What serves as feedback to the individual and provides the basis for future behavior in similar situations?

Stimulus Generalization

Stimulus generalization occurs when a response that has been reinforced in the presence of one stimulus occurs for the first time in the presence of a structurally similar stimulus (Fields, Reeve, Adams, & Verhave, 1991; see Honig & Urcuioli, 1981, for a review). For example, consider an individual having an embarrassing experience in a nightclub (e.g., being “turned down” when requesting to dance with someone). If the individual worries that “everyone in the nightclub saw this interaction and is now laughing” at him, feelings of relief likely will result after leaving the situation (i.e., negative reinforcement via escape). Because of this history of negative reinforcement, the individual may leave future situations at the first instance of distress or even come to avoid such situations altogether (e.g., avoidance of inviting someone to dance, or avoidance of the nightclub altogether). Following from these experiences, a stimulus generalization account of social anxiety disorder helps explain why structurally similar settings such as parties or informal social gatherings may result in escape or complete avoidance for this individual even though these situations had not previously produced anxiety, as with the embarrassing experience at the nightclub in the example above.

Thus, stimulus generalization is a useful concept that describes how a response may begin to occur in a variety of contexts without being directly reinforced in those contexts. Consequently, this concept provides the basic explanation of how social anxiety disorder may generalize without any further operant or respondent conditioning events. The processes underlying generalization, however, often are considerably more complex than simple structural similarities. As a result, more complex behavior principles are needed.

Generalization

Stimulus generalization occurs when the same behavior is evoked by similar but not identical antecedents (Catania, 2012). In the above case example, stimulus generalization occurred when the mother and sister correctly implemented the same DRA procedure to teach the 8-year-old child how to cross a variety of driveways that differed in stimulus features (e.g., some had curbs while others did not, width of the crossing varied, bushes partially blocked the view of some but not others). Response generalization happens when untrained responses occur that are functionally equivalent to the trained behavior (Catania). In the above case example, response generalization would occur if the mother and sister gave a slightly different rule that functioned in the same way. For example, instead of saying “If you cross the driveway safely, you’ll get a token,” they might say “Remember to look both ways when you cross the driveway.” The words changed, but these phrases are functionally equivalent.

It is important to specifically program for generalization because the trained person is likely to respond to new situations and to implement new functionally equivalent teaching procedures after the behavior analyst is no longer providing close oversight. Therefore, during initial training, the behavior analyst should have staff or caregivers practice implementation in new settings and under slightly different antecedent conditions, providing feedback and reinforcement under these generalization conditions. Additionally, multiple exemplar training consisting of implementation of the same procedure but with slightly different skills may prove useful. Periodic probes can occur to ensure the skill is durable over time, occurs in a variety of contexts, and spreads to a variety of behaviors.

Ducharme and Feldman (1992) provided an excellent example of programming for generalization in a training setting. In this study, the authors compared the use of programming with multiple stimuli and with multiple learners to an overall general case training approach (i.e., multiple exemplar training). General case training consisted of multiple exemplar training with multiple client programs in a simulated situation and was successful in promoting generalized use of teaching skills across clients, settings, and client programs. Single case training involved a single client program exemplar with simulated clients and performance-based training using real clients as the trainees. This general case training was found to be the most effective in the promotion of generalization.

10 The role of similarity in learning

One feature that clearly distinguishes the conceptual level from the symbolic is that similarity plays a central role on the conceptual level. Judgments of similarity are central to a large number of cognitive processes. Similarity relations between objects or properties, for example, that 'green' is closer to 'blue' than to 'red,' can be represented by distances in conceptual spaces. The learning mechanism presented in the previous section, which is based on distances in conceptual spaces, would be cumbersome to capture in a nonarbitrary way by symbolic representations and it could only be modeled in a roundabout way on the connectionist approach [see, for example, Schyns (1991)].

The representations formed in artificial neuron networks tend to be difficult to interpret. One reason for this is that dimensions are normally not represented explicitly in connectionist systems. It is true that ANNs learn about similarities but, in general, they do so very slowly and only after an exorbitant amount of training. The main reason for this is the high dimensionality of ANNs [see, for example, van Gelder (1995), p. 371)]. The sluggishness of the learning is a result of each connection weight's being adjusted independently of all the others. In addition to this, the adjustments are normally made in very small steps in order to avoid causing instabilities in the learning process. The assumption that the connection weights learn independently is not realistic from a neuroscientific point of view.

