Applied Quantitative Analysis of Behavior: What It Is, and Why We Care—Introduction to the Special Section

Abstract

Science evolves from prior approximations of its current form. Interest in changes in species over time was not a new concept when Darwin made his famous voyage to the Galapagos Islands; concern with speciation stretches back throughout the history of modern thought. Behavioral science also does and must evolve. Such change can be difficult, but it can also yield great dividends. The focus of the current special section is on a common mutation that appears to have emerged across these areas and the critical features that define an emerging research area—applied quantitative analysis of behavior (AQAB). In this introduction to the “Special Issue on Applications of Quantitative Methods,” we will outline some of the common characteristics of research in this area, an exercise that will surely be outdated as the research area continues to progress. In doing so, we also describe how AQAB is relevant to theory, behavioral pharmacology, applied behavior analysis, and health behaviors. Finally, we provide a summary for the articles that appear in this special issue. The authors of these papers are all thinking outside the Skinner box, creating new tools and approaches, and testing them against relevant data. If we can keep up this evolution of methods and ideas, behavior analysis will regain its place at the head of the table!

Science evolves from prior approximations of its current form. Interest in changes in species over time was not a new concept when Darwin made his famous voyage to the Galapagos Islands; concern with speciation stretches back throughout the history of modern thought. The early Greek philosopher Anaximander (c. 610–546 bce), posited that land animals possibly descended from sea animals as an adaptation to the earth’s drying up (Kirk et al., 1983; Krebs, 2004). Although this interpretation has been debated (Gregory, 2017, p. 34–35), it nevertheless points to an early recognition that species are not static—and that some mechanism drives their change. This view may have been displaced by the essentialism of Plato (c. 428–348 BCE) and Aristotle (c. 384–322 bce), but evolutionary thought remained commonplace among elite Greeks through the Hellenistic era (Mayr, 1982). Although these musings were in line with evolution, they fell short of a comprehensive theory.

Philosophical thought on speciation, however, may have been the primordial ooze from which the ideas that became the backbone of evolutionary thought were selected. Lamarckian transmutation of species emerged—which contended that simple forms of life were generated and pushed by a “life force” towards greater complexity (Bowler, 2003). Although he did not believe in a common ancestor, Lamarck acknowledged that environmental pressures interacted with this process to create intergenerational adaptions to environmental circumstances—which created differing species. Darwin’s natural selection (Darwin, 1859) deploys this notion of intergenerational selection by environmental pressures, adding a clear mechanism (i.e., differential survival/reproduction) and greater contiguity (i.e., a common ancestor). Whereas the process of evolution and Darwin’s approach was eventually selected by the scientific community, the mechanism (i.e., natural selection) was not accepted until its combination with Mendelian Genetics in the modern synthesis (Huxley, 1974)—the heart of the evolutionary framework dominant to this day.

Behavioral science also does and must evolve. Such change can be difficult, but it can also yield great dividends. For example, the evolution of Herrnstein’s quantitative analysis of behavior from Skinner’s experimental analysis of behavior opened the door to sophisticated and precise approaches to theory development (Baum, 2002; Killeen, 1994). Likewise, the emergence of behavioral pharmacology (Laties, 2003) and applied behavior analysis (ABA; Baer et al., 1968) from their roots in the experimental analysis of behavior have yielded remarkable treatments for a range of conditions. Although a tome could be penned about the adaptations that these new environments have spurred (e.g., the acceptance of direct observation as a datum; Wolf (1993), the emergence of rapidly testable assays), the focus of the current special section is on a common mutation that appears to have emerged across these areas, and the critical features (Layng, 2019) that define an emerging research area—applied quantitative analysis of behavior (AQAB).

What is Applied Quantitative Analysis of Behavior?

Applied quantitative analysis of behavior is a new term, and thus deserves an introduction. It may be helpful to start with what is meant by each of the components in the title: What do “applied,” “quantitative,” “analysis,” and “behavior” mean? Doing so should not be construed as some sort of checklist for what defines research in the area. As a science, we have tried that approach in ABA (based on Baer et al., 1968), and there is reason to believe that that was a bad idea (Critchfield & Reed, 2017). Instead, we will outline some of the common characteristics of research in this area, an exercise that will surely be outdated as the research area continues to progress.

