Minimization of a class of matrix trace functions by means of refined majorization

A procedure is described for minimizing a class of matrix trace functions. The procedure is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization. It contains a recently proposed algorithm by Koschat and Swayne for weighted Procrustes rotation as a special case. A number of trial analyses demonstrate that the refined majorization procedure is more efficient than the earlier majorization-based procedure. The research of H. A. L. Kiers has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences.     

A simple technique for improving the quality of parameter estimates in learning hierarchy validation studies

Learning hierarchy research has been characterized by the use of ad hoc statistical procedures to determine the validity of postulated hierarchical connections. The two most substantial attempts to legitimize the procedure are due to White & Clark and Dayton & Macready, although both of these methods suffer from serious inadequacies. Data from a number of sources is analyzed using a restricted maximum likelihood estimation procedure and the results are compared with those obtained using the method suggested by Dayton and Macready. Improved estimates are evidenced by an increase in the computed value of the log likelihood function.     

Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization

This paper presents a multiple-objective metaheuristic procedure—Pareto simulated annealing. The goal of the procedure is to find in a relatively short time a good approximation of the set of efficient solutions of a multiple-objective combinatorial optimization problem. The procedure uses a sample, of so-called generating solutions. Each solution explores its neighbourhood in a way similar to that of classical simulated annealing. Weights of the objectives, used for their local aggregation, are tuned in each iteration in order to assure a tendency for approaching the efficient solutions set while maintaining a uniform distribution of the generating solutions over this set. A computational experiment shows that the method is a better tool for approximating the efficient set than some previous proposals. © 1998 John Wiley & Sons, Ltd.     

An interactive multiobjective programming approach to combinatorial data analysis

Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. Multiobjective programming is an operations research methodology that enables the quantitative analyst to investigate tradeoffs among relevant objective criteria. In this paper, we describe an interactive procedure for multiobjective asymmetric unidimensional seriation problems. This procedure uses a dynamic-programming algorithm to partially generate the efficient set of sequences for small to medium-sized problems, and a multioperation heuristic to estimate the efficient set for larger problems. The interactive multiobjective procedure is applied to an empirical data set from the psychometric literature. We conclude with a discussion of other potential areas of application in combinatorial data analysis.Stephanie Stahl is a freelance writer and editor. She can be reached via e-mail at s-stahl@worldnet.att.net.     

Relative costs and statistical power in the extreme groups approach

The relationship between variables in applied and experimental research is often investigated by the use of extreme (i.e., upper and lower) groups. Recent analytical work has provided an extreme groups procedure that is more powerful than the standard correlational approach for all values of the correlation and extreme group size. The present article provides procedures to optimize power by determining the relative number of subjects to use in each of two stages of data collection given a fixed testing budget.The opinions or assertions contained herein are those of the writers and are not to be construed as official or reflecting the views of the Navy Department.Edward F. Alf, Jr. is also affiliated with the Department of Psychology, San Diego State University.     

Clustering with relational constraint

The paper deals with clustering problems where grouping is constrained by a symmetric and reflexive relation. For solving clustering problems with relational constraints two methods are adapted: the standard hierarchical clustering procedure based on the Lance and Williams formula, and local optimization procedure, CLUDIA. To illustrate these procedures, clusterings of the European countries are given based on the developmental indicators where the relation is determined by the geographical neighbourhoods of countries.Extended version of the paper presented at the European meeting of the Psychometric Society, Groningen, June, 19–21, 1980.This work was supported in part by the Boris Kidri Fund, Yugoslavia.     

A convex approach for multicriteria decision making in hierarchical systems

In this paper hierarchical multicriteria optimization problems are addressed in a convex programming framework. It is assumed that the criteria are aggregated into a nonlinear function, which renders the problem nonseparable, in general. The projection of the problem onto the criteria space is used to obtain an equivalent separable problem, solved through a relaxation procedure implemented on basis of a multilevel structure. At the upper level of the structure, the decision making process involves the solution of a multicriteria problem formulated in the criteria space. The solution encountered at the upper level originates a lower level parametric optimization problem with separable structure that can be treated by standard coordination-decomposition techniques. The convergence of the overall procedure is ensured. The paper includes an application of the approach proposed for the control of dynamic systems with linear quadratic structure. © 1998 John Wiley & Sons, Ltd.     