Since the vectorial representations of conceptual spaces have a much lower dimensionality and hence many fewer parameters that must be estimated, learning different kinds of patterns can be speeded up considerably by exploiting the conceptual level. This is an aspect of the learning economy of categorization that is often neglected. In brief, using conceptual spaces as the representational framework facilitates learning in artificial systems. The geometric structure of a dimension functions as a constraint that will make learning more efficient than it would be, for example, in an unstructured artificial neuron network. Of course, the geometric structure must have some correspondence in the external world – otherwise, what is learned may be useless or even dangerous.

For example, an explanation of how stimulus generalization works may become complicated, if the associationist approach is adopted. Stimulus generalization is the ability to behave in a new situation in a way that has been learned in other similar situations. The problem is how to learn which aspects of the learning situations should be generalized. This is an enigma for both symbolic and associationist representations5. On the other hand, when conceptual spaces are used, the stimulus is represented as being categorized along a particular dimension or domain. The applicability of a generalization can then be seen as a function of the distance from a prototype stimulus, where the distances are determined with the aid of an underlying conceptual space.

One way of making learning in ANNs more efficient is to build in structural constraints when setting up the architecture of a network. In other words, one can reduce the dimensionality of the learning process by making neurons dependent variables. However, adding structural constraints often means that some form of information about the relevant domains or other dimension-generating structures is added to the network. Consequently, this strategy presumes a conceptual level in the very construction of the network. For example, one can use the technique of principal components in ANNs, which exploits redundancies in input data [see, for example, Schyns (1991), pp. 471–472, Schyns, Goldstone and Thibaut (1998), p. 15]. If the dimensions of the input data are correlated, principal component analysis finds the number (determined by the user) of orthogonal directions in the dimensions of the input data that has the highest variation. Thus, the first principal component is the spatial direction in the data set that has the highest variation and which thus is the maximally “explanatory” dimension. In this manner, the user can help himself or herself to some dimensional information that brings the representation of the ANN close to that of a conceptual space.

4.2.2 Stimulus Generalization Model

Almost from its inception, transfer research has been associated with the concept of stimulus generalization developed from the behaviorist laboratory research of Pavlov’s classical conditioning paradigm. Stimulus generalization is the evocation of a nonreinforced response to a stimulus that is very similar to an original conditioned stimulus. The stimulus generalization model presupposes identical elements that enable generalization to occur. Stimulus generalization, then, can be viewed as a basic physiological learning “theory” explanation of how transfer occurs. Despite this historical association with generalization, virtually no recent empirical or theoretical work has been conducted.

Generalization

Whereas discrimination entails discerning differences, generalization entails glossing over differences. ‘Stimulus generalization occurs when behavior becomes more probable in the presence of one stimulus or situation as a result of having been reinforced in the presence of another stimulus or situation’ (Martin & Pear, 1999, p. 145). This can occur due to physical similarity or due to conceptual learning. An example based on physical similarity is that pigeons that have been reinforced in the presence of a yellow light also respond in the presence of a green light. Pigeons have excellent color vision.

Response generalization ‘… occurs when a behavior becomes more probable in the presence of a stimulus or situation as a result of another behavior having been strengthened in the presence of that stimulus or situation’ (Martin & Pear, 1999, p. 149). This can occur due to physical similarity or due to conceptual learning. For example, having learned a forehand stroke in tennis facilitates performing a forehand stroke in squash or racquetball.

1 Stimulus Generalization and Discrimination Learning

Similar levels of responding to male and female quail appears to be an example of stimulus generalization from one sex to the other. As I described earlier, if males are presented with visual access to a female just before a chance to copulate with the female, the males will come to approach and remain near the female visual cues. Once this social proximity behavior has been established to female cues, the substitution of a male stimulus bird behind the window will elicit similar responses (Nash, Domjan, & Askins, 1989). Thus, social proximity behavior conditioned to female cues strongly generalizes to male cues.

Can males ever tell male and female quail apart, and how do they learn to do so? With sufficient social experience, male quail do come to respond differentially to the sex of conspecifics. As other forms of discrimination learning, discrimination between stimulus males and stimulus females can be achieved by differential reinforcement. The subjects have to be exposed to female cues paired with copulatory reinforcement and male cues presented in the absence of copulatory opportunity (Nash et al., 1989). Discriminative performance improves with increased numbers of female-reinforced trials and with increased exposure to male stimuli in the absence of reinforcement (see Nash et al, 1989).

