphs display mean baseline response rate and indicate the extent to which responding during extinction might be considered a burst. Importantly, y-axis scales for graphs in the right column are different than the scales in the left column. The differences are intended to allow readers to see nuanced differences in between-groups patterns. Ext = extinction; S^R+^ = reinforcers
Figure 3 Interquartile Ranges and Means Comparisons for Peak Response Rates, Scaled to Include Ranges Introduced by OutliersNote. The box plots in the left column show the median (the dark line in the middle), interquartile range (the scores between 25% and 75% in the boxes), the min and the max scores (the whiskers) and the outliers. The line plots in the right column show the means and standard errors.
We found no significant interaction with peak response rates (M = 12.8 [inelastic EO], 8.7 [inelastic AO], 24.4 [elastic EO], 7.7 [elastic AO]), peak response rates considered as proportions of baseline (M = 1.6 [inelastic EO], 0.9 [inelastic AO], 1.3 [elastic EO], 0.4 [elastic AO]), total reinforcers “missed” during extinction (M = 48.2 [inelastic EO], 8.7 [elastic AO], 17.1 [inelastic EO], 2.9 [inelastic AO]), or latencies to extinction (M = 213.3 s [inelastic EO], 114.4 s [inelastic AO], 467.4 [elastic EO], 119.8 s [elastic AO]).
As displayed in Table 1, we considered group participation in relation to within-construct variation of each value parameter (i.e., consumption, unit price) in isolation. That is, we considered between-groups differences for participants who were randomized to EO and AO conditions. We then considered between-group differences for participants who were randomized to inelastic and elastic conditions.
When we manipulated preextinction consumption parameters relative to demand intensity (i.e., EO/AO), we found statistically significant (p < .05) differences in extinction performances across all variables considered. Specifically, robust differences were observed for peak response rates (M = 18.6 [EO], 8.2 [AO]), peak response rates considered as proportions of baseline responding (M = 1.4 [EO], 0.6 [AO]), total responses emitted during extinction (M = 178 [EO], 43.5 [AO]), total reinforcers “missed” during extinction (M = 32.6 [EO], 5.8 [AO]), and latencies to extinction (M = 340.4 s [EO], 107.9 s [AO]). In the right-hand columns of Figures 2 through 5, this finding is reflected by the fact that open circles (i.e., performances in the EO condition) are consistently elevated above closed squares (i.e., performances in the AO condition) and that EO and AO data paths never cross.
In contrast, when we manipulated preextinction value parameters associated with unit price (i.e., inelastic/elastic), we did not find statistically significant differences in peak rates of responding (M = 10.8 [inelastic], 16.02 [elastic]), in peak rates of responding considered as proportions of baseline (M = 1.2 [inelastic], 0.9 [elastic]), or in differences in latencies to extinction (M = 154.6 s [inelastic], 293.6 s [elastic]). Thus, even though peak rates of responding considered as a proportion of baseline increased as ratio requirements decreased (i.e., as schedules got richer/became inelastic) in both EO and AO conditions in the top rows of Figures 2 and 3, we could not rule out the possibility that observed differences were attributable to uncontrolled between-groups variance. For the same reason, observed decreases in peak rates of responding (bottom row of Figure 3) and latency to extinction (bottom row of Figure 4) could not be attributed to decreases in ratio requirements.
Figure 4 Interquartile Ranges and Means Comparisons for Total Responses Emitted and Latency to Extinction, Scaled to Include Ranges Introduced by OutliersNote. The box plots in the left column show the median (the dark line in the middle), interquartile range (the scores between 25% and 75% in the boxes), the min and the max scores (the whiskers) and the outliers. The line plots in the right column show the means and standard errors.
We did, however, find significant differences in total responses emitted during extinction (M = 60.5 [inelastic], 161.02 [elastic]) and total reinforcers “missed” during extinction (M = 28.47 [inelastic], 9.97 [elastic]). That is, observed decreases in total responses emitted during extinction (second row of Figure 2; top of Figure 4) and corresponding increases in total reinforcers “missed” during extinction (bottom row of Figure 2; Figure 5) could be attributed to decreases in ratio requirements. Said differently, participants assigned to elastic conditions consistently worked harder (i.e., they responded more often) to obtain less information about extinction (i.e., they contacted fewer reinforcer omissions).
