The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features

A method is discussed which extends principal components analysis to the situation where the variables may be measured at a variety of scale levels (nominal, ordinal or interval), and where they may be either continuous or discrete. There are no restrictions on the mix of measurement characteristics and there may be any pattern of missing observations. The method scales the observations on each variable within the restrictions imposed by the variable's measurement characteristics, so that the deviation from the principal components model for a specified number of components is minimized in the least squares sense. An alternating least squares algorithm is discussed. An illustrative example is given.Copies of this paper and of the associated PRINCIPALS program may be obtained by writing to Forrest W. Young, Psychometric Laboratory, Davie Hall 013-A, Chapel Hill, NC 27514.     

Correspondence analysis used complementary to loglinear analysis

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.     

A value focused model for a C4 network1

This effort provides a quantitative method that incorporates the objectives of a C4I system. A systematic methodology, which incorporates expert opinion and operational necessities, is provided to evaluate communications networks. While the specific weighting and measures for a value hierarchy will depend upon the operational environment and the decision makers, a framework to develop such a hierarchy is provided. The approach produced graphical displays that provide a great deal of insight into the tradeoffs which could be made and the driving factors behind the system scores. Copyright © 2000 US Government     

Four simultaneous component models for the analysis of multivariate time series from more than one subject to model intraindividual and interindividual differences

A class of four simultaneous component models for the exploratory analysis of multivariate time series collected from more than one subject simultaneously is discussed. In each of the models, the multivariate time series of each subject is decomposed into a few series of component scores and a loading matrix. The component scores series reveal the latent data structure in the course of time. The interpretation of the components is based on the loading matrix. The simultaneous component models model not only intraindividual variability, but interindividual variability as well. The four models can be ordered hierarchically from weakly to severely constrained, thus allowing for big to small interindividual differences in the model. The use of the models is illustrated by an empirical example.This research has been made possible by funding from the Netherlands Organization of Scientific Research (NWO) to the first author. The authors are obliged to Tom A.B. Snijders, Jos M.F. ten Berge and three anonymous reviewers for comments on an earlier version of this paper, and to Kim Shifren for providing us with her data set, which was collected at Syracuse University.     

Some uniqueness results for PARAFAC2

Whereas the unique axes properties of PARAFAC1 have been examined extensively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy have recently shown, subject to mild assumptions, that PARAFAC2 is unique when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2. The authors are obliged to Richard Harshman for stimulating this research, and to the Associate Editor and reviewers for suggesting major improvements in the presentation.     

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.     

Interview‐informed synthesized contingency analyses: Thirty replications and reanalysis

The speed with which a functional analysis (FA) provides a convincing demonstration of the variables that influence problem behavior may be termed efficiency. Multiple FA formats have been developed to improve analytic efficiency while the core components of the Iwata, Dorsey, Slifer, Bauman, and Richman (1982/1994) procedures are maintained. We attempted to illustrate an alternative efficient process for conducting FAs of problem behavior that relied on modifying those core components. In Study 1, we describe 30 applications of the interview‐informed synthesized contingency analysis (Hanley, Jin, Vanselow, & Hanratty, 2014), which required an average of 25 min of analysis. The first sessions of these analyses were reanalyzed in Study 2 to determine if contingencies that controlled problem behavior could be identified in only 3 to 5 min. This was the case in 80% of analyses.     

Functional analysis screening for multiple topographies of problem behavior

The current study evaluated a screening procedure for multiple topographies of problem behavior in the context of an ongoing functional analysis. Experimenters analyzed the function of a topography of primary concern while collecting data on topographies of secondary concern. We used visual analysis to predict the function of secondary topographies and a subsequent functional analysis to test those predictions. Results showed that a general function was accurately predicted for five of six (83%) secondary topographies. A specific function was predicted and supported for a subset of these topographies. The experimenters discuss the implication of these results for clinicians who have limited time for functional assessment.     

Simplimax: Oblique rotation to an optimal target with simple structure

Factor analysis and principal component analysis are usually followed by simple structure rotations of the loadings. These rotations optimize a certain criterion (e.g., varimax, oblimin), designed to measure the degree of simple structure of the pattern matrix. Simple structure can be considered optimal if a (usually large) number of pattern elements is exactly zero. In the present paper, a class of oblique rotation procedures is proposed to rotate a pattern matrix such that it optimally resembles a matrix which has an exact simple pattern. It is demonstrated that this method can recover relatively complex simple structures where other well-known simple structure rotation techniques fail.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences. The author is obliged to Jos ten Berge for helpful comments on an earlier version.     

Reaffirming The Importance Of ��Analysis�� In Applied Behavior Analysis: A Review Of A. C. Repp And R. H. Horner��s Edited Book, Functional Analysis Of Problem Behavior: From Effective Assessment To Effective Support.

