A comparison of sources of baseline data for treatments of problem behavior following a functional analysis

It is common practice in research on the treatment of problem behavior to compare levels of targeted behaviors during treatment to levels when treatment is not in place. Some researchers use data collected as part of a multielement functional analysis as the initial baseline, whereas others collect new baseline data following completion of the functional analysis. We evaluated whether the source of baseline data influences the reliability and efficiency of decision-making. Results suggest that similar decisions are made in regard to treatment efficacy using the different sources of baseline data, but using data from a multielement functional analysis as baseline may save time. Interrater agreement was adequate, but lower for some graphs than has been observed in past studies. Several potential explanations for this discrepancy are discussed.     

Modelling monotonic effects of ordinal predictors in Bayesian regression models

Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the information contained. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modelling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter b representing the direction and size of the effect and a simplex parameter modelling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may be applied not only to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies we show that the model is well calibrated and, if there is monotonicity present, exhibits predictive performance similar to or even better than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects which allows us to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.     

Bayesian analysis of order-statistics models for ranking data

In this paper, a class of probability models for ranking data, the order-statistics models, is investigated. We extend the usual normal order-statistics model into one where the underlying random variables follow a multivariate normal distribution. Bayesian approach and the Gibbs sampling technique are used for parameter estimation. In addition, methods to assess the adequacy of model fit are introduced. Robustness of the model is studied by considering a multivariate-t distribution. The proposed method is applied to analyze the presidential election data of the American Psychological Association (APA).The author is grateful to K. Lam, K.F. Lam, the Editor, an associate editor, and three reviewers for their valuable comments and suggestions. This research was substantially supported by the CRCG grant 335/017/0015 of the University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7169/98H). Upon completion of this paper, I became aware that similar work had been done independently by K.G. Yao and U. Böckenholt (1999).     

A step forward: Bayesian hierarchical modelling as a tool in assessment of individual discrimination performance

Individual assessment of infants’ speech discrimination is of great value for studies of language development that seek to relate early and later skills, as well as for clinical work. The present study explored the applicability of the hybrid visual fixation paradigm (Houston et al., 2007) and the associated statistical analysis approach to assess individual discrimination of a native vowel contrast, /aː/ - /eː/, in Dutch 6 to 10-month-old infants. Houston et al. found that 80% (8/10) of the 9-month-old infants successfully discriminated the contrast between pseudowords boodup - seepug. Using the same approach, we found that 12% (14/117) of the infants in our sample discriminated the highly salient /aː/ -/eː/ contrast. This percentage was reduced to 3% (3/117) when we corrected for multiple testing. Bayesian hierarchical modeling indicated that 50% of the infants showed evidence of discrimination. Advantages of Bayesian hierarchical modeling are that 1) there is no need for a correction for multiple testing and 2) better estimates at the individual level are obtained. Thus, individual speech discrimination can be more accurately assessed using state of the art statistical approaches.     

Evaluating the function of applied behavior analysis a bibliometric analysis

Analysis of scholarly citations involving behavioral journals reveals that, consistent with its mission, applied behavior analysis research frequently references the basic behavioral literature but, as some have suspected, exerts narrow scholarly influence.     

Assessment of generalised Bayesian structural equation models for continuous and binary data

The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive $p$-values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework presented in the paper focuses on the approximate zero approach (Psychological Methods, 17 , 2012, 313), which involves formulating certain parameters (such as factor loadings) to be approximately zero through the use of informative priors, instead of explicitly setting them to zero. The introduced model assessment procedure monitors the out-of-sample predictive performance of the fitted model, and together with a list of guidelines we provide, one can investigate whether the hypothesised model is supported by the data. We incorporate scoring rules and cross-validation to supplement existing model assessment metrics for BSEM. The proposed tools can be applied to models for both continuous and binary data. The modelling of categorical and non-normally distributed continuous data is facilitated with the introduction of an item-individual random effect. We study the performance of the proposed methodology via simulation experiments as well as real data on the ‘Big-5’ personality scale and the Fagerstrom test for nicotine dependence.     

Functional analysis of aberrant behavior through measurement of separate response topographies

Functional analysis results for multiple topographies of aberrant behavior were graphed in an aggregate fashion and then separately for 48 clients. The results indicated that multiple topographies of behavior may be maintained by different contingencies. These results indicate that graphing functional analysis data in an aggregate fashion and then separately may improve the accuracy of their interpretation.     

