Generalized structured component analysis

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method avoids the principal limitation of partial least squares (i.e., the lack of a global optimization procedure) while fully retaining all the advantages of partial least squares (e.g., less restricted distributional assumptions and no improper solutions). The method is also versatile enough to capture complex relationships among variables, including higher-order components and multi-group comparisons. A straightforward estimation algorithm is developed to minimize the criterion.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We wish to thank Richard Bagozzi for permitting us to use his organizational identification data and Wynne Chin for providing PLS-Graph 3.0.     

Kuczynski on Partial Knowledge and the Paradox of Analysis

John–Michael Kuczynski says the "paradox of analysis" can be resolved with the proper definition of "partial knowledge." He says that this definition will not do: (K) S has partial knowledge of x = _df S knows some, but not all, of x 's parts. He offers an alternative account of incomplete or partial knowledge. I argue here that: (a) Kuczynski's chief criticisms of (K) are defective; (b) his proposed solution to the paradox of analysis has no clear application to the paradox in its familiar forms; and (c) his solution may not avoid the puzzle about partial knowledge it was designed to resolve.     

Using pretreatment and posttreatment assessments to enhance and evaluate existing treatment packages.

Pretreatment assessment data were used to enhance an existing treatment package to reduce aggression and to increase positive social interactions between a young boy and his peers. Based on the results of pretreatment assessments, additional reinforcement (differential reinforcement of alternative behavior with adult attention) and punishment (performing a nonpreferred task during time-out) components were added to an existing nonresetting differential reinforcement of other behavior (access to peers unless aggression occurred) plus time-out procedure. A posttreatment component analysis of the additional treatment components indicated that the reinforcement component facilitated positive social interactions and the punishment component suppressed aggression towards peers.     

On component analyses

Principal components analysis can be redefined in terms of the regression of observed variables upon component variables. Two criteria for the adequacy of a component representation in this context are developed and are shown to lead to different component solutions. Both criteria are generalized to allow weighting, the choice of weights determining the scale invariance properties of the resulting solution. A theorem is presented giving necessary and sufficient conditions for equivalent component solutions under different choices of weighting. Applications of the theorem are discussed that involve the components analysis of linearly derived variables and of external variables.Preparation of this article was supported in part by National Institute of Aging Grant NIA-AG03164-03 to William Meredith.     

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.     

Signaled alternative reinforcement and the persistence of operant behavior

Differential reinforcement of alternative behavior (DRA) is a treatment designed to eliminate problem behavior by reinforcing an alternative behavior at a higher rate. Availability of alternative reinforcement may be signaled, as with Functional Communication Training, or unsignaled. Whether or not alternative reinforcement is signaled could influence both the rate and persistence of problem behavior. The present study investigated whether signaling the availability of alternative reinforcement affects the rate and persistence of a concurrently available target response with pigeons. Three components of a multiple concurrent schedule arranged equal reinforcement rates for target responding. Two of the components also arranged equal reinforcement rates for an alternative response. In one DRA component, a discrete stimulus signaled the availability of response‐contingent alternative reinforcement by changing the keylight color upon reinforcement availability. In the other DRA component, availability of alternative reinforcement was not signaled. Target responding was most persistent in the unsignaled DRA component when disrupted by satiation, free food presented between components, and extinction, relative to the signaled DRA and control components. These findings suggest the discrete stimulus functionally separated the availability of alternative reinforcement from the discriminative stimuli governing target responding. These findings provide a novel avenue to explore in translational research assessing whether signaling the availability of alternative reinforcement with DRA treatments reduces the persistence of problem behavior.     

The analysis of multitrait-multimethod matrices via constrained components analysis

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to three anonymous reviewers and an associate editor for constructive suggestions on the first version of this paper.     

A fast method for choosing the numbers of components in Tucker3 analysis

Recently, Timmerman and Kiers proposed an effective procedure for choosing the numbers of components in Tucker3 analysis, a kind of component analysis of three‐way data. The procedure, however, is rather time‐consuming, relying on very many complete Tucker3 analyses. Here, an alternative procedure is proposed, which basically relies on a single, quick analysis of the three‐way data set. In a simulation study it was found that the new procedure is comparable in its effect to the original procedure.     