Working backwards, what do we mean by behavior? Defining behavior might seem to be a simple task for a behavior analyst, but maybe it’s not. Topography-based definitions of directly observed behavior are common in ABA. This approach dates back to the early recognition that mechanical recording of behavior in natural settings is often not feasible (Wolf, 1993) and represents a methodological compromise that likely facilitated applied behavior analysts’ entry into a wide range of relevant settings. The compromise, however, built a structural measurement tradition that markedly differed from the functional measurement tradition prominent in the experimental analysis of behavior, wherein responses are typically defined by their impact on the environment (e.g., closing a circuit behind a lever or response key) rather than their physical properties (e.g., the rat depressing the lever enough to close the circuit with its rear is treated as equivalent to closing it with their paw). Moreover, as the quantitative analysis of behavior emerged, measures such as time allocation (Baum & Rachlin, 1969) by animals responding under concurrent schedules emerged - separating measurement from the operative contingencies. Respecting the individuality of responding, many studies in behavioral pharmacology and other areas have adopted proportion-of-baseline as viable measure of change (Branch, 1991). And in areas of decision-making research, such as behavioral economics, self-report of hypothetical choices have been profitably used (Madden et al., 1997; Odum, 2011; Rachlin et al., 1991). This list is far from exhaustive. The key point is that data that can be useful for AQAB need not be restricted in form. Instead, the value of data to be used should be defined more pragmatically. If the use of a particular measure can be justified as revealing important order in nature, who are we to oppose it based on some outdated checklist-based approach to judging science? The responsibility to establish the value of the data, however, falls on the investigator.

Continuing from the back, what is the analysis of behavior? This also seems simple. Baer et al. (1968) likened their analytic dimension to establishing experimental control over behavior. We can be thankful that they did not hold their own work to that criterion or we would have been deprived of the solely correlational Meaningful Differences (Hart & Risely, 1995), which, it can be argued, is the most influential behavior analytic research to date (i.e., if measured by the number of times references in presidential speeches). Moreover, there are endless examples of correlational AQAB research that has added to our understanding of behavior and/or clinical conditions. The commonality between the experimental and correlational analyses of behavior in AQAB to date rests solidly on the demonstration of order in natural phenomena. Thus, it does not matter if the demonstration of order is experimental (Bickel et al., 2011b; Koffarnus et al., 2013; Rung & Epstein, 2020; Sofis et al., 2016; Sweeney & Shahan, 2013), cross sectional (Bruce et al., 2016; Madden et al., 1997), or correlational (Jarmolowicz et al., 2014; Sheffer et al., 2014; Vollmer & Bourret, 2000; Washio et al., 2011) if order is highlighted, the study can classify as the experimental analysis of behavior.

We must next consider the quantitative analysis of behavior. This is a well-established area of research centered around a shared love of finding theoretical order in observed behavior via the use of sophisticated quantitative models. Exemplars of this tradition can be seen at the annual meeting of the Society for the Quantitative Analysis of Behavior (SQAB), held just prior to the Association for Behavior Analysis International’s annual convention. We encourage anyone who can to attend SQAB at least once, or if you cannot attend, examine them in their published form in a special issue each year. Most of the models used in AQAB were developed and refined by this research area—thus, AQAB owes a great debt to the quantitative analysis of behavior. Given the robustness of the area, and the importance of basic science to developing actionable interventions, regular consultation with those proceedings should be on everyone’s to-do list.

