Erik Arntzen

Probability of Equivalence Formation: Familiar Stimuli and Training Sequence.

The present study was conducted to show how responding in accord with equivalence relations changes as a function of position of familiar stimuli, pictures, and with the use of nonsense syllables in an MTO-training structure. Fifty college students were tested for responding in accord with equivalence in an AB, CB, DB, and EB training structure. The results showed that familiar stimuli presented as A-stimuli gave the highest yields (10 of 10 participants), whereas introducing the pictures at the end of the training (as E-stimuli) gave lower yields (5 of 10), and using nonsense syllables gave even lower yields (4 of 10). In addition, when all stimuli were Greek/Arabic letters only, 3 of 10 participants responded in accord with equivalence. When familiar stimuli were A-stimuli, but with a requirement of using keys on the keyboard, only 4 of 10 subjects responded in accord with equivalence. Furthermore, there was a high correlation between responding in accord with equivalence and reports of class consistent naming. Reaction time data also showed a typical pattern, in which there was an increase from training to test and a decrease during testing.

The Effects of Different Training Structures in the Establishment of Conditional Discriminations and Subsequent Performance on Tests for Stimulus Equivalence

Previous studies comparing groups of subjects have indicated differential probabilities of stimulus equivalence outcome as a function of training structures. One-to-Many (OTM) and Many-to-One (MTO) training structures seem to produce positive outcomes on tests for stimulus equivalence more often than a Linear Series (LS) training structure does. One of the predictions from the discrimination analysis of R. R. Saunders and Green (1999) is that the differences in outcome between training structures should increase with number of class members. The purpose of the present experiment was to replicate and expand earlier findings on the effect of training structures and the stimulus equivalence outcome in a single-subject design. We wanted to compare the stimulus equivalence outcome in three 3-member classes to the outcome in three 4-member classes. In addition, we included all trial types in the tests and also changed the density of feedback before testing. The results from the current study replicated some earlier findings and showed that OTM gave a slightly better outcome on the stimulus equivalence test than MTO, and that both gave better outcome than LS. Thus, we did not find that MTO was superior to OTM with increasing number of members in each class. Reaction time data also replicated earlier findings that showed an increase from baseline to testing, and a more pronounced increase in reaction time on equivalence than symmetry trials. Differential procedural issues and some contingencies that could be important in understanding the results are discussed.

Equivalence Outcome in Single Subjects as a Function of Training Structure

Previous studies comparing groups of subjects have indicated differential probabilities of stimulus equivalence outcome as a function of training structure. Both one-to-many (OTM) and many-to-one (MTO) training structures seem to produce stimulus equivalence more often than a linear series training structure. The purpose of the present study was to explore whether or not corresponding differential probabilities of equivalence outcome as a function of training structure can be demonstrated in the performances of single subjects. In Experiment 1, equivalence outcome was tested successively following training according to each of the three training structures. All subjects responded in accord with equivalence following the OTM training structure independent of the training order, except for 1 subject who did not respond in accord with equivalence following neither of the three training structures. Furthermore, 2 subjects demonstrated individual success following both one-to-many and many-to-one training even when they did not demonstrate success following linear series training, while the reverse never happened. In Experiment 2, equivalence outcome was tested successively following training according to a many-to-one and a one-to-many training structure with both 2 and 3 classes of stimuli. The results showed that all subjects responded in accord with equivalence following the OTM training structure, while 2 subjects did not respond in accord with equivalence following the MTO training structure. In Experiment 3, equivalence outcome was tested successively following training according to a many-to-one training structure and one-to-many training structure with both 3 and 4 members in each class. In accord with the results of Arntzen and Holth (1997) the present results indicated a superiority of the one-to-many over alternative training structures as regards the probability of an equivalence outcome. There was no difference in the probability of an equivalence outcome following one-to-many and many-to-one as a function of increasing number of members. The difference in number of comparisons connected to each sample as a consequence of the dissimilarity in the training structures is discussed as a possible explanation for the difference in equivalence outcome.