The stimulus generalization of sexual learning, and subsequent discriminative performance, are illustrated by an experiment by Domjan and Ravert (1991). On each of the first 19 days of this experiment, the subjects received a reinforced trial that consisted of exposure to a female stimulus bird behind a window, followed by the opportunity to copulate with that female. Two test trials were then conducted, one with a female bird behind the window and the other with a male stimulus bird. The results of these tests are summarized by the first two bars in each panel of Fig. 4. The behavior of the male subjects was measured in four different ways. We measured the total percentage of time the subjects spent near the window, the number of times they entered the criterial zone in front of the window, how long they spent in the criterial zone per entry, and locomotor activity in the criterial zone. Notice that during the first pair of tests, the subjects responded similarly to male and female stimulus birds. These results illustrate that the responding that had developed to the stimulus females substantially generalized to the stimulus males.

After the first test series, the subjects were given nonreinforced exposure to male stimulus birds. On each of the next 16 days (not shown), a male stimulus bird was placed in the side compartment, and the window was opened for 75 min. At the end of the 75 min, the window was closed and the subjects remained in their chambers until the next day without sexual reinforcement. The effects of these nonreinforced exposures to the male stimulus birds were assessed in tests with male and female stimulus birds at the end of the experiment, the results of which are summarized by the bars to the right of each panel of Fig. 4. This time strong differential responding occurred. The subjects spent a much larger percentage of their time near the window when a stimulus female was present behind the window than when a stimulus male was on the other side. The stimulus female stimulated fewer entries into the criterial zone than the stimulus male, but the subjects spent much more time in the criterial zone on each entry. The stimulus female also elicited less locomotion in the criterial zone.

The various responses that were measured during the tests conducted at the end of the experiment indicate that when a female was visible on the other side of the window, the subjects approached the window and stayed there. The subjects also approached the window when a stimulus male was visible, but when they saw a stimulus male they did not remain near the window but kept moving about. Thus, only the stimulus female came to elicit social proximity behavior. Other experiments have shown that nonreinforced exposure to male stimuli is necessary for the development of this discriminative performance (see Nash et al., 1989).

A Conventions Adopted in Developing the Model

Some of the implications of our Spencian model of conceptualization were examined with computer simulations of the experiments previously described. Several conventions were adopted in generating these simulations. One of our first decisions concerned how to represent similarities within and between categories. Although many other options were available, we chose to represent stimuli within a conceptual category as uniformly spaced along a single, common dimension. We refer to such dimensions as "categorical dimensions." The distance between stimuli along a conceptual dimension is an inverse function of their similarity to one another. The left–right ordering of stimuli along the dimension is arbitrary. To simplify the model, we represented stimuli from different basic-level categories as if they fell along separate and orthogonal dimensions. We do not now have data that would allow us to quantify the similarity relations among the stimuli that we used in the preceding studies. Multidimensional scaling of stimulus similarity has proven to be highly productive in accounting for the behavior of humans categorizing complex visual stimuli (e.g., Nosofsky, 1992); this technique might productively be applied to the sorts of stimuli that we have used in our projects.

Our model adopts the Spencian notion that reinforced responding to a stimulus results in excitation accruing to that stimulus. In the model, excitation generated by reinforced responding to one stimulus generalizes to others along the same categorical dimension to the extent that the others are similar to the reinforced stimulus. Likewise, we assume that nonreinforced responding to a stimulus results in inhibition accruing to that stimulus and to similar stimuli on the same categorical dimension. Our simulations represent generalization from one stimulus to another along a categorical dimension as a decaying exponential function of the similarity between them (Shepard, 1987). The model also assumes faster acquisition of excitation than inhibition (see Herrnstein, 1966, p. 37; Rescorla & Wagner, 1972, pp. 85–86); thus, preasymptotically, the inhibitory gradient will be shallower than the excitatory gradient. We use the term "response tendency" to refer to the net value resulting from the combination of excitatory and inhibitory tendencies to an individual stimulus on the categorical dimension.

Trial-by-trial changes in excitation and inhibition in our simulations were modeled according to the general principles of the Rescorla-Wagner (1972) model. Specifically, the trial-by-trial changes in excitation and inhibition that accrue to individual stimuli reflect the product of a rate parameter and the distance between the current associative level and the associative asymptote. Two factors affect the level of response tendency in this simulation: (a) directly reinforced or nonreinforced presentations of stimuli, and (b) generalization from neighboring stimuli along the categorical dimension. Approach to asymptote is a function of the summed (direct + generalized) response tendency to a stimulus.