A minimum-cost network-flow solution to the case V thurstone scaling problem

This paper presents an approach for determining unidimensional scale estimates that are relatively insensitive to limited inconsistencies in paired comparisons data. The solution procedure, shown to be a minimum-cost network-flow problem, is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on traditional Thurstone (ordinary least squares) scale estimates. When the diagnostic indicates some source of distortion in the data, the network technique appears to be more successful than Thurstone scaling in preserving the interval scale properties of the estimates.My special thanks go to Alvin Silk, Thomas Magnanti, and Roy Welsch for their support and advice throughout the formative stages of this paper, and to V. Srinivasan for his helpful comments on a later draft of this paper. I also wish to thank the Editor, Associate Editor, and two reviewers for their constructive suggestions.James M. Lattin is Associate Professor of Marketing and Management Science and the James and Doris McNamara Faculty Fellow for 1988-1989.     

A model and algorithm for multidimensional scaling with external constraints on the distances

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configurationX relative to the proximity dataP and the loss ofX relative to a pseudo-data matrixR. The matrixR is set up such that the side constraints to be imposed onX's distances are expressed by the relations amongR's numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solutionX. Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matricesP andR. Further generalizations are introduced by substitutingR by a set ofR matrices,R _i ,i=1, ...r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.     

A numerical approach to the approximate and the exact minimum rank of a covariance matrix

A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.The authors are obliged to Paul Bekker for stimulating and helpful comments.     

Compiling Measurement Invariant Short Scales in Cross-Cultural Personality Assessment Using Ant Colony Optimization

Examining the influence of culture on personality and its unbiased assessment is the main subject of cross-cultural personality research. Recent large-scale studies exploring personality differences across cultures share substantial methodological and psychometric shortcomings that render it difficult to differentiate between method and trait variance. One prominent example is the implicit assumption of cross-cultural measurement invariance in personality questionnaires. In the rare instances where measurement invariance across cultures was tested, scalar measurement invariance—which is required for unbiased mean-level comparisons of personality traits—did not hold. In this article, we present an item sampling procedure, ant colony optimization, which can be used to select item sets that satisfy multiple psychometric requirements including model fit, reliability, and measurement invariance. We constructed short scales of the IPIP-NEO-300 for a group of countries that are culturally similar (USA, Australia, Canada, and UK) as well as a group of countries with distinct cultures (USA, India, Singapore, and Sweden). In addition to examining factor mean differences across countries, we provide recommendations for cross-cultural research in general. From a methodological perspective, we demonstrate ant colony optimization's versatility and flexibility as an item sampling procedure to derive measurement invariant scales for cross-cultural research. © 2020 The Authors. European Journal of Personality published by John Wiley & Sons Ltd on behalf of European Association of Personality Psychology     

Order-Constrained Solutions in <Emphasis Type="Italic">K</Emphasis>-Means Clustering: Even Better Than Being Globally Optimal

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that although the usual K-means sum-of-squared-error criterion is not guaranteed to be minimal, a true underlying cluster structure may be more accurately recovered. Also, substantive interpretability seems generally improved when constrained solutions are considered. We illustrate the procedure with several data sets from the literature.     

Using the teaching interaction procedure to train interventionists to implement the Cool versus Not CoolTM procedure

The teaching interaction procedure is a behavior analytic procedure that has been used to target the development of social skills. The teaching interaction procedure consists of labeling the target skill, providing a meaningful rationale, describing the steps of the target skill, modeling the skill, role‐play, and providing feedback throughout the interaction. Although the teaching interaction procedure has been used to teach a variety of social skills for individuals diagnosed with autism spectrum disorder (ASD), it has only been used to train staff in two studies. The purpose of this study was to evaluate the use of the teaching interaction procedure to teach three interventionists to implement the Cool versus Not Cool? procedure to target the development of social skills for children diagnosed with ASD. The results of a multiple baseline design demonstrated that the teaching interaction procedure was effective for all three interventionists. Results of the child participants' skill acquisition are also provided.     