Delayed Matching to Sample: Probability of Responding in Accord with Equivalence as a Function of Different Delays

The present series of 4 experiments investigated the probability of responding in accord with equivalence in adult human participants as a function of increasing or decreasing delays in a many-to-one (MTO) or comparison-as-node and one-to-many (OTM) or sample-as-node conditional discrimination procedure. In Experiment 1, 12 participants started with simultaneous matching, followed by O-s, 2-s, and 4-s delayed matching, while the other 12 participants started with 4-s delayed matching, followed by the decreasing delays in a MTO training structure. Results suggested that the likelihood of responding in accord with equivalence is enhanced as a function of increasing delays during training, and also that starting with longer delays increases the probability of responding in accord with equivalence in simultaneous matching. In Experiment 2,6 participants started with simultaneous matching, followed by O-s, 2-s, and 4-s delayed matching in a OTM training structure. Results showed that 6 of 6 participants responded in accord with equivalence. In Experiment 3, 6 participants started with simultaneous matching, followed by O-s, 3-s, and 9-s delayed matching in a OTM training structure. Results showed that 6 of 6 participants responded in accord with equivalence. In Experiment 4, 6 participants started with simultaneous matching, followed by O-s and 3-s delayed matching with a restriction to engage in mediating behavior during testing. Results showed that none of the 6 participants responded in accord with equivalence during 3-s delay. It is argued that if delayed matching mquires (or evokes) precurrent behavior (responses that increase the effectiveness of a subsequent current behavior in obtaining a reinforcer), precurrent behavior may in turn facilitate responding in accord with equivalence. Higher reaction times durin~l initial testing may indicate precurrent problem-solving behavior prior to the selection of a comparison stimulus.

Implications of Motivating Operations for the Functional Analysis of Consumer Choice

The present article introduces the concept of Motivating Operation (MO) to the context of consumer choice and discusses the function of the concept of MO in the context of the Behavioral Perspective Model (BPM). Including MO as part of the consumer behavior setting leads to a more comprehensive analysis and, as a result, improves our understanding of the complex world of contingencies operating within consumer situations. First, the concept of MO helps to distinguish between discriminative and motivational functions of antecedents in the consumer behavior setting. Second, the MO concept includes both unlearned and learned motivating effects. Third, we will argue that some types of rules could also be MOs. A functional analysis of consumer choice should take into consideration the concept of MO because it is a contribution to the ongoing discussion to describe and classify antecedent variables that influence consumer behavior.

Training and Testing Parameters in Formation of Stimulus Equivalence: Methodological Issues

Research on stimulus equivalence has been prominent for more than 40 years in behavior analysis. The present article will focus on issues related to methodological considerations in stimulus equivalence research. An introduction to stimulus equivalence is provided, followed by a discussion of parameters in training conditional discriminations and testing for the emergence of equivalence classes. Some issues related to different training structures, the use of instructions, simultaneous versus delayed matching to sample, the role of familiar stimuli, response requirements for the sample stimulus, and criteria for (a) defining responding in accordance with equivalence and (b) establishing conditional discrimination are discussed in more detail.

Discriminative functions and over-training as class-enhancing determinants of meaningful stimuli

Likelihood of equivalence class formation (yield) was influenced by pre-class formation of simultaneous and successive discriminations, their mastery criteria, and overtraining of the successive discriminations. Each undergraduate in seven groups attempted to form two 3-node, 5-member equivalence classes (ABCDE). In the pictorial (PIC) group, meaningless nonsense syllables were used as the A, B, D, and E stimuli and meaningful pictures as the C stimuli. Nonsense syllables only were used in the other groups. The abstract (ABS) or 0-0-0 group involved no pre-class training. In the 84-0-0, 84-5-0 and 84-20-0 groups, simultaneous discriminations were trained among C stimuli to a mastery criterion of 84 trials, followed by successive discriminations trained to mastery criteria of 0, 5, and 20 trials, respectively. In the 84-20-0, 84-20-100, and 84-20-500 groups, simultaneous and successive discriminations were trained as noted, followed by overtraining with 0, 100, 500 successive-discrimination trials, respectively. The ABS group produced a 6% yield with the 84-0-0, 84-5-0, and 84-20-0 groups producing further modest increments. Overtraining produced a linear increase in yield, reaching 85% after 500 overtraining trials, a yield matching that produced by classes containing pictures as C stimuli (PIC). Thus, acquired discriminative functions and the overtraining of at least one function can account for class enhancement by meaningful stimuli.

