Falsification of matching theory: changes in the asymptote of Herrnstein''s hyperbola as a function of water deprivation.

Five rats pressed levers on variable-interval schedules of water reinforcement at various levels of water deprivation. In one phase of the experiment, three deprivation conditions that replicated conditions in Heyman and Monaghan (1987) were arranged, along with three less extreme deprivation conditions. In a second phase, water deprivation was arranged so that subjects were exposed to a greater range of access to water per day. Herrnstein's hyperbola described the rats' response-rate data well. The y asymptote, k, of the hyperbola appeared roughly constant over the conditions that replicated those of Heyman and Monaghan, but decreased markedly when less extreme deprivation conditions were included. In addition, k varied systematically when the second method of arranging deprivation was used. These results falsify a strong form of matching theory and confirm predictions made by linear system theory.     

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.     

Empirical support for the gender‐as‐culture hypothesis.

This investigation provided a test of the gender‐as‐culture, or ‘two cultures’, hypothesis proposed by Maltz and Borker (1982) to explain male/female differences in language use. Analysis of previous empirical investigations located 16 language features that had consistently been shown to indicate communicator gender and these were tested within the framework of the four dimensions of intercultural style proposed by Gudykunst and Ting‐Toomey (1998): direct versus indirect, succinct versus elaborate, personal versus contextual and instrumental versus affective. Study 1 provided preliminary evidence supporting the hypothesized language‐feature‐by‐dimension relationships (e.g., male directives were rated more direct and female uncertainty verbs more indirect). In Study 2, respondents rated multiple exemplars of the 16 language features, as well as 16 contrasting foil sentences, on all four dimensions, finding that nearly all of the variables fell on the hypothesized intercultural dimensions. In Study 3, respondents rated four sets of naturally occurring target sentences and matching foil sentences, representing all language variables, on their appropriate intercultural dimensions in order to establish dimensional polarity. Results across the three studies supported the hypothesized language feature‐by‐stylistic dimension relationship for 15 of the 16 variables: The 6 male language features were rated as more direct, succinct, personal, and instrumental, whereas 9 of the 10 female features were perceived as more indirect, elaborate, and affective. The findings demonstrate that gender preferences for language use function in ways that are consistent with stylistic preferences that distinguish national cultures.     

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.