Lastly, let’s consider AQAB. We would argue that AQAB is a distinct research area born out of both ABA and the quantitative analysis of behavior. It is distinct from the quantitative analysis of behavior in focus. In particular, rather than a focus on the development and refinement of theoretical statements (Smith, 2015), AQAB builds from these theories and analyses to understand issues of societal concern (Baer et al., 1968). Many researchers working in this tradition have worked absent a formal title for the endeavor. For example, extensive research has been conducted applying behavioral economic concepts and analyses such as delay discounting and demand to understand clinically relevant behavior such as substance use disorders (Bickel, Landes, et al., 2011a; Greenwald & Steinmiller, 2009, 2014; Yoon et al., 2021), and other poor health behaviors such as that manifest in obesity (Epstein et al., 2010; Stojek & MacKillop, 2017). These analyses and tools have given us sensitive and formal approaches to assessing abuse liability of drugs (Hursh et al., 2005; Hursh & Winger, 1995) and application of related analyses (e.g., probability discounting) have contributed significantly to our understanding of health behavior such as medication adherence (Bruce et al., 2018a; Bruce et al., 2018b; Jarmolowicz et al., 2017).

AQAB remains distinct from ABA in two respects: (1) the methodological differences related to behavior and the analysis of behavior described above may prevent some from considering this work under the ABA umbrella; and (2) AQAB is defined “by the interest society shows in the problem being studied” (Baer et al., 1968, p. 92) rather than in the subject or client benefiting from the research—as is often the interpretation of Baer et al.'s (1968) applied dimension. Although many of these analyses (e.g., applications of the matching law to athletic performance; Vollmer & Bourret, 2000) have continued to be published alongside more traditional ABA articles, they are often deemed translational and given separate editorial consideration. We argue that AQAB is a more accurate designation, particularly given the wide range of definitions of translational research.

How is AQAB Relevant to Theory?

Much of science is analogical, ranging from the ordinary language meaning of reinforce, to reflex reserves, internal clocks, and relational frames. Roediger (1980) listed three dozen analogies for memory, ranging from Plato’s wax tablet to Pribram’s hologram. What is the nature and role of such models? “A useful model then, represents the real world, not by correspondence or isomorphism, but by analogy, and this may be strong or weak” (Hesse, 2017, p. 305). Traditional scientific inference in psychology tends to be weak: “when I do x, y will change” as tested by null hypothesis statistics. The more data you collect, the more likely you are to find that the differences are “significant.” The best quantitative models make point predictions. The more data you collect, the more likely you are to find that they significantly deviate from the thing modeled. Mathematics thus puts a fine point on the dull pencil of analogy. Most of the quantitation in our field is descriptive—what physicists call “phenomenological”—as it attempts to find simple models to describe relationships: think of Herrnstein’s and Rachlin’s different hyperbolas, and the generalized matching law. These provide clarification but not understanding. For understanding, one requires a theory: a framework that in the best case includes efficient causes, mechanisms, and functions, along with the formal description provided by models. Such a theoretical analysis of behavior is at this point largely aspirational, but the excellent quantitative analysis of behavior we see in every issue of this journal affords us a large step toward it.

How is AQAB Relevant to Behavioral Pharmacology?

Like AQAB, behavioral pharmacology itself is a field that resulted from the marrying of behavior analysis and pharmacology. In general terms, behavior analysts study objective and observable behavior at the level of the individual, and this area has been described in some detail already. Pharmacologists, on the other hand, study how drugs and other chemical substances act on biological systems and how those systems respond to drugs. These two disciplines combine to form behavioral pharmacology. Behavioral pharmacologists rely on the principles of behavior analysis to explain behavioral effects of drugs. Though there may be some debate about how behavioral pharmacology began as a field in its own right, Peter Dews is often credited with its inception. Prior to Dews (1955), early behavioral pharmacology experiments involved unstructured observations of laboratory animals such as gross measures of locomotor activity, sleeping, and overt convulsions or sedation. In his clever experiment in 1955, Dews demonstrated that the effects of experimenter-administered pentobarbital on response rates depended on the schedule of reinforcement. Several important conclusions were drawn from this pivotal article. First, the effects of drugs on schedule-controlled behavior were observable at much lower doses than were required to result in grossly observable effects like uncoordinated movement, ataxia, or loss of righting reflexes. This gave behavioral pharmacologists a tool to evaluate drug effects under stable baselines (i.e., under steady-state conditions), and these baselines were quantifiable and sensitive to drug effects. Second, Dews found that pentobarbital had both rate-increasing and -decreasing effects on behavior depending on whether the schedule of reinforcement was a fixed-ratio or fixed-interval schedule. This was revolutionary for pharmacologists who largely had thought of drug effects through their interactions with a biological system and not as much as an interaction that also involved environmental factors.