In recent years, much has been written about the topics of functional assessment and functional analysis in applied settings. In their book, Functional Analysis of Problem Behavior: From Effective Assessment to Effective Support, Repp and Horner (1999) have compiled a series of essays from experts on the topic. In this article, we review their work and comment on each chapter's contribution to the relevant literature. We conclude that the book meets its primary goals of expanding our view of functional analysis as well as providing those new to the field with a stronger understanding of the topic. We do, however, note some concerns with inconsistent use of functional analysis terminology and a lack of practical guidance regarding its implementation in applied settings, but we believe these limitations are inherent in the empirical literature and are not unique to this book. Thus, we strongly endorse this book as “must reading” for behaviorally oriented researchers, students, and practitioners.     

Interpreting functional analysis outcomes using automated nonparametric statistical analysis

Current methods employed to interpret functional analysis data include visual analysis and post-hoc visual inspection (PHVI). However, these methods may be biased by dataset complexity, hand calculations, and rater experience. We examined whether an automated approach using nonparametric rank-based statistics could increase the accuracy and efficiency of functional analysis data interpretation. We applied Automated Nonparametric Statistical Analysis (ANSA) to a sample of 65 published functional analyses for which additional experimental evidence was available to verify behavior function. Results showed that exact behavior function agreement between ANSA and the publications authors was 83.1%, exact agreement between ANSA and PHVI was 75.4%, and exact agreement across all 3 methods was 64.6%. These preliminary findings suggest that ANSA has the potential to support the data interpretation process. A web application that incorporates the calculations and rules utilized by ANSA is accessible at https://ansa.shinyapps.io/ansa/     

Bridging the Marketing Gap: A Review of How to Think Like a Behavior Analyst: Understanding the Science That Can Change Your Life by Jon Bailey and Mary Burch

The field of applied behavior analysis has suffered from a relative dearth of user-friendly books appropriate to a lay audience. Bailey and Burch''s book fills this niche with a work that is both entertaining and informative. The book is reviewed in terms of the strengths and limitations of its content, as well as in the context of the importance of effective marketing of behavior analysis.     

结构方程模型的应用及分析策略

差不多所有心理、教育、社会等概念,均难以直接准确测量,结构方程（SEM,Struc－tulalEquationModelling）提供一个处理测量误差的方法,采用多个指标去反映潜在变量,也令估计整个模型因子间关系,较传统回归方法更为准确合理。本文主要用一系列有关学习动机的虚拟例子,指出每个问题的主要分析策略,以展示SEM在教育及心理学可以应用的研究范畴。文内探讨的方法包括：验证性因素、高阶因子、路径及因果分析、多时段（multiwave）设计、单形模型（SimpleModel）、及多组比较等。     

Can I use TA? Should I use TA? Should I not use TA? Comparing reflexive thematic analysis and other pattern‐based qualitative analytic approaches

Thematic analysis methods, including the reflexive approach we have developed, are widely used in counselling and psychotherapy research, as are other approaches that seek to develop ‘patterns’ (themes, categories) across cases. Without a thorough grounding in the conceptual foundations of a wide variety of across‐case analytic approaches, and qualitative research more broadly—something rarely offered in counselling training—it can be difficult to understand how these differ, where they overlap, and which might be appropriate for a particular research project. Our aim in this paper is to support researchers in counselling and psychotherapy to select an appropriate across‐case approach for their research, and to justify their choice, by discussing conceptual and procedural differences and similarities between reflexive thematic analysis (TA) and four other across‐case approaches. Three of these are also widely used in counselling and psychotherapy research—qualitative content analysis, interpretative phenomenological analysis and grounded theory. The fourth—discourse analysis—is less widely used but importantly exemplifies the critical qualitative research tradition. We contextualise our comparative approach by highlighting the diversity within TA. TA is best thought of as a spectrum of methods—from types that prioritise coding accuracy and reliability to reflexive approaches like ours that emphasise the inescapable subjectivity of data interpretation. Although reflexive TA provides the point of comparison for our discussion of other across‐case approaches, our aim is not to promote reflexive TA as ‘best’. Rather, we encourage the knowing selection and use of analytic methods and methodologies in counselling and psychotherapy research.     

The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.     

From Complexity Concepts to Creative Applications

A complexity cosmography is introduced as construing a world that is self-organizing, dynamic, and emergent, and that comprises organic entities that too are self-organizing, dynamic, and emergent. Following critical reflection into the nature of utilising complexity in social inquiry, specific images, vocabularies and complexity-based methods and techniques as developed by the authors are introduced.     

Empirical Guidance for Time-Window Sequential Analysis of Single Cases

Time-window sequential analyses test whether a target behavior occurs within a temporal window (e.g., within 2 seconds) after an antecedent behavior more than is expected by chance. This type of question is common when we need to know how one person or event may immediately affect another event or person in the natural environment. Theoretically, the significance of sequential associations from time-window analysis can be tested on the single subject level (Bakeman & Quera, 1995). The present Monte Carlo study was conducted to test the Type I error rates and the difference in sequential associations derived from four methods of time-window sequential analysis. The four methods vary according to whether they analyze the duration of antecedent and target behaviors. The results indicate that time-window sequential analysis method is generally valid. The results were most accurate when antecedent duration and target onset was analyzed. Although analyzing duration of the antecedent did affect the results, the effect size for the difference in results due to presence or absence of measuring duration of the antecedent was extremely small. Time-window analysis results appear unaffected by the decision to analyze the duration of the target event.