Variable-ratio schedules as variable-interval schedules with linear feedback loops.

The mathematical theory of linear systems has been used successfully to describe responding on variable-interval (VI) schedules. In the simplest extension of the theory to the variable-ratio (VR) case, VR schedules are treated as if they were VI schedules with linear feedback loops. The assumption entailed by this approach, namely, that VR and VI-plus-linear-feedback schedules are equivalent, was tested by comparing responding on the two types of schedule. Four human subjects' lever pressing produced monetary reinforcers on five VR schedules, and on five VI schedules with linear feedback loops that reproduced the feedback properties of the VR schedules. Pressing was initiated by instructions in 2 subjects, and was shaped by successive approximation in the other 2. The different methods of response initiation did not have differential effects on behavior. For each of the 4 subjects, the VR and the comparable VI-plus-linear-feedback schedules generated similar average response rates and similar response patterns. The subjects' behavior on both types of schedule was similar to that of avian and rodent species on VR schedules. These results indicate that the assumption entailed by the VI-plus-linear-feedback approach to the VR case is valid and, consequently, that the approach is worth pursuing. The results also confute interresponse-time theories of schedule performance, which require interval and ratio contingencies to produce different response rates.     

On the classic and modern theories of matching

Classic matching theory, which is based on Herrnstein's (1961) original matching equation and includes the well-known quantitative law of effect, is almost certainly false. The theory is logically inconsistent with known experimental findings, and experiments have shown that its central constant-k assumption is not tenable. Modern matching theory, which is based on the power function version of the original matching equation, remains tenable, although it has not been discussed or studied extensively. The modern theory is logically consistent with known experimental findings, it predicts the fact and details of the violation of the classic theory's constant-k assumption, and it accurately describes at least some data that are inconsistent with the classic theory.     

Third‐Order Thinking in Family Therapy: Addressing Social Justice Across Family Therapy Practice

We contend that the field of family therapy is undergoing a notable shift from second‐ to third‐order thinking. We offer theoretical support and examples to demonstrate how third‐order thinking provides a framework for integrating heightened sociocultural attunement into family therapy practice. We discuss the importance of third‐order thinking relative to being prepared to invite families into third‐order change. Finally, we offer a case example to show specific guidelines for third‐order practice.     

The WIG (weighted individual and group) shrinkage estimator

Regularization, or shrinkage estimation, refers to a class of statistical methods that constrain the variability of parameter estimates when fitting models to data. These constraints move parameters toward a group mean or toward a fixed point (e.g., 0). Regularization has gained popularity across many fields for its ability to increase predictive power over classical techniques. However, articles published in JEAB and other behavioral journals have yet to adopt these methods. This paper reviews some common regularization schemes and speculates as to why articles published in JEAB do not use them. In response, we propose our own shrinkage estimator that avoids some of the possible objections associated with the reviewed regularization methods. Our estimator works by mixing weighted individual and group (WIG) data rather than by constraining parameters. We test this method on a problem of model selection. Specifically, we conduct a simulation study on the selection of matching‐law‐based punishment models, comparing WIG with ordinary least squares (OLS) regression, and find that, on average, WIG outperforms OLS in this context.     

Interobserver agreement, intraobserver reliability, and the Rorschach Comprehensive System

Interrater agreement and reliability for the Rorschach have recently come under increasing scrutiny. This is the second report examining methods of Comprehensive System reliability using principles derived from observational methodology and applied behavioral analysis. This study examined a previous nonpatient sample of 20 protocols (N = 412 responses) and also examined a new clinical sample of 20 protocols (N = 374 responses) diagnosed with Research Diagnostic Criteria. Reliability was analyzed at multiple levels of Comprehensive System data, including response-level individual codes and coding decisions and ratios, percentages, and derivations from the Structural Summary. With a number of exceptions, most Comprehensive System codes, coding decisions, and summary scores yield acceptable, and in many instances excellent, levels of reliability. Limitations arising from the nature of Rorschach data and Comprehensive System coding criteria are discussed.