Time-series analysis in operant research

A time-series method is presented, nontechnically, for analysis of data generated in individual-subject operant studies, and is recommended as a supplement to visual analysis of behavior change in reversal or multiple-baseline experiments. The method can be used to identify three kinds of statistically significant behavior change: (a) changes in score levels from one experimental phase to another, (b) reliable upward or downward trends in scores, and (c) changes in trends between phases. The detection of, and reliance on, serial dependency (autocorrelation among temporally adjacent scores) in individual-subject behavioral scores is emphasized. Examples of published data from the operant literature are used to illustrate the time-series method.     

SOCIAL-SKILLS TRAINING FOR UNASSERTIVE CHILDREN: A MULTIPLE-BASELINE ANALYSIS1

The effects of social-skills training consisting of instructions, feedback, behavior rehearsal, and modelling were examined in a multiple-baseline analysis in four unassertive children. The treatment was effective in that the behaviors selected for modification changed markedly. The effects of treatment generalized from trained to untrained items (interpersonal situations requiring assertive responding) and gains were maintained at the two- and four-week followup probe sessions. In addition, overall assertiveness in all subjects increased from baseline assessment to the conclusion of treatment and into followup.     

TEACHING COIN EQUIVALENCE TO THE MENTALLY RETARDED1

A program was designed to teach coin equivalence to mentally retarded adolescents. Coin equivalence was defined as choosing several different combinations of coins to equal specified target values. A pretest-posttest matched-groups design was employed with an experimental group receiving the monetary training, and a no-training control group. A multiple baseline across coin-counting responses was also incorporated in the experimental group. Training was divided into six stages, each teaching one specific method of combining coins to equal 10 target values from 5¢ through 50¢. A three-component response chain was used, requiring (a) naming, (b) selecting and counting, and (c) depositing target monetary values into a coin machine. Experimental subjects improved significantly in coin equivalence performance and maintained their skill on follow up tests; control subjects did not.     

On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.     

Positive contrast, negative induction, and inhibitory stimulus control in the rat

In Experiment I, 24 rats were trained on a multiple variable-interval variable-interval schedule with a doorlight and white noise serving as component cues. Two groups were then shifted to a multiple extinction variable-interval schedule, and a third group was maintained on the multiple variable-interval variable-interval schedule. The multiple extinction variable-interval condition produced positive contrast when either the light or noise signalled extinction, and both of these cues acquired inhibitory stimulus control as measured by a combined cue test. In Experiment II, the multiple variable-interval variable-interval condition was shifted to multiple extinction variable-interval for one group, to multiple variable-time variable-interval for a second group, and was unchanged for the third group. The two experimental conditions produced identical patterns of response-rate reduction in the altered component, but the multiple extinction variable-interval condition produced positive contrast, whereas the multiple variable-time variable-interval condition did not. Subsequent combined cue and resistance to reinforcement tests revealed that the cue signalling extinction acquired stronger inhibitory stimulus control than the cue signalling variable time.     

Choice, time allocation, and response rate during stimulus generalization

Six pigeons were trained to discriminate between two noise intensities using a procedure that assessed choice, time allocation, and response rate simultaneously and independently. Responses on the left or right key (R1 or R2) were respectively correct in the presence of two different intensities, S1 and S2. After a correct response, reinforcement became available for pecks on the center key. Reinforcement density for R1¦S1 relative to R2¦S2 was varied across experimental conditions. Generalization tests followed extensive training at each condition. As a function of stimulus intensity, proportions of initial choices of R2, of time spent in R2-initiated components, and of center-key responses emitted in R2-initiated components all yielded sigmoidal gradients of similar slope, which shifted slightly in location when relative reinforcement density changed. Changeovers were maximal where initial choice proportions approximated 0.5. Gradients relating the absolute number of center-key responses to stimulus intensity were also roughly sigmoidal, but were more sensitive to changes in reinforcement density. Gradients of momentary response rate also depended on reinforcement density. During training, large but transitory shifts in choice responding occurred when reinforcement density changed, while differences in momentary response rate developed slowly, suggesting separate control of choice and response rate by the contingencies of reinforcement.     

Correctness of Kruskal's algorithms for monotone regression with ties

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.Comments by Dr. J. B. Kruskal have been most helpful.     