Behavioral pharmacology experiments have become highly sophisticated in many ways, including the use of quantitative approaches. The matching law, behavioral-economic approaches, delay discounting, and other topics rooted in the experimental analysis of behavior quickly took hold in the laboratories of behavioral pharmacologists doing preclinical, laboratory research and shortly thereafter in applied laboratories and clinical trials. It is not possible to describe all the ways that AQAB is alive and well in the field of behavioral pharmacology, but some examples are worth highlighting. Within this special issue, Luc, Pizzagalli, and Kangus used principles of the generalized matching law and signal detection theory to confirm that individuals with anhedonia (i.e., loss of pleasure in previously rewarding activities and a core symptom of several psychiatric illnesses) demonstrate a blunted bias toward the alternative that provides richer access to rewards compared with control participants. From an applied perspective, a computerized task like the one used by these researchers could be used to detect ongoing and perhaps predict future occurrences of anhedonia as well as being used as a tool to detect treatment response during drug development. Another well-established finding in behavioral pharmacology research is that individuals with substance-use disorders display steeper discounting of delayed outcomes compared with control participants and these individuals discount hypothetical drug outcomes more steeply than hypothetical monetary outcomes (e.g., Amlung et al., 2017; Madden et al., 1997). Steep discounting predicts initiation of smoking in adolescents and young adults (Audrain-McGovern et al., 2009), progression and escalation of substance misuse in adolescents (Khurana et al., 2015), and treatment effectiveness and recidivism (Krishnan-Sarin et al., 2007; Washio et al., 2011; Yoon et al., 2007). Researchers are now using delay discounting and related behavioral-economic procedures and quantitative approaches to determine whether treatment strategies like episodic future thinking, mindfulness, choice bundling, and others can change discounting in individuals with substance-use disorders and whether this corresponds to drug abstinence and prevention of relapse (e.g., Stein et al., 2016).

How is AQAB Relevant to ABA?

The relevance of AQAB to ABA has historically taken one of two general forms: description of clinical or nonclinical behavior of interest and prospective simulation and testing of the conditions predicted by relevant quantitative models of behavior to improve clinical outcomes. Glimpses of a newer, third form of relevance between AQAB and ABA can be seen in recent translational studies for which clinical outcomes have failed to capture predicted yet potentially weak effects of certain independent variables. Thus, this third form of relevance between the two has as much bearing on guiding future AQAB work as it does on affecting practice.

Quantitative models of behavior have a longstanding tradition in ABA to describe and interpret both clinical and nonclinical behavior of interest. Perhaps nowhere else in the realm of the quantitative analysis of behavior is this truer than relating the matching law to clinical outcomes. Clear examples of this can be found throughout the ABA literature when researchers conceptualize the efficacy of treatments for problem behavior that are based on differential reinforcement of alternative behavior that do not arrange extinction for problem behavior. As just one example, Piazza et al. (1997) showed that the problem behavior of two participants remained low and compliance elevated when compliance resulted in positive reinforcement even though problem behavior continued to produce escape (see Payne & Dozier, 2013, for a review of such treatments, and Vollmer et al., 2020, for related commentary). The authors stated, “One potential explanation of these findings is that the relative rates of compliance and destructive behavior were a function of the relative value of the reinforcement produced by each response” (p. 293), which is nothing more than a restatement of the concatenated matching equation (Baum & Rachlin, 1969). Likewise, the matching law and other quantitative models of behavior have routinely been used outside clinical contexts to describe everyday behavior of interest (e.g., allocation of two- and three-point shots by college basketball players; Vollmer & Bourret, 2000).

