What is the optimal penalty for errors in infant skill learning? Behavioral analyses indicate that errors are frequent but trivial as infants acquire foundational skills. In learning to walk, for example, falling is commonplace but appears to incur only a negligible penalty. Behavioral data, however, cannot reveal whether a low penalty for falling…

Symmetry considerations are important in science, and Group Theory is a theory of symmetry. Classical Measurement Theory is the most used measurement theory in the social and behavioral sciences. In this article, the author uses Matrix Lie (Lee) group theory to formulate a measurement model. Symmetry is defined and illustrated using symmetries of…

Bayesian approach is becoming increasingly important as it provides many advantages in dealing with complex data. However, there is no well-defined model selection criterion or index in a Bayesian context. To address the challenges, new indices are needed. The goal of this study is to propose new model selection indices and to investigate their…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

Purpose: Repeated duration data are frequently used in behavioral studies. Classical linear or log-linear mixed models are often inadequate to analyze such data, because they usually consist of nonnegative and skew-distributed variables. Therefore, we recommend use of a statistical methodology specific to duration data. Method: We propose a…

Direct observation recording procedures produce reductive summary measurements of an underlying stream of behavior. Previous methodological studies of these recording procedures have employed simulation methods for generating random behavior streams, many of which amount to special cases of a statistical model known as the alternating renewal…

Serving as Rachlin's teaching assistant for his graduate course on animal learning in 1973 determined the direction of the author's career, which has been to build computer models and robots based mostly on the equations from that course and related ones. These artificial beings behave and learn very much like animals, and creating them forces a…

Single-case designs are a class of research methods for evaluating treatment effects by measuring outcomes repeatedly over time while systematically introducing different condition (e.g., treatment and control) to the same individual. The designs are used across fields such as behavior analysis, clinical psychology, special education, and…

The process-component approach has become quite popular for examining many psychological concepts. A typical example is the model with internal restrictions on item difficulty (MIRID) described by Butter (1994) and Butter, De Boeck, and Verhelst (1998). This study proposes a hierarchical generalized random-situation random-weight MIRID. The…

A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an…

In the structural equation modeling literature, the normal-distribution-based maximum likelihood (ML) method is most widely used, partly because the resulting estimator is claimed to be asymptotically unbiased and most efficient. However, this may not hold when data deviate from normal distribution. Outlying cases or nonnormally distributed data,…

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this…

Two experiments were conducted to identify the conditions likely to produce resurgence among adult human participants. The preparation was a simulated caregiving context, wherein a recorded infant cry sounded and was terminated contingent upon targeted caregiving responses. Results of Experiment 1 demonstrated resurgence with human participants in…

Generalization from single-case designs can be achieved by replicating individual studies across different experimental units and settings. When replications are available, their findings can be summarized using effect size measurements and integrated through meta-analyses. Several procedures are available for quantifying the magnitude of…

Confidence intervals (CIs) for parameters are usually constructed based on the estimated standard errors. These are known as Wald CIs. This article argues that likelihood-based CIs (CIs based on likelihood ratio statistics) are often preferred to Wald CIs. It shows how the likelihood-based CIs and the Wald CIs for many statistics and psychometric…