Our simulations modeled only the effects of categorical generalization on the tendency to respond to a particular stimulus. In an actual experimental situation, responding will be affected by the specific category to which a stimulus belongs and by any noncategorical attributes (such as shape, brightness, location, etc.) that the stimulus shares with others given in the experimental situation. For example, our simulations of the go–no go procedures of Experiment 7 can generally be expected to underestimate the amount of actual responding. This underestimation may be clearest in cases where the simulation results in net inhibition to an S– or to novel stimuli from the S– category, but the actual data show some tendency to respond to them. The last section in this chapter describes the full set of parameters and operations of our computer simulations.

Our simulations are not unlike the recent efforts of Gluck (1991) and Shanks (1991) in emphasizing stimulus generalization and in incorporating the Rescorla-Wagner theory of learning. These other simulations are different from our own, however, in that the association of elementary features to categories is their central explanatory principle (also see Medin & Schaeffer, 1978, and Pearce, 1988, for more on related approaches). In our simulations, the stimuli to be categorized are treated as indivisible wholes. 4 We are not prepared at this point to make quantitative comparisons between other approaches and our own, nor are we ready to say that our general model incorporates all of the many elements that are necessary to account for complex categorization behavior. We wish only to show how a very simple set of principles with a long history in learning theory can account for a wide range of categorization phenomena.

Stimulus equivalence

Earlier discussions of generalization of stimulus control were limited to antecedents that are, for the most part, physically similar; accounts of stimulus generalization have used the physical similarity between training and novel stimuli to explain some instances of stimulus generalization. In reality, however, behavior is often under the stimulus control of stimuli that are physically very different from those involved in initial acquisition of behavior. Therefore, generalization occurs on bases other than physical similarity of stimuli. For example, a person with a phobia might respond fearfully when seeing any clown, no matter how physically dissimilar they may be but not when seeing someone wearing excessive, almost clownish make-up, and might also respond fearfully when hearing others mention clowns, seeing a colorful circus tent, or hearing circus music. In this example, all the different antecedent stimuli are functionally equivalent, since they all evoke fearful behavior, even though the stimuli are physically quite different. Moreover, the person can discriminate between stimuli that have some level of physical similarity (i.e., a clown and someone wearing excessive make-up). The person did not learn many of these fearful responses directly. So, how can behavior analysis begin to address this issue? Stimulus equivalence is a behavioral account of this phenomenon.

A set of stimuli is said to be equivalent when it shows the four properties of reflexivity, symmetry, transitivity, and equivalence. For example, suppose we consider three stimuli: A, B, and C. These stimuli would be said to be equivalent only if (1) the participant matches each stimulus to itself (reflexivity); (2) after learning that A is the same as B, the participant responds as if B is the same as A (symmetry); (3) after further learning that B is the same as C, the participant then responds as if A is the same as C (transitivity); and finally, (4) the participant responds as if C is the same as A (equivalence) (Sidman, 1994).

In experiments, stimulus equivalence is typically taught using matching-to-sample (MTS) training. In MTS training, several classes of stimuli are presented, often on a computer screen—for example, dogs (Class 1), trees (Class 2), and tables (Class 3). (Researchers often use experimenter-designated arbitrary stimulus sets, each comprised of nonsense syllables, symbols or visual stimuli without common semantic meaning, to avoid the effect of any prior-learned equivalence relationships (Doran & Fields, 2012; Rippy & Doughty, 2017). Each class contains stimuli in different formats, such as photos, line drawings, and written words. Hence, for each class there are several stimuli, such as a photo of a dog (A1), a line drawing of a dog (A2), and the written word “dog” (A3). During training, a sample stimulus, such as a photo of a dog (A1), is presented followed by the presentation of two or more comparison stimuli, such as the words “dog” (A3), “tree” (B3), and “table” (C3). The participant then selects one of the comparison stimuli, typically by pressing a key. Feedback is given for correct (A3) and incorrect (B3 or C3) responses, such as presenting the word “right” or “wrong.”

The learning that takes place in stimulus equivalence training, resulting in the formation of an equivalence class, has several interesting features. First, many relations that are not directly taught emerge. For example, after learning the relations A1–B1 and B1

The resulting behavior that emerges after stimulus equivalence training corresponds in many ways to what, in everyday language, would be said to “understanding an idea.” A person who points to a dog when someone says “dog” and who points to a photograph of a novel dog when someone says “chien” after being taught that “chien” is the same as “dog” appears to understand the idea “dog.”