Temporal constraint on choice: Sensitivity and bias in multiple schedules

In multiple schedules of reinforcement, ratios of responses in successive components are relatively insensitive to ratios of obtained reinforcers. An analysis is proposed that attributes changes in absolute response rates to concurrent interactions between programmed reinforcement and extraneous reinforcement in other components. The analysis predicts that ratios of responses in successive components vary with reinforcer ratios, qualified by a term describing the reinforcement context, that is, programmed and extraneous reinforcers. Two main predictions from the analysis were confirmed in an experiment in which pigeons' responses were reinforced in the components of a multiple schedule and analog extraneous reinforcement was scheduled for an alternative response in each component. Sensitivity of response and time ratios to reinforcer ratios in the multiple schedules varied as a function of the rate of extraneous reinforcers. Bias towards responding in one component of the multiple schedule varied as an inverse function of the ratios of extraneous reinforcer rate in the two components. The data from this and previous studies of multiple-concurrent performance were accurately predicted by our analysis and supported our contention that the allocation of behavior in multiple-schedule components depends on the relative values of concurrently-available reinforcers within each component.     

The structure and reliability of the teacher temperament questionnaire

The Teacher Temperament Questionnaire is a recently developed instrument designed for personality assessment with preschool and early school children. The present study employed a sample of 116 in order to study the reliability and structure of the TTQ. A principal-components analysis yielded four well-defined components, which were labeled Compliance, Extraversion, Interpersonal Affect, and Environmental Sensitivity. These results did not support the theoretical scales. The component patterns were well defined and stable across the two administrations of the inventory. Internal consistency and test-retest reliability coefficients were determined for each of the four new scales. A second administration involving only items from the first three components provided a partial replication.An initial version of this paper was presented at the Northeastern Educational Research Association Meeting, Ellenville, New York, October 1979.     

Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution. Supported by The Netherlands Organization for Scientific Research (NWO) by grant nr. 030-56403 for the “PIONEER” project “Subject Oriented Multivariate Analysis” to the third author. We would like to thank the anonymous referees for their valuable remarks that have improved the quality of this paper.     

Utility of extinction-induced response variability for the selection of mands

Functional communication training (FCT; Carr & Durand, 1985) is a commonly used differential reinforcement procedure for replacing problem behavior with socially acceptable alternative responses. Most studies in the FCT literature consist of demonstrations of the maintenance of responding when various treatment components (e.g., extinction, punishment) are present and absent (e.g., Fisher et al., 1993; Wacker et al., 1990). Relatively little research on FCT has (a) evaluated the conditions under which alternative responses are acquired or (b) described procedures with technological precision. Thus, additional research on a cogent technology for response acquisition appears to be warranted. In the current study, we evaluated the efficacy of exposing problem behavior to extinction for inducing response variability as a tool for selecting an alternative response during FCT. Once participants engaged in appropriate alternative responses, the reinforcer identified in the functional analysis as maintaining problem behavior was delivered contingent on the alternative behavior. Results showed that exposing problem behavior to extinction was a useful method for producing alternative behaviors during FCT.     

Component analysis of verbal versus spatial working memory training in adolescents with ADHD: A randomized,controlled trial

Adaptive training of working memory (WM) using the Cogmed-RM intervention has recently shown some efficacy as an alternative treatment for ADHD, but this intervention may not be optimally designed. A recent component analysis of WM has suggested that maintenance in primary memory (PM) appears to be largely intact whereas recall from secondary memory (SM) appears to be deficient in ADHD relative to age-matched controls. However, extrapolating from basic research, there is reason to believe that Cogmed-RM may target the PM component more than the SM component; though training with spatial exercises may target the SM component more than training with verbal exercises. To investigate, participants diagnosed with ADHD were randomly assigned to either a verbal training condition (n?=?24) or a spatial training condition (n?=?23) using a randomized, controlled design, and both groups were instructed to complete at least 20 days of training. The PM and SM components of WM were assessed immediately before and after training using both verbal and spatial free recall tasks. The main findings showed that both versions of the intervention enhanced the maintenance of information in PM regardless of test modality, but not the recall of information from SM. Therefore, the component of WM that is improved by Cogmed-RM is not the same component of WM that is deficient in ADHD.     

