Investigating the effect of mental set on insight problem solving

Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of noninsight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves noninsight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralization.     

Hyperstructures, Topology and Datasets

In the natural sciences higher order structures often occur. There seems to be a need for good methods of describing what we mean by higher order structures in various contexts. This is what hyperstructures are intended to do. We motivate and introduce this new concept. Next we illustrate how it can be applied in various types of genomic analysis—particular the correlations between single nucleotide polymorphisms and diseases. The suggested structure is quite general and may be applied to a variety of situations. Finally we discuss how data sets (f. ex. genomic) may lead to topological spaces, giving new invariants and lead to the prediction of hyperstructures.     

Approaches to univocal factor scores

Two current methods of deriving common-factor scores from tests are briefly examined and rejected. One of these estimates a score from a multiple-regression equation with as many terms as there are tests in the battery. The other limits the equation to a few tests heavily saturated with the desired factor, with or without tests used to suppress the undesired factors. In the proposed methods, the single best test for each common factor is the starting point. Such a test ordinarily has a very few undesired factors to be suppressed, frequently only one. The suppression test should be univocal, or nearly so. Fortunately, there are relatively univocal tests for factors that commonly require suppression. Equations are offered by which the desired-factor test and a single suppression test can be weighted in order to achieve one or more objectives. Among the objectives are (1) maximizing the desired factor variance, (2) minimizing the undesired factor variance, (3) a compromise, in which the undesired variance is materially reduced without loss in desired variance, and (4) a change to any selected ratio of desired to undesired variance. A more generalized solution is also suggested. The methods can be extended in part to the suppression of more than one factor. Equations are derived for the suppression of two factors.     

A note on the use of directional statistics in weighted euclidean distances multidimensional scaling models

The weighted euclidean distances model in multidimensional scaling (WMDS) represents individual differences as dimension saliences which can be interpreted as the orientations of vectors in a subject space. It has recently been suggested that the statistics of directions would be appropriate for carrying out tests of location with such data. The nature of the directional representation in WMDS is reviewed and it is argued that since dimension saliences are almost always positive, the directional representations will usually be confined to the positive orthant. Conventional statistical techniques are appropriate to angular representations of the individual differences which will yield angles in the interval (0, 90) so long as dimension saliences are nonnegative, a restriction which can be imposed. Ordinary statistical methods are also appropriate with several linear indices which can be derived from WMDS results. Directional statistics may be applied more fruitfully to vector representations of preferences.     

Forming all pairs in a minimal number of steps

How can N individuals in a closed space meet and greet each other most efficiently? This paper presents a general solution to this problem—an algorithm or “dance” that will achieve universal pairing in the least possible number of moves or steps. A proof of the suggested algorithm is included, showing that it guarantees that every two participants will greet each other once and only once, and that no procedure with this property can be accomplished with fewer steps. Slightly different procedures are required for the odd and even cases. The algorithm has been applied in classroom settings, and could be applied in any social setting where the objective is to initiate efficiently a sense of group cohesion and common purpose.     

Reichenbach, induction, and discovery

Conclusion I have applied a fairly general, learning theoretic perspective to some questions raised by Reichenbach's positions on induction and discovery. This is appropriate in an examination of the significance of Reichenbach's work, since the learning-theoretic perspective is to some degree part of Reichenbach's reliabilist legacy. I have argued that Reichenbach's positivism and his infatuation with probabilities are both irrelevant to his views on induction, which are principally grounded in the notion of limiting reliability. I have suggested that limiting reliability is still a formidable basis for the formulation of methodological norms, particularly when reliability cannot possibly be had in the short run, so that refined judgments about evidential support must depend upon measure-theoretic choices having nothing to do in the short run with the truth of the hypothesis under investigation. To illustrate the generality of Reichenbach's program, I showed how it can be applied to methods that aim to solve arbitrary assessment and discovery problems in various senses. In this generalized Reichenbachian setting, we can characterize the intrinsic complexity of reliable inductive inference in terms of topological complexity. Finally, I let Reichenbach's theory of induction have the last say about hypothetico-deductive method.     

