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.

Replicability and randomization test logic in behavior analysis.

Randomization tests are a class of nonparametric statistics that determine the significance of treatment effects. Unlike parametric statistics, randomization tests do not assume a random sample, or make any of the distributional assumptions that often preclude statistical inferences about single-case data. A feature that randomization tests share with parametric statistics, however, is the derivation of a p-value. P-values are notoriously misinterpreted and are partly responsible for the putative "replication crisis." Behavior analysts might question the utility of adding such a controversial index of statistical significance to their methods, so it is the aim of this paper to describe the randomization test logic and its potentially beneficial consequences. In doing so, this paper will: (1) address the replication crisis as a behavior analyst views it, (2) differentiate the problematic p-values of parametric statistics from the, arguably, more useful p-values of randomization tests, and (3) review the logic of randomization tests and their unique fit within the behavior analytic tradition of studying behavioral processes that cut across species.

Randomization tests as alternative analysis methods for behavior-analytic data.

Randomization statistics offer alternatives to many of the statistical methods commonly used in behavior analysis and the psychological sciences, more generally. These methods are more flexible than conventional parametric and nonparametric statistical techniques in that they make no assumptions about the underlying distribution of outcome variables, are relatively robust when applied to small-n data sets, and are generally applicable to between-groups, within-subjects, mixed, and single-case research designs. In the present article, we first will provide a historical overview of randomization methods. Next, we will discuss the properties of randomization statistics that may make them particularly well suited for analysis of behavior-analytic data. We will introduce readers to the major assumptions that undergird randomization methods, as well as some practical and computational considerations for their application. Finally, we will demonstrate how randomization statistics may be calculated for mixed and single-case research designs. Throughout, we will direct readers toward resources that they may find useful in developing randomization tests for their own data.

Instrumental variable estimation of reinforcer effects.

Obtained reinforcement (whether measured as counts or as rates) is frequently used as a predictor in regression analyses of behavior. This approach, however, often contradicts the strict requirement that predictors in a regression be statistically independent of behavior. Indeed, by definition, reinforcement in operant scenarios depends on behavior, creating a causal feedback loop. The consequence of this feedback loop is bias in the estimation of regression parameters. This manuscript describes the technique of instrumental variable estimation (IVE), which allows unbiased regression parameters to be obtained through the use of "instruments," variables that are known a priori to be independent of both compromised predictors and of regression outcomes. Instruments also allow the strength of the bias to be assessed. Two examples of this technique are provided (one relying on real data and one relying on simulation) in the context of regression models of generalized matching.

International publication trends in the Journal of Applied Behavior Analysis: 2000-2014.

Dymond, Clarke, Dunlap, and Steiner's (2000) analysis of international publication trends in the Journal of Applied Behavior Analysis (JABA) from 1970 to 1999 revealed low numbers of publications from outside North America, leading the authors to express concern about the lack of international involvement in applied behavior analysis. They suggested that a future review would be necessary to evaluate any changes in international authorship in the journal. As a follow-up, we analyzed non-U.S. publication trends in the most recent 15 years of JABA and found similar results. We discuss potential reasons for the relative paucity of international authors and suggest potential strategies for increasing non-U.S. contributions to the advancement of behavior analysis.