It is also important to note that equivalence is only one kind of relationship that exists between stimuli. Other relationships are also possible, such as opposites, bigger-smaller, faster-slower, before-after, smaller-larger, and others. When people derive relationships among stimuli that are all equivalent, they learn that all members of the stimulus class are somewhat equivalent or, more loosely, “the same”. However, when relationships are derived among stimuli that are not equivalent, the derived relationships are more complex. For example, if an anxious person has already learned that “A is more fearful than B” and “B is more fearful than C,” and now learns that “D is more fearful than A” and “E is as fearful as D,” then the person will now learn multiple new derived relationships that are not equivalent (Hayes, Barnes-Holmes & Roche, 2001).

5 Future Directions in Operant Conditioning Research and Treatment

In the last 15 years there have been significant advances in operant theory. Perhaps the most important advances address the limitations of the application of the operant conceptualization of stimulus generalization to verbal behavior. Humans are unique in their ability to engage in certain kinds of verbal behavior. Earlier, stimulus generalization was defined as when a stimulus with similar physical or formal properties to the original discriminative stimulus is also followed by a response that is subsequently reinforced. However, in the instance of verbal behavior, there are stimuli that have no formal properties in common that can still serve equivalent functions. A simple instance is when the written word ‘g-r-e-e-n,’ the sound of the word ‘green’ when pronounced, and the color green all serve the same stimulus function without necessarily ever having appeared together. There are no physical similarities shared by these stimuli. They can be trained to substitute for each other so that any one stimulus can entail the functions of each of the others. When each stimulus can entail the functions of all the others and demonstrate certain experimental properties (reflexivity, symmetry, transitivity), they are said to form an equivalence class.

The clinical implication for humans is that stimuli can take on the functions of other stimuli without ever having been directly learned. Though the process is debated (Barnes-Holmes et al. in press, Sidman 1986, 1994), it is clear that one can construct functionally equivalent relationships between stimuli in complex ways. What this means clinically is that a client can respond to a variety of stimuli as if they all had the same direct learning history, even if they did not. While there are experimental methods for training these relationships, they often emerge without a person knowing that an equivalent relationship is functioning or how it came to be. A client might learn to respond to an event—for example, a relationship failure—in the same way that they might to a catastrophic event, even though a failed relationship had never previously entailed a horrible outcome. Its implications for therapy are just beginning to emerge (Hayes et al. 1999) (see Acceptance and Change, Psychology of). The promise of the exploration of the relational operant in the analysis of language and therapy is one of the more interesting innovations for those doing research on the cutting edge of operant theory.

In the last decade, an analysis of how to apply operant learning principles in interpersonal psychotherapy has also begun (see Interpersonal Psychotherapy). Kohlenberg and Tsai (1991) have detailed functional analytic psychotherapy, which describes the reinforcing functions of the therapeutic relationship that the therapist can use to affect significant behavior change in adult outpatient populations.

Advances in basic operant research are emerging at an increasing rate. Innovations in therapy are addressing new classes of problems that have not previously been the focus of an operant analysis. The role of operant conditioning will continue to maintain a prominent position in applied clinical psychology.

6 Conclusion

The empirical examples provided above indicate that advances in data analysis progress through steps of less and less aggregation combined with identification of new controlling variables at each step. For example, stimulus generalization gradients may differ depending on how session data are segmented (Section 3.1). Similarly, IRT distributions may differ when IRTs are sampled conditional upon the moment-to-moment occurrence of collateral behavior (Section 5.4.3). Even though successive emissions of the same response can be of the same topography they may nonetheless differ in terms of their relation to controlling variables. Pecks on a key in one time zone are ‘tagged’ by the contingency of reinforcement operating during that zone, and pecks in a second time zone are tagged differently if the conditions of reinforcement differ in that time zone. The different local rates of pecking during COD and non-COD periods provide one case in point (Section 3.2). When one encounters unexplained variability in behavior between conditions presumed to be equal, the behavior could possibly be tagged differently by unknown variables. Progress from variability to explanation then consists of the identification of the conditions (the tags) that are responsible for the variation one sees in the data. Once such conditions are identified, for example by conditional data analysis, a next step is to conduct an experimental analysis where the conditions that before were considered equal are now dissociated experimentally. When the different conditions reliably produce different data, a functional relation has been obtained (Sidman, 1960).