Clarifying the task

Those who would enquire into therelationship between “health conceptions” and “health care consequences” are faced with a formidable task. In order to make this challenge manageable it is necessary to define the scope of the task as precisely as possible. Are we, for instance, faced with a purely theoretical challenge; a task for applied philosophy, or must we employ multi-disciplinary methods? This paper argues that while philosophy has a central clarifying role, inquiry into the relationship between “health conceptions” and “health care organisation” can be done properly only through the combined efforts of several disciplines. Unless we are to be concerned only with abstract models it is essential to take account of the reality of health care situations. Given this it is suggested that the study of “health conceptions” is only a part of a greater task (unless all conceptions are to count as “health conceptions”). What is needed is understanding of the possible and actual purposes of health care, and detailed study of their practical implications.     

THE SPLIT LEVEL PROBLEM AS RELATED TO THE TASK OF EVALUATING ITEMS IN THE CLINICAL AREA

H olley , J. W. & H ansson , K. The split level problem as related to the task of evaluating items in the clinical area. Scand.J. Psychol ., 1969, 10, 124–128—It is pointed out that correlational values can be distorted in item evaluation when the proportions of persons in the criterion groups are variant. The use of a 'K ratio' is suggested as a possible solution to be applied under restrictive conditions.     

Why and How to Learn Why: Analysis-based Generalization of Procedures

Max Wertheimer, in his classic Productive Thinking, linked understanding to transfer: Understanding is important because it provides the ability to generalize the solution of one problem to apply to another. Recent work in human and machine learning has led to the development of a new class of generalization mechanism, called here analysis-based generalization, which can be used to provide a concrete account of the linkage Wertheimer suggested: these mechanisms all, in different ways, use understanding of examples in the generalization process. In this paper I review this class of mechanism, and describe a method for causal attribution that can produce the analyses of examples that the generalization methods require, in the domain of simple procedures in human-computer interaction. This causal analysis method is linked with analysis-based generalization to form EXPL, an implemented model which is a concrete, though limited, instontiation of Wertheimer s scheme. EXPL constructs an understanding of an example procedure and generalizes it on the basis of that understanding. Results of an empirical study suggest that some of EXPL's attribution heuristics are used by people, and that while a subclass of analysis-based methods, called superstitious methods, seem to provide a more plausible account of people's generalization under the conditions of the study than a contrasting class of rationalistic methods, at least some participants appear to use methods from both classes. The results also show that explanation-based methods, which rely on comprehensive domain theories, must be used in conjunction with a means for extending the domain theory. If thus enhanced, explanation-based methods are able to mimic the effects of other analysis-based methods, and can provide a good account of the data, though combinations of other methods must also be considered. Finally, I return to Wertheimer s ideas to argue that none of the current analysis-based generalization methods fully captures Wertheimer s notion of understanding. Proper choice among different possible analyses of an example is crucial for Wertheimer, but I argue that this problem may be beyond the reach of learning systems.     

Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach

A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats.     

A Multiobjective Diet Planning Support System Using the Satisficing Trade-off Method

This paper shows that the satisficing trade-off method (STOM), one of the interactive multiobjective programming techniques, can be applied effectively to the formulation of livestock rations. Nutrient requirements are considered as soft constraints whose right-hand sides are flexible to some extent. This is easily done by regarding the values of the right-hand sides of the constraints as aspiration levels of the decision maker for objective functions. In this way a well-balanced solution can be obtained by STOM with automatic trade-off analysis. In STOM, moreover, because the objective functions and the constraint functions are interchangeable, decision makers are not required to consider the role of objective and constraint as fixed from the beginning. The authors’ experience is that the method makes ration formulation very easy, rapid and flexible. In addition, this paper shows how effectively STOM can be applied not only to diet planning but also to nutritional diagnosis. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 131–139 (1997) No. of Figures: 1. No. of Tables: 3. No. of References: 28.     

Sensory responsiveness and the effects of equal subjective rewards on tactile learning and memory of honeybees

In tactile learning, sucrose is the unconditioned stimulus and reward, which is usually applied to the antenna to elicit proboscis extension and which the bee can drink when it is subsequently applied to the extended proboscis. The conditioned stimulus is