Function invariant and parameter scale-free transformation methods

The parameter matrices of factor analysis and principal component analysis are arbitrary with respect to the scale of the factors or components; typically, the scale is fixed so that the factors have unit variance. Oblique transformations to optimize an objective statement of a principle such as simple structure or factor simplicity yield arbitrary solutions, unless the criterion function is invariant with respect to the scale of the factors, or the parameter matrix is scale free with respect to the factors. Criterion functions that are factor scale-free have a number of invariance characteristics, such as being equally applicable to primary pattern or reference structure matrices. A scale-invariant simple structure function of previously studied function components is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing.Aspects of this paper were presented at the 1970 and 1974 annual meetings, Society of Multivariate Experimental Psychology, and the 1975 annual meeting, Psychometric Society. This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and research grants (MH24149 and DA01070) from the U. S. Public Health Service. The assistance of Bonnie Barron, Sik-Yum Lee, and several extremely helpful reviewers is gratefully acknowledged.     

Assessing the stability of principal components using regression

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.The authors would like to thank the four anonymous reviewers and the two editors for their valuable comments. Atanu R. Sinha gratefully acknowledges the research support received from the Marketing Studies Center, AGSM, UCLA. Send requests for reprints to Atanu R. Sinha, B418 Gold Hall, 110 Westwood Plaza, Los Angeles, CA 90095.     

The Effectiveness of Partial Information about Attribute Weights for Ranking Alternatives in Multiattribute Decision Making

Weighted additive evaluation functions are widely used to rank alternatives in decision making under certainty with multiple evaluation attributes. Some researchers have suggested that approximate attribute weights may be adequate to accurately rank alternatives. Use of approximate weights would simplify decision analysis since detailed elicitation of weights can be time consuming and controversial. This article investigates the degree to which partial information about the relative magnitudes of attribute weights is sufficient to rank alternatives as a function of the number of decision alternatives, the number of attributes, and the number of allowed levels for each attribute. A simulation analysis, as well as a reanalysis of an actual application, shows that partial information about weights is often not sufficient to determine the most preferred alternative for realistic decision problems. Hence, approximation procedures for specifying weights may lead to errors. However, our work also shows that a simple analysis procedure can be used to accurately determine whether partial information about weights is adequate to correctly specify the most preferred alternative. This procedure can be useful for identifying situations in which detailed elicitation of weights is not needed.     

Reinforcement schedule thinning following treatment with functional communication training

We evaluated four methods for increasing the practicality of functional communication training (FCT) by decreasing the frequency of reinforcement for alternative behavior. Three participants whose problem behaviors were maintained by positive reinforcement were treated successfully with FCT in which reinforcement for alternative behavior was initially delivered on fixed-ratio (FR) 1 schedules. One participant was then exposed to increasing delays to reinforcement under FR 1, a graduated fixed-interval (FI) schedule, and a graduated multiple-schedule arrangement in which signaled periods of reinforcement and extinction were alternated. Results showed that (a) increasing delays resulted in extinction of the alternative behavior, (b) the FI schedule produced undesirably high rates of the alternative behavior, and (c) the multiple schedule resulted in moderate and stable levels of the alternative behavior as the duration of the extinction component was increased. The other 2 participants were exposed to graduated mixed-schedule (unsignaled alternation between reinforcement and extinction components) and multiple-schedule (signaled alternation between reinforcement and extinction components) arrangements in which the durations of the reinforcement and extinction components were modified. Results obtained for these 2 participants indicated that the use of discriminative stimuli in the multiple schedule facilitated reinforcement schedule thinning. Upon completion of treatment, problem behavior remained low (or at zero), whereas alternative behavior was maintained as well as differentiated during a multiple-schedule arrangement consisting of a 4-min extinction period followed by a 1-min reinforcement period.     

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.     

An Experimental Analysis of the Effects of Reading Interventions in a Small Group Reading Instruction Context

The current study examined the effects of several combinations of instructional and motivational interventions on oral reading fluency in the context of small group reading instruction. A treatment package consisting of acquisition, fluency, and motivational components was examined and then dismantled. Results were evaluated individually for each participant using a multiple-probe design in order to identify the most effective, yet efficient reading intervention package for each member of the group. The results indicated that, although all potential combinations of the package were effective, the experimental analysis was able to identify an effective yet more efficient package that produced substantial increases in performance across all students. Results are discussed in terms of effective instructional components in small group instruction and how to adapt methods for the experimental analysis of behavior to make decisions about the effectiveness of small group instruction in reading.This study is based on a dissertation submitted by the first author in partial fulfillment of requirements for the doctoral degree.