Shopping as a coping behavior for stress

The purpose of this study was to demonstrate the effectiveness of diversion buying for stress release. Diversion buying was examined by survey, and it was found that women engaged in it more often than men. In Experiment 1, diversion buying was divided into an expenditure factor and an acquisition factor, in order to examine which was more effective for stress release; both had a significant main effect. The effectiveness of the acquisition factor was confirmed in Experiment 2. In Experiment 3, the expenditure factor was divided into the amount available for expenditure and the amount spent, in order to examine the effectiveness of each. It was shown that a certain amount of expenditure was needed for stress release; however, a high expenditure rate (spending most of the money) did not relieve stress.     

Behavior-based robotics as a tool for synthesis of artificial behavior and analysis of natural behavior

Work in behavior-based systems focuses on functional modeling, that is, the synthesis of life-like and/or biologically inspired behavior that is robust, repeatable and adaptive. Inspiration from cognitive science, neuroscience and biology drives the development of new methods and models in behavior-based robotics, and the results tie together several related fields including artificial life, evolutionary computation, and multi-agent systems. Ideas from artificial intelligence and engineering continue to be explored actively and applied to behavior-based robots as their role in animal modeling and practical applications is being developed.     

Multilevel analysis of matching behavior

Multilevel modeling has been considered a promising statistical tool in the field of the experimental analysis of behavior and may serve as a convenient statistical analysis for matching behavior because it structures data in groups (or levels) to account simultaneously for the within‐subject and between‐subject variances. Heretofore, researchers have sometimes pooled data erroneously from different subjects in a single analysis by using average ratios, average response and reinforcer rates, aggregation of subjects, etc. Unfortunately, this leads to loss of information and biased estimations, which can severely undermine generalization of the results. Instead, a multilevel approach is advocated to combine several subjects' matching behavior. A reanalysis of previous data on matching behavior is provided to illustrate the method and point out its advantages. It illustrates that multilevel regression leads to better estimations, is more convenient, and offers more behavioral information. We hope this paper will encourage the use of multilevel modeling in the statistical practices of behavior analysts.     

Bayesian data analysis for newcomers

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.     

Bayesian generalized structured component analysis

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modelling, which adopts components of observed variables as proxies for latent variables and examines directional relationships among latent and observed variables. GSCA has been extended to deal with a wider range of data types, including discrete, multilevel or intensive longitudinal data, as well as to accommodate a greater variety of complex analyses such as latent moderation analysis, the capturing of cluster-level heterogeneity, and regularized analysis. To date, however, there has been no attempt to generalize the scope of GSCA into the Bayesian framework. In this paper, a novel extension of GSCA, called BGSCA, is proposed that estimates parameters within the Bayesian framework. BGSCA can be more attractive than the original GSCA for various reasons. For example, it can infer the probability distributions of random parameters, account for error variances in the measurement model, provide additional fit measures for model assessment and comparison from the Bayesian perspectives, and incorporate external information on parameters, which may be obtainable from past research, expert opinions, subjective beliefs or knowledge on the parameters. We utilize a Markov chain Monte Carlo method, the Gibbs sampler, to update the posterior distributions for the parameters of BGSCA. We conduct a simulation study to evaluate the performance of BGSCA. We also apply BGSCA to real data to demonstrate its empirical usefulness.     

Functional analysis of problem behavior: a review

Functional analysis methodology focuses on the identification of variables that influence the occurrence of problem behavior and has become a hallmark of contemporary approaches to behavioral assessment. In light of the widespread use of pretreatment functional analyses in articles published in this and other journals, we reviewed the literature in an attempt to identify best practices and directions for future research. Studies included in the present review were those in which (a) a pretreatment assessment based on (b) direct observation and measurement of (c) problem behavior was conducted under (d) at least two conditions involving manipulation of an environmental variable in an attempt (e) to demonstrate a relation between the environmental event and behavior. Studies that met the criteria for inclusion were quantified and critically evaluated along a number of dimensions related to subject and setting characteristics, parametric and qualitative characteristics of the methodology, types of assessment conditions, experimental designs, topographies of problem behaviors, and the manner in which data were displayed and analyzed.     

