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.     

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.     

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.     

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.     

The significance and future of functional analysis methodologies

Iwata, Dorsey, Slifer, Bauman, and Richman (1982) presented the first comprehensive and standardized methodology for identifying operant functions of aberrant behavior. This essay discusses the significance functional analysis has had for applied behavior analysis. The methodology has lessened the field's reliance on default technologies and promoted analysis of environment-behavior interactions maintaining target responses as the basis for selecting treatments. It has also contributed to the integration of basic and applied research. Future directions for this research are suggested.     

Fitting the off-diagonal dedicom model in the least-squares sense by a generalization of the harman and jones minres procedure of factor analysis

Harshman's DEDICOM model providesa framework for analyzing square but asymmetric materices of directional relationships amongn objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straight-forward computational solution for this model is offered in the present paper. The solution can be interpreted as a generalized Minres procedure suitable for handing asymmetric matrices.     

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     

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.     

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.     

Functional assessment: Contributions and future directions

Functional assessment is at once redefining the standards for clinical interventions and reemphasizing the importance of studying basic behavioral mechanisms. This commentary describes one perception of what we are learning from current research on functional assessment and suggests directions for the future.     

Use of Brief Experimental Analyses in Outpatient Clinic and Home Settings

We describe the historic and current use of brief experimental analysis procedures in outpatient clinic and home settings. We discuss some applications of the designs and suggest design modifications for improving internal validity. We describe our application of the designs to longitudinal, in-home programs for children with severe behavior disorders and demonstrate how related versions of brief experimental analysis procedures can be linked to form a more comprehensive evaluation.     

Improving an optimization‐based framework for sensitivity analysis in multi‐criteria decision‐making

The framework for sensitivity analysis in discrete multi‐criteria decision analysis developed by Rios Insua and French allows simultaneous variation of all parameters and applies to many paradigms for decision analysis. However, its computational load may inhibit use, particularly in the context of a decision conference where results are required in near real time. In order to improve on the current algorithm and its implementation, we investigate, on the one hand, an opportunistic approach aimed at reducing the number of optimization problems solved in the original framework and, on the other, an alternative framework based on distance analysis. Computational results on linear and bilinear models are reported. Copyright © 2001 John Wiley & Sons, Ltd.     

Behavioral analysis of clinical cases

The behavior-analytic approach to clinical phenomena is presented. An operationalized framework for conducting behavioral analysis with clinical cases is provided. Idiographic analysis and treatment innovation are conceptualized and conducted within the framework of the experimental method. Differences between technological and behavior-analytic approaches are illustrated.     

Stepwise Latent Class Models for Explaining Group-Level Outcomes Using Discrete Individual-Level Predictors

Explaining group-level outcomes from individual-level predictors requires aggregating the individual-level scores to the group level and correcting the group-level estimates for measurement errors in the aggregated scores. However, for discrete variables it is not clear how to perform the aggregation and correction. It is shown how stepwise latent class analysis can be used to do this. First, a latent class model is estimated in which the scores on a discrete individual-level predictor are used to construct group-level latent classes. Second, this latent class model is used to aggregate the individual-level predictor by assigning the groups to the latent classes. Third, a group-level analysis is performed in which the aggregated measures are related to the remaining group-level variables while correcting for the measurement error in the class assignments. This stepwise approach is introduced in a multilevel mediation model with a single individual-level mediator, and compared to existing methods in a simulation study. We also show how a mediation model with multiple group-level latent variables can be used with multiple individual-level mediators and this model is applied to explain team productivity (group level) as a function of job control (individual level), job satisfaction (individual level), and enriched job design (group level).     

Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.1978 Psychometric Society Presidential Address.This research has been supported by the Bank of Sweden Tercentenary Foundation under the project entitledStructural Equation Models in the Social Sciences, Karl G. Jöreskog, project director.     

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.     

Procrustes matching by congruence coefficients

Matching by Procrustes methods involves the transformation of one matrix to match with another. A special least squares criterion, the congruence coefficient, has advantages as a criterion for some factor analytic interpretations. A Procrustes method maximizing the congruence coefficient is given. This solution is identical to Mosier's [1939] approximate solution, but is an exact solution for maximum congruence.