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.     

Indclus: An individual differences generalization of the adclus model and the mapclus algorithm

We present a new model and associated algorithm, INDCLUS, that generalizes the Shepard-Arabie ADCLUS (ADditive CLUStering) model and the MAPCLUS algorithm, so as to represent in a clustering solution individual differences among subjects or other sources of data. Like MAPCLUS, the INDCLUS generalization utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach to impose discrete (0,1) constraints on parameters defining cluster membership. All subjects in an INDCLUS analysis are assumed to have a common set of clusters, which are differentially weighted by subjects in order to portray individual differences. As such, INDCLUS provides a (discrete) clustering counterpart to the Carroll-Chang INDSCAL model for (continuous) spatial representations. Finally, we consider possible generalizations of the INDCLUS model and algorithm.We are indebted to Seymour Rosenberg for making available the data from Rosenberg and Kim [1975]. Also, this work has benefited from the observations of S. A. Boorman, W. S. DeSarbo, G. Furnas, P. E. Green, L. J. Hubert, L. E. Jones, J. B. Kruskal, S. Pruzansky, D. Schmittlein, E. J. Shoben, S. D. Soli, and anonymous referees.This research was supported in part by NSF Grant SES82 00441, LEAA Grant 78-NI-AX-0142, and NSF Grant SES80 04815.     

Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

Combining standardized mean differences using the method of maximum likelihood

A maximum likelihood procedure for combining standardized mean differences based on a noncentratt-distribution is proposed. With a proper data augmentation technique, an EM-algorithm is developed. Information and likelihood ratio statistics are discussed in detail for reliable inference. Simulation results favor the proposed procedure over both the existing normal theory maximum likelihood procedure and the commonly used generalized least squares procedure.     

"Automaintenance": the role of reinforcement

A key was illuminated on the average of every 30 sec for a duration of 6 sec and this was followed by food presentations. When key pecks in the presence of the light produced immediate access to grain (autoshaping procedure) pigeons were likely to peck. When pecks terminated the keylight but prevented access to grain (automaintenance procedure) pigeons were much less likely to peck. Seven of 12 pigeons failed to develop responding during the automaintenance procedure. Four of the five pigeons that responded during the automaintenance procedure were exposed to a procedure in which responses could not immediately terminate the light. Three of the four ceased to respond during optimal automaintenance conditions, suggesting that the response-dependent offset of the keylight had been reinforcing their pecking. Responding during the automaintenance procedure was eliminated for a fifth pigeon by eliminating the contiguity of light-offset and food-onset on those trials in which the pigeon did not peck. These results suggest that: (1) automaintenance (unlike autoshaping) is not an effective procedure for reliably generating responding; (2) responding that does occur during the automaintenance procedure is reinforced by the response-dependent offset of the keylight.     

Pairwise agreement of gradient directions in interactive multicriterion optimization

Statistical tests involving mean directions have in the past been limited to two- and three-dimensional settings, perhaps owing to their primary applications to such fields as geology, meteorology and related earth sciences. In the study of interactive multicriterion optimization it becomes necessary to compare gradient directions obtained from decision makers by two or more methods. Typically these direction vectors are in a higher-dimensional space. This paper provides a general procedure based on Householder transformations which is potentially suitable for any finite dimension. An illustration and comparison of the method are provided.     

Postcriterion overlearning reduces the effectiveness of the method of adjusted learning

One goal of the method of adjusted learning (“dropout procedure”) is to equate the strength of different Items for subsequent retention. Some studies have yielded results in accord with this goal while others have not, with no known reason for the discrepancy. We manipulated the number of postcriterion overlearning trials and found that the adjusted learning procedure was effective in equating items for subsequent retention when learning terminated after one correct response per item but ineffective when postcriterion overlearning trials occurred. This finding is especially important for those versions of the adjusted learning procedure, such as the frequently utilized variant developed by Battig (1965), that incorporate overlearning of the to-be-equated items.