A related but distinct relation between AQAB and ABA takes the form of prospective simulation and testing of the conditions predicted by relevant quantitative models of behavior to improve clinical outcomes. This second relation between AQAB and ABA is perhaps most clearly demonstrated by clinical evaluations of the predictions of behavioral momentum theory (BMT) as it relates to resurgence (Shahan & Sweeney, 2011). For example, Fisher et al. (2018) reanalyzed the data from four translational studies designed around the quantitative predictions of BMT for mitigating the resurgence of problem behavior and concluded that applications of BMT “can substantially improve the durability of common treatments for destructive behavior” (p. 281). Quantitative models of relapse and other problematic patterns of responding (e.g., resurgence as choice [Shahan & Craig, 2017; Shahan et al., 2020]) suggest alternative strategies for improving clinical practice, some of which have been explored through model simulation (e.g., Greer & Shahan, 2019) and retrospective quantitative analysis (e.g., Shahan & Greer, 2021).

When clinical or otherwise translational evaluations fail to capture the predicted effects of an independent variable described by a quantitative model of behavior, those results have the potential to guide future AQAB work, suggesting a third potential relation between AQAB and ABA. As an example, Greer et al. (2020) recently failed to detect an effect of treatment duration on the resurgence of problem behavior across six participants, findings at odds with the predictions of some quantitative models of relapse (e.g., BMT). Replication of such findings may not only guide the future selection and evaluation of other promising techniques for improving longstanding applied problems, but such data may also facilitate the refinement of relevant quantitative models of behavior via more targeted experimentation in the laboratory (i.e., reverse translation).

How is AQAB Relevant to Health Behavior?

Behavior analysts often work to facilitate individuals’ engagement in healthy behavior. Behavioral health is the sort of “under the dome” issue towards which some behavior analysts have long suggest we pivot (Friman, 2010). It is also an area that includes many researchers who may not be behavior analysts, but they are behavior-analysis adjacent. For example, behavioral health/health psychology programs reportedly cover Skinner’s work in their training (Kathy Goggin, personal communication, 2015). These are often skilled researchers who don’t necessarily appreciate the single-case designs that we use to evaluate our interventions but are open-minded to our interventions and their theoretical backing.

Quantitative analyses provide a concise shorthand of our theoretical positions that transcend the methodological differences that may divide us. If our colleagues believe impulsivity may govern poor health decisions, redirecting the conversation to considering patients’ ability to value future rewards is not a heavy lift (Bickel et al., 2012; Bickel & Yi, 2008), and has been successful across a wide range of health behaviors (Rung et al., 2019). For example, delay discounting is associated with obesity (Bickel et al., 2014; Jarmolowicz et al., 2014; Rasmussen et al., 2010; Weller et al., 2008), medication adherence (Epstein et al., 2021), and exercise (LeComte et al., 2020; Tate et al., 2015). In fact, delay discounting is even reduced by exercise (Sofis et al., 2016; Strickland et al., 2016). If our colleagues believe that risk tolerance affects medication uptake, models built on the back of probability discounting may be a solution (Bruce et al., 2016; Bruce et al., 2018a; Bruce et al., 2018b; Jarmolowicz et al., 2016; Jarmolowicz et al., 2018a). If our colleagues believe that patients don’t take their medications because they don’t value them, demand curves may provide an answer (Jarmolowicz et al., 2020). If our colleagues are puzzled by the dire issue of vaccine hesitancy, behavioral economic models seem to provide some valuable information (Hursh et al., 2020; Jarmolowicz et al., 2018b; Strickland et al., in press). This list is by no means exhaustive. The point is that our quantitative models can be successfully turned to help colleagues in behavioral health. This remains an emerging area—yet one that we could fruitfully find a home for AQAB.

Summary of the Special Section

“Math,” you might think, “is fine in theory, but in practice is too precise and brittle to be of much use.” If that is what you think, we hope that this special section will change your mind. It provides a sampling of creative and clearly described quantitative approaches of great potential for the analysis and synthesis of behavior. You may find some useful, and you may even be inspired to create your own.

