Comparing Latent Structures of the Grade of Membership,Rasch, and Latent Class Models

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other population parameters fixed, in the marginal space (based on marginal probabilities) and in the full parameter space (based on cell probabilities). The case of a 2 × 2 contingency table is discussed in detail, and a generalization to 2^J tables with J ≥ 3 is sketched. Our approach highlights the main distinction between the GoM model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships. By using the geometric approach we show that, in special cases, the GoM model can be thought of as being similar to an item response theory (IRT) model in representing population heterogeneity. Finally, we show that the GoM item parameters can provide quantities analogous to more general logistic IRT item parameters. As a latent structure model, the GoM model might be considered a useful alternative for a data analysis when both classes of extreme responses, and additional heterogeneity that cannot be captured by those latent classes, are expected in the population. This work was supported by Award #1R03 AG18986-01 from the National Institute on Aging and NIH grant #1R01 CA94212-01. The presentation of the ideas in this paper owes much to discussions with Stephen Fienberg and Brian Junker, Carnegie Mellon University. The author thanks Jim Ramsay and two anonymous reviewers for their valuable comments on earlier drafts of this paper.     

Wolfhart Pannenberg's Engagement with the Natural Sciences

Wolfhart Pannenberg's engagement with the natural sciences is surveyed. A critique is given of his treatment of these themes: the concept of a field; contingency; the role of the future.     

A GROUP-ORIENTED CONTINGENCY TO INCREASE LEISURE ACTIVITIES OF ADULTS WITH TRAUMATIC BRAIN INJURY

An interdependent group-oriented contingency and graphic feedback were used to increase the activity levels of residents of a group home for persons with traumatic brain injury. Results showed that the intervention was effective for 4 of the 6 subjects. Individual performances must be examined when implementing group contingencies because all subjects may not respond.     

WILDFLOWERS AND WONDER: A PASTOR'S WANDERINGS IN THE RELIGION-SCIENCE WILDERNESS

Abstract. In this paper, I explore, as a Christian and a parish pastor, what drew me into the religion-science dialogue and what keeps me involved. Encounters with nature and readings of evolutionary theory answer some questions and raise others, especially questions about chance and the nature of God. I persist in my quest for understanding because creedal affirmations of God as Creator demand an examination of the relationship between God and the world, and because I want to proclaim the Christian message in a credible way to parishioners raised with a scientific worldview. Along the way I am reaping unexpected spiritual dividends.     

The analysis of group contingency data

The data analyses utilized in group contingency projects are reviewed. Previous studies are cited to emphasize advantages of nonconsolidated ("individual") over consolidated analyses. Several procedures are described that enable applied researchers to incorporate nonconsolidated data analyses in group contingency studies.     

ASSESSING AND TRAINING TEACHERS IN THE GENERAUZED USE OF BEHAVIOR MODIFICATION WITH AUTISTIC CHILDREN1

This study investigated the feasibility of developing reliable, valid criteria for measuring and training the skills necessary to teach autistic children. The behaviors of 11 teachers and 12 autistic children were recorded in a series of different teaching situations. Teacher-training was initiated at different times for different teachers. The results showed: (1) it was possible to assess empirically whether a teacher was correctly using defined behavior-modification techniques; (2) generally, for any given session, systematic improvement in the child's behavior did not occur unless the teacher working in that session had been trained to use the techniques to a high criterion; (3) all 11 teachers were rapidly trained to use these techniques; and (4) the teachers learned generalized skills effective with a variety of children and target behaviors.     