On the role of trial types in tests for stimulus equivalence

Some studies which have shown that differences in outcome on tests for stimulus equivalence dependent on different training structures, have run the tests as separate blocks without baseline trials interspersed in between test trials. Saunders and co-workers have argued that the differences in test outcome could be related to differences in the retention of trained discriminations during testing (R. R. Saunders, Drake, & Spradlin, 1999; R. R. Saunders & Green, 1999). In the current experiment, 20 adult participants were taught conditional relations by employing a linear series training structure. Following this training, non-reinforced trials of the directly trained relations were randomly interspersed in a mixed test for symmetry, transitivity, and global equivalence. After being exposed to the training procedure once, 17 of the participants did not perform in accord with stimulus equivalence, but 9 of these participants still responded in accord with the directly trained relations. After being exposed to the training procedure again, 10 participants still did not respond in accord with stimulus equivalence, while 7 out of these did respond consistent with the directly trained relations. This indicates that a “destroyed” baseline could not be responsible for these participants’ failure to respond in accord with stimulus equivalence. In addition the reaction time between the appearance of comparison stimuli and subsequent responding during the test were recorded. Data show that the average reaction time varies as a function of which type of relation that is presented. There were also distinct differences in reaction time patterns for those participants who responded in accord with stimulus equivalence compared to those not responding in such a manner.

Training Structures and the Formation of Equivalence Classes

Different training structures have produced different outcomes of equivalence yields when using a simultaneous training protocol. According to the discrimination analysis by R. R. Saunders and Green (1999), the number of simple discriminations required in conditional discrimination differs for the different training structures. Hence, for the MTO (many-to-one) structure, all the simple discriminations are required during training of the conditional discriminations, while they are not in the OTM (one-to-many) or LS (linear series) training structures. The differences in the number of discriminations will be greater when the number of members in the classes increases; thus, there should be a more pronounced difference in the outcome on equivalence tests. The purpose of the present experiment was to train 3 potential classes of 3 members each and 3 potential classes of 6 members each with MTO, OTM, and LS training structures. Thirty adult participants were randomly assigned to 6 groups, that is, 3 or 6 members with MTO, OTM, or LS. The results showed that there were small differences in the outcome following MTO or OTM. However, the equivalence outcome was lowest following the LS training structure. The data from the follow-up tests showed that none of the participants in the LS groups responded in accordance with stimulus equivalence, while 6 of 10 did so in the OTM groups and 3 of 8 did in the MTO groups. Moreover, the reaction time data showed that there was an increase from directly trained trials to the symmetry and equivalence trials, with a more pronounced increase for equivalence trials.

Trained and Derived Relations with Pictures versus Abstract Stimuli as Nodes.

Earlier studies have shown divergent results concerning the use of familiar picture stimuli in demonstration of equivalence. In the current experiment, we trained 16 children to form three 3-member classes in a many-to-one training structure. Half of the participants were exposed first to a condition with all abstract stimuli and then to a condition with new abstract stimuli as samples and 3 picture stimuli as comparisons (and nodes). The other participants were given the 2 conditions in the reverse order. The results, regardless of order, showed that the condition with picture stimuli as nodes was more effective in producing responding in accord with equivalence than stimulus sets with abstract stimuli only. In addition, more participants responded in accord with equivalence when they were trained with picture stimuli first. Reaction time to the comparison stimuli showed a greater increase with abstract stimuli than with pictures as nodes.