TEACHING CONVERSATION-RELATED SKILLS TO PREDELINQUENT GIRLS1

The use of conversation-related skills by youthful offenders can influence social interactions with adults. These behaviors are also likely to be useful to adolescents after their release from a treatment program (Journal of Applied Behavior Analysis, 1972, 5 , 343–372). Four girls, aged 13 to 15 yr, residing at Achievement Place for Girls in Lawrence, Kansas, received training on conversation-related behaviors. A multiple-baseline design across youths and across behaviors was used. Youth answer-volunteering in response to questions and three youth nonverbal components (“hand on face”, “hand at rest”, and “facial orientation”) were measured during daily 10-min sessions with a simulated guest in the group home's living room. Answer-volunteering was scored each session as the per cent of 13 “secondary” questions that the simulated guest did not have to ask following 10 “primary” questions. The three nonverbal components were scored according to their occurrence during 10-sec intervals and the resultant scores were averaged per session for an overall appropriate nonverbal score. The girls individually earned points within the home's token economy for participating in each session and additional points were awarded after training if preselected behavioral criteria were achieved for each of the two behavior categories per girl. Some of the training sessions were led by a “teaching-parent” (specially trained houseparent) while others were led by individual girls. Point consequences were administered by both the teaching-parent and by the “peer-trainers”. The average observed rate of answer-volunteering by the girls during pretraining sessions was 30% for S₁, 30% for S₂, 23% for S₃, and 68% for S₄. The average rate of answer-volunteering during posttraining sessions was: S₁ = 92%, S₂ = 89%, S₃ = 90%, and S₄ = 98%. The average nonverbal score during pretraining sessions was 82% for S₁, 53% for S₂, 60% for S₃, and 82% for S₄. The average nonverbal score during posttraining sessions was: S₁ = 98%, S₂ = 98%, S₃ = 98%, and S₄ = 100%. Videotapes of the sessions were shown in a random sequence to four adults (probation officer, social worker, etc who represented “significant others” for the youths' future success in the community. The adults judged posttraining tapes on the average as more appropriate 100% of the time for S₁, 100% of the time for S₂, 90% of the time for S₃, and 70% of the time for S₄. The study demonstrated that training of conversation-related skills is feasible with predelinquent girls, that the girls can help train each other, and that social validation of the training results is possible.     

SELF-RECORDING IN TRAINING GIRLS TO INCREASE WORK AND EVOKE STAFF PRAISE IN AN INSTITUTION FOR OFFENDERS1

Self-recording procedures were used by four adolescent girls to increase work and comments (cues) that evoked staff praise during vocational training sessions in a maximum-security institution for offenders. The girls were selected on the basis of their not responding to a staff-directed token program. The self-recording procedures were directed by a therapist who saw the girls outside the vocational training sessions. According to a multiple-baseline design, self-recording of work was introduced sequentially to each of the two or three settings the girls attended each day. A few days after work had increased, self-recording of cues was introduced. Tokens were delivered by the therapist for work and cues recorded by the girls. Work and cues increased following self-recording for three of the girls and increased cues evoked higher rates of staff praise. Girl and staff behaviors were maintained during short follow-up periods when tokens were not given for the girls' records. The procedures failed to effect desirable changes with a fourth girl's work, and self-recording of work was terminated without introducing cueing.     

TEACHING PEDESTRIAN SKILLS TO RETARDED PERSONS: GENERALIZATION FROM THE CLASSROOM TO THE NATURAL ENVIRONMENT1

Little attention has been given to teaching adaptive community skills to retarded persons. In this study, five retarded male students were taught basic pedestrian skills in a classroom. Training was conducted on a model built to simulate city traffic conditions. Each subject was taught five specific skills involved in street crossing in sequence, viz. intersection recognition, pedestrian-light skills, traffic-light skills, and skills for two different stop-sign conditions. Before, during, and after training, subjects were tested on generalization probes on the model and under actual city traffic conditions. Results of a multiple-baseline design across both subjects and behaviors indicated that after receiving classroom training on the skills, each subject exhibited appropriate pedestrian skills under city traffic conditions. In addition, training in some skills appeared to facilitate performance in skills not yet trained.