A BRIEF FUNCTIONAL ANALYSIS OF AGGRESSIVE AND ALTERNATIVE BEHAVIOR IN AN OUTCLINIC SETTING

We conducted a brief functional analysis to identify maintaining variables for aggressive behavior and an alternative replacement response during a 90-min outpatient evaluation of 3 individuals with severe handicaps. During the initial analogue assessment, which focused on identifying maintaining contingencies for aggressive behavior, each participant displayed a substantially greater frequency of aggressive behavior during one condition than during any other. The contingency that produced the highest percentage of aggressive behavior was then presented for the occurrence of a specific alternative behavior (a mand). During this contingency reversal phase, each participant displayed a substantial reduction in aggressive behavior and a substantial increase in alternative behavior, thus providing a direct analysis of the equivalency of the contingency for maintaining either behavior.     

Transient effects of acquisition history on generalization in a matching-to-sample task

This study examined the role of learning history on the acquisition of a matching-to-sample task. Twelve preschool children learned four stimulus classes through instructions, shaping, or imitation. After reaching criterion, the subjects were exposed to changed discrimination contingencies to determine how each learning history affected the acquisition of responses appropriate to the new contingencies. All subjects reached criterion on the new relations, although the subjects with a shaping history adapted slightly more quickly than those subjects with a history of instructions or imitation. Given sufficient exposure to changed contingencies, rule-driven insensitivity to contingencies was overcome by experience with consequences. This result may be specific to younger subjects, but it suggests that instructions can be used in education without creating insensitivity to contingencies.     

Interresponse-time punishment: a basis for shock-maintained behavior.

Lever pressing of squirrel monkeys postponed brief electric shock according to a free-operant shock-postponement procedure. Pressing also produced shock with a probability proportional to the duration of the current interresponse time in some conditions, or to the fifth ordinally-preceding interresponse time in others. These conditions provided equal frequencies and temporal distributions of response-produced shocks either contingent on or independent of the current interresponse-time duration, respectively. Shock delivered contingent on the current interresponse-time duration resulted in shorter mean interresponse times and higher overall response rates that shock delivered independent of the current interresponse time. In subsequent conditions, response-produced shocks were sufficient to maintain responding following suspension of the postponement procedure only when those shocks were contingent on the current interresponse time. Presenting shock independent of the current interresponse time, conversely, suppressed response rate and ultimately led to cessation of responding in the absence of a conjoint shock-postponement procedure. These results demonstrate interresponse-time punishment in the absence of any indirect avoidance contingencies based on overall shock-frequency reduction, and strongly support similar interpretation at the more local level of shock-frequency reduction correlated with particular interresponse times. Differential punishment of long interresponse times also provides both an a priori basis for predicting whether a schedule of shock presentation will maintain or suppress responding and a framework for interpreting many of the functional relations between overall response rate and parameters of consequent shock presentation. Finally, these results and others indicate the importance of response-consequence contiguity above and beyong any notion of noncontiguous contingency in the control of behavior.     

Escalating schedules of incentives increase physical activity with no differences between deposit and no-deposit groups: A systematic replication

Physical inactivity has increasingly affected public health in the United States during the COVID-19 pandemic as it is associated with chronic diseases such as arthritis, cancer, and heart disease. Contingency management has been shown to increase physical activity. Therefore, the present study sought to evaluate the effects of an escalating schedule of monetary reinforcement with a reset contingency on physical activity, as compared between 2 counterbalanced groups in which a monetary deposit of $25 was either required (deposit group) or not (no-deposit group). Twenty-five adults wore Fitbit accelerometers to monitor step counts. An ABA reversal design was used; in the 2 baseline phases, no programmed contingencies were in place for step counts. During intervention, step goals were set using a modified 70^th percentile schedule with a 7-day window: Reaching the first goal would result in $0.25, and incentives increased by $0.25 for each subsequent day in which the goal was met. Failure to reach a goal resulted in a reset of the monetary incentive value to $0.25. Ten out of 12 participants from the deposit group were determined to be responders to intervention, whereas 8 out of 13 participants from the no-deposit group were determined to be responders to intervention. Overall, there were no significant differences between the groups' step counts. However, the deposit group's intervention was cheaper to implement, which suggests that deposit contracts are a viable modification for physical activity interventions.