Advances in scientific discovery can take place through less and less aggregation along both independent and dependent variables. Reduced aggregation along the dependent variable corresponds to improved sampling conditions (e.g., increased sensitivity of recording spatial response location). Reduced aggregation along the independent variable, on the other hand, corresponds to refinement in experimental control (e.g., differential reinforcement of small-scale motor behavior). Scientific progress is associated with reduced aggregation along both variables. However, aggregation done after progress is made may have some unfortunate consequences. For example, a well established finding is that overall response rate maintained under a VI schedule of reinforcement is a function of rate of reinforcement provided by the VI schedule. This means that behavior differs under different experimental conditions. Once this function is obtained, progress would be reversed if one were to consider the different reinforcement rates the same by representing them by one value, the overall average reinforcement rate. In a crude analogy, a composer of a piece of music would be more than insulted if someone were to represent the piece by playing it as one, average note. Investigators who have labored to obtain a functional relation, showing how the response rate of a subject depends upon an identified and manipulated experimental variable, similarly are sensitive to aggregation along ‘their’ independent variable because this is tantamount to neglecting the experimental control, sought so hard. Even though aggregation along the independent variable is not a method of analysis, it is nonetheless a recognized tactic in the sociology of science (e.g, Kuhn, 1970; Gleick, 1987), as when one group of investigators neglects the functional relations obtained by another group of investigators working on the same problems.

Conflicting approaches in data treatment prevail within science of behavior, and a common consensus is lacking as to what is the right or wrong method of analysis. Contemporary approaches range from the study of behavior in great detail to aggregation of as much data as possible. Szechtman et al. (1988), for example, argued that “in order to provide meaningful correlations between brain mechanisms and behavior, the analysis of behavior will require as much sophistication and attention to detail as does the analysis of the brain” (p. 172). On the other hand, Baum (1989) proposed that “with maturity, a science of behavior should be able to make quantitative predictions. Since quantitative predictions are only possible with molar laws, behavioral analysis can progress toward this goal only by looking beyond momentary events to molar variables and molar relations.” (p. 176). The contrast between these views may be rooted in differences in underlying philosophy regarding what constitutes an explanation of behavior. Nonetheless, the difference between these views is considerable and might conceivably be a source of hardship for new investigators who favor one view but happen to be exposed to the social contingencies of the opposing view.

When different levels of data analysis force different conclusions about how behavior is controlled, a natural question is where to set the boundary between determinism and noise. Maybe tradition has dictated that an analysis stops when data become chaotic and unpredictable. Some new developments within contemporary science recognize that seemingly chaotic events can stem from deterministic sources; even popular books have been written on the subject (e.g., Eigen and Winkler, 1981; Prigogine and Stengers, 1984; Gleick, 1987). For example, mathematical description is not necessarily restricted to molar data analyses only. In a review of some new methods, Steen (1988) thus wrote that “mathematical science has become the science of patterns, with theory built on relations among patterns and on applications derived from the fit between pattern and observation” (p. 611). Similarly, Jurs (1986) described how pattern recognition methods can be used to find functional relations in complex data and even to build quantitative models (e.g., in chemistry). Also, Bradshaw et al. (1983) provided a provocative computerized simulation of scientific discovery that generates quantitative relations solely by means of data-driven induction in advance of theory formulation. Additional examples of quantitative pattern analyses of moment-to-moment events within other areas of the neurosciences are provided in Tam et al. (1988) and Montgomery (1989).

Which level of analysis to select is a difficult problem. Response rate calculated over a whole session has been the prevaling analysis method for decades. IRTs also can be units of analysis, showing functional relations with experimental variables. Concurrent response events within IRTs can serve as units as well, as when collateral response topography can be used to predict IRT length. Even a part of a response can be a unit, as when interbeak distance was differentially reinforced. Each of these units of analysis is valid because replicable functional relations can be established within the domain of the analytic unit. Given the wide range of successful application of conditioning techniques involving units both large and small, units of analysis could profitably be considered as functional and not structural. Baer (1982) discussed whether behavior has a necessary structure, that is, should units of analysis be fixed or can they vary? Baer (1986) suggested that the proper unit is whatever emerges when a contingency is applied. Units of analysis can therefore themselves be considered as scientific findings rather than based on a priori assumptions regarding behavior structure. As behavior recording and control techniques become more refined, behavior units and scales of analysis may become smaller, and possibly new functional relations may be obtained. A functional relation established at one level of analysis may therefore not be the final answer because explanations of behavior in terms of other functional relations established at subunits of analysis may be discovered later.