An effect size measure and Bayesian analysis of single-case designs

This article describes a linear modeling approach for the analysis of single-case designs (SCDs). Effect size measures in SCDs have been defined and studied for the situation where there is a level change without a time trend. However, when there are level and trend changes, effect size measures are either defined in terms of changes in R² or defined separately for changes in slopes and intercept coefficients. We propose an alternate effect size measure that takes into account changes in slopes and intercepts in the presence of serial dependence and provides an integrated procedure for the analysis of SCDs through estimation and inference based directly on the effect size measure. A Bayesian procedure is described to analyze the data and draw inferences in SCDs. A multilevel model that is appropriate when several subjects are available is integrated into the Bayesian procedure to provide a standardized effect size measure comparable to effect size measures in a between-subjects design. The applicability of the Bayesian approach for the analysis of SCDs is demonstrated through an example.     

Progressing toward data intimacy: a review of within-session data analysis

Visual inspection of data is a common method for understanding, responding to, and communicating important behavior-environment relations in single-subject research. In a field that was once dominated by cumulative, moment-to-moment records of behavior, a number of graphic forms currently exist that aggregate data into larger units. In this paper, we describe the continuum of aggregation that ranges from distant to intimate displays of behavioral data. To aid in an understanding of the conditions under which a more intimate analysis is warranted (i.e., one that provides a richer analysis than that provided by condition or session aggregates), we review a sample of research articles for which within-session data depiction has enhanced the visual analysis of applied behavioral research.     

Mediation analysis and categorical variables: Some further frontiers

Iacobucci (2012) provides a conceptually appealing, readily implemented measure to assess mediation for a far wider range of data type combinations than traditional OLS-based analyses permit. Here, we consider potential applications and extensions along several lines, particularly in terms of random utility models, simulation-based estimation, and potential nonlinearities, as well as some methodological and cultural impediments.     

Bayesian factor analysis for multilevel binary observations

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics. The authors thank Ian Westbury, University of Illinois at Urbana Champaign for kindly providing the SIMS data for the application.     

Bayesian change-point analysis reveals developmental change in a classic theory of mind task

Although learning and development reflect changes situated in an individual brain, most discussions of behavioral change are based on the evidence of group averages. Our reliance on group-averaged data creates a dilemma. On the one hand, we need to use traditional inferential statistics. On the other hand, group averages are highly ambiguous when we need to understand change in the individual; the average pattern of change may characterize all, some, or none of the individuals in the group. Here we present a new method for statistically characterizing developmental change in each individual child we study. Using false-belief tasks, fifty-two children in two cohorts were repeatedly tested for varying lengths of time between 3 and 5 years of age. Using a novel Bayesian change point analysis, we determined both the presence and—just as importantly—the absence of change in individual longitudinal cumulative records. Whenever the analysis supports a change conclusion, it identifies in that child’s record the most likely point at which change occurred. Results show striking variability in patterns of change and stability across individual children. We then group the individuals by their various patterns of change or no change. The resulting patterns provide scarce support for sudden changes in competence and shed new light on the concepts of “passing” and “failing” in developmental studies.     

An overview of Bayesian reasoning in the analysis of delay‐discounting data

Statistical inference (including interval estimation and model selection) is increasingly used in the analysis of behavioral data. As with many other fields, statistical approaches for these analyses traditionally use classical (i.e., frequentist) methods. Interpreting classical intervals and p‐values correctly can be burdensome and counterintuitive. By contrast, Bayesian methods treat data, parameters, and hypotheses as random quantities and use rules of conditional probability to produce direct probabilistic statements about models and parameters given observed study data. In this work, we reanalyze two data sets using Bayesian procedures. We precede the analyses with an overview of the Bayesian paradigm. The first study reanalyzes data from a recent study of controls, heavy smokers, and individuals with alcohol and/or cocaine substance use disorder, and focuses on Bayesian hypothesis testing for covariates and interval estimation for discounting rates among various substance use disorder profiles. The second example analyzes hypothetical environmental delay‐discounting data. This example focuses on using historical data to establish prior distributions for parameters while allowing subjective expert opinion to govern the prior distribution on model preference. We review the subjective nature of specifying Bayesian prior distributions but also review established methods to standardize the generation of priors and remove subjective influence while still taking advantage of the interpretive advantages of Bayesian analyses. We present the Bayesian approach as an alternative paradigm for statistical inference and discuss its strengths and weaknesses.