The generalized matching law is a quantitative analysis that fills the pages of the Journal of the Experimental Analysis of Behavior (JEAB), totaling some 350 articles. How can it be used in an applied context? Most subjects rationally prefer the better of two alternatives. But what if they have difficulty deriving hedonic value stimuli (i.e., have anhedonia), as is the case with individuals suffering from major depressive disorder? Luc, Pizzagalli, and Kangas studied this issue and confirmed that people experiencing anhedonia are less biased toward the better alternative. These authors used this finding to develop a translational approach for measuring anhedonia in neuropsychiatric disorders to more precisely gauge the effectiveness of treatments.

Jack McDowell is an expert, creative quantitative analyst, and he is also a practicing clinician. We can think of no more perfect author for this review of 60 years of basic research on choice as relevant to clinical problems. Four decades ago, Jack published an influential article in the American Psychologist suggesting four new clinical interventions based on Herrnstein’s matching law (McDowell, 1982). In this special section, he reviews those and many other implications of quantitative approaches for clinical issues. He then introduces the reader to a line of work he and his students have been pursuing through the 20^th century—recovering the basic operant phenomena in animated artificial organisms (AOs)—his evolutionary theory of behavior dynamics. He shows how AOs can evolve characters that exhibit psychopathologies, an analysis of which can suggest novel treatment approaches.

In a following article, Morris and McDowell go into detail about the construction and evaluation of AOs to better understand the subtypes of automatically reinforced self-injurious behavior and to simulate potential treatments for them. This approach seeks to provide insight on the mechanisms that separate clinically distinct subtypes of automatically reinforced behavior—work that is both important for our conceptual understanding of such behavior yet also potentially impossible to conduct through other means.

We confess that we procrastinated in contributing to this introduction; but who among us hasn’t at some time? Sokolowski and Tonneau note that procrastination has received little attention from quantitative behavior analysts compared to, for example, delay discounting. In a well-designed experiment, they showed that in general students procrastinated in completing tests, their degree of procrastination was constant over a series of such tests (i.e., it has the character of a trait), and that the group scallop was well-described as a hyperbola. This is bad news for us, because some of us thought we would outgrow our tendency to procrastinate.

In a kind of Catch-22, when you are depressed, it is hard to get motivated to do anything, including seeking help for the depression. Trusty, Swift, and Rasmussen address this problem by outlining how behavioral-economic analyses can enlighten us as to what components of help-seeking behavior (i.e., sensitivity to gains and losses, response costs of various types, biases) are largely to blame. Targeted therapies might then be designed for each individual; it is a kind of theoretical functional analysis.

Behavior analysis is an N-of-1 science. This doesn’t mean only one subject, but rather treating each subject in its own right, and not immediately lumping them together. Cox, Klapes, and Falligant provide an important extension of this concept. They apply it to over 2,000 individuals and over 8 million observations, testing whether the generalized matching law applies to each, what its parameters are, and how it can inform us of other aspects of behavior. Behavior analysts, welcome the age of Big Data, done right!

Delay discounting has become a cottage industry (as Len Green told one of us 20 years ago). That doesn’t mean it should use only the tools you’d find in a typical cottage. Berk, Gupta, and Sanabria introduce immediacy premium, a creative new measure that can be used to calculate degree of discounting. One of the great strengths of this approach is that it linearizes the effect of delay on choice. Check it out. You may decide it is time for a new loom in your cottage!

Machines are getting smarter than people. Why are computers not used more extensively in psychology in general and behavior analysis in particular? Bailey, Baker, Rzeszuek, and Lanovaz show how to do it. They applied machine learning to understand and improve a paper analysis of the functions controlling behavior. When the first pass was good but not perfect, they created artificial samples with which to improve the performance of their artificial neural net. It then outperformed all other models. Their research provides insight into the conditions that should be present in functional analysis. A clever use of AQAB.

Nobel-prize–winning scientist Percy Bridgeman once stated that science is “doing one’s damnedest with one’s mind, no holds barred.” We are proud that the behavior analysts in this special section are doing just that. They are all thinking outside the Skinner box, creating new tools and approaches, and testing them against relevant data. If we can keep up this evolution of methods and ideas, behavior analysis will regain its place at the head of the table!

Declarations

Conflicts of interest

The authors have no potential conflicts of interest to disclose.