During extinction, 14.4% (10 of 69) of all participants emitted a response pattern that could be categorized as an extinction burst, according to the definition offered in our Method section. Because only 10 bursts occurred across all experimental groups, no statistical inference is reported for this variable (see Table 3). We observed extinction bursts for 26.67% (4 of 15) of inelastic EO participants, 5.26% (1 of 19) of inelastic AO participants, 27.78% (5 of 18) of elastic EO participants, and 0% (0 of 17) of elastic AO participants. When we explored the potential isolated influence of manipulations on price and consumption, we found no apparent differences in bursting between inelastic (14.71% [5 of 34]) and elastic (14.29% [5 of 35]) groups. In contrast, differences in bursting between EO (27.27% [9 of 33]) and (AO 2.78% [1 of 36]) groups were more robust.
In this study, we manipulated preextinction variables in accordance with two empirical representations of value (i.e., consumption relative to QFree, unit price relative to Pmax). We found that each could individually influence target responding during extinction and that they interacted to influence performance in ways not predicted at the study onset. We also found that no single manipulation guaranteed the occurrence or nonoccurrence of bursting for all participants. Each finding merits discussion.
First, we found that consumption (relative to Qfree) was the variable that most consistently produced robust between-group differences in extinction across all variables measured. Specifically, individuals whose consumption prior to extinction had not approximated equilibrium were more likely both to persist in (as evidenced by differentially high response and latency outputs) and to escalate responding (as evidenced by the proportion of baseline measures and the prevalence of bursting) prior to response elimination. One apparent and important implication of this finding relates to demand intensity. Specifically, there appears to be a quantifiable threshold of reinforcer consumption (i.e., Qfree) that, if achieved or surpassed, can circumvent many of the adverse collateral effects of extinction. That is, there appears to be an inverse relation between the extent to which participants’ needs have been met (so to speak) and the extent to which the operation of extinction is problematic (e.g., Goh et al., 2000; Marcus & Vollmer, 1996; cf. Lambert et al., 2021).
A second important finding is that baseline unit price (relative to Pmax) did not produce significant differences in variables associated with persistence and escalation (i.e., proportion of baseline responding, bursting). However, they did produce significant differences in measures that were not relative (i.e., total responses emitted, reinforcers “missed”). Said differently, participants in the elastic group worked harder to obtain less information during extinction (a potentially frustrating experience).
To the extent to which extinction is viewed more favorably when it produces an immediate and precipitous drop in responding relative to baseline, one important implication of this second finding is that there does not appear to be any value added, from a social-validity perspective, to arranging preextinction baseline schedules that ensure target responding has first contacted elastic reinforcement schedules. By extension, it may be the case that placing challenging behavior on thin schedules of reinforcement to induce ratio strain (without consideration of Pmax) would be an equally fruitless preextinction endeavor.
Paradoxically, decades of research inspired by behavioral momentum theory have demonstrated that dense schedules of reinforcement enhance context-specific response persistence (Nevin & Grace, 2000). One apparent implication of this fact is that when reducing persistence is desirable, it is better to intervene on behavior maintained by thin schedules of reinforcement. Notwithstanding, persistence is a transient phenomenon. Despite reinforcer density and relative differences in resistance to change, contact with extinction alters baseline patterns of challenging behavior fairly quickly (e.g., Fisher et al., 2018, 2019; Lambert et al., 2016). Thus, the finding that lean schedules yield less persistent responding is not necessarily clinically actionable.
Relevant to this point, translational researchers who have studied the differential effects of dense and thin schedules on the persistence of challenging behavior will often, in the service of science, keep participants in a countertherapeutic baseline for longer than what is clinically prudent (i.e., after functional analysis). The purpose of delaying treatment in these paradigms is to establish context-specific histories with functional reinforcers so that theory-informed predictions relevant to intervention can be tested. In these studies, relative reductions in persistence are most robust after responding has been artificially accelerated by intermittent schedules and data have been transformed into proportion-of-baseline measures. The differences are more equivocal when considered in absolute terms (e.g., Lambert et al., 2016). Consequently, the methods used in these studies should not be considered a model for clinical practice (i.e., interventionists should neither reinforce challenging behavior on intermittent schedules nor keep their clients in countertherapeutic baselines for longer than is necessary). This is especially true in light of our results and the partial reinforcement extinction effect (e.g., Baum, 2012; Shull & Grimes, 2006; Thrailkill, 2023).
A final point worth emphasizing from our results is that even though no extinction bursts were observed in the elastic AO condition, no single antecedent manipulation of value (i.e., either consumption relative to equilibrium or unit price relative to Pmax) guaranteed the elimination of bursts. Thus, although our data appear to suggest an effective pathway through which bursting can be mitigated (i.e., AO manipulation), substantially more refined and theoretically driven work clarifying the roles of each of multiple and dynamic interacting variables is required before an effective technology of mitigation can be expected (Fisher et al., 2023).
For example, substance-use research has reliably demonstrated that demand intensity and Pmax can be predictive of treatment success for specific intervention programs. That is, participants who consumed larger quantities of alcohol (Murphy et al., 2015) and nicotine (Mackillop et al., 2016) at QFree or who exhibited stronger demand to defend Qfree consumption patterns in the face of increasing costs were also more likely to relapse when competing incentives were arranged to disrupt consumption. Given these findings, it may be that functional reinforcers for challenging behavior that yield high demand intensities and/or large Pmax values will support behavior that is more persistent in the face of extinction and more susceptible to treatment relapse than functional reinforcers that yield low demand intensities. This possibility should serve as the focus of future research efforts.
A few limitations of this study should be noted. First, although we attempted to operate within a closed economy, we could not guarantee that this occurred for all participants. Second, our randomization process did not control for commodity type (i.e., some participants earned music or crafts, others earned food). Third, because the timing of extinction within appointments differed for AO and EO participants, the differential effects of fatigue on performance may be a plausible rival hypothesis for between-groups differences in response persistence. Fourth, the general use of prompting and rules in our study likely ensured that some elements of participant performance were rule-governed. Fifth, the use of verbal prompting during PRA control sessions likely deflated and possibly even punished responding. Sixth, because we only sampled one equilibrium point for each schedule value during PFRAs, our demand estimates are more vulnerable to extraneous influences than estimates generated by PFRAs with more conservative sampling.
As a final note, basic researchers have previously demonstrated how fluctuations in motivation can differentially affect resistance to extinction (e.g., Marx, 1963, 1971; Mueller & Davenport, 1970; Reynolds et al., 1952). Similarly, Gilroy et al. (2018), Kodak et al. (2007), and Roane et al. (2005) all demonstrated that allowing access to reinforcement outside of experimental sessions consistently decreased various economic value metrics (e.g., demand intensity, Pmax). Consequently, we should emphasize that neither our method nor our results are particularly novel. However, this study retains value because it demonstrates the potential clinical utility of understudied metrics unique to the operant demand framework and provides the first conceptual analysis, as far as we know, linking economic accounts of value to motivation and response persistence.
We would like to thank Dr. Greg Madden for the feedback he provided during the conceptualization of this project. We also thank Olivia Pierce, Brianna Campbell, Kelley Fowler, Amanda Kelley, Kristal Orta, Alyssa Broaddus, Caroline Collins, and Caitlin Price for their assistance with data collection and project management. Finally, we thank Shawnee Collins for logistical support.
National Institute of Child Health and Human Development, Grant/Award Number: 1R03HD099445-01A1
Statistical calculations, individual participant graphs, individual participant data, and disaggregated baseline data for each partcipant have been made available as Supporting Information in files D, E, F, and G.
Statistical calculations, individual participant graphs, individual participant data, and disaggregated baseline data for each partcipant have been made available as Supporting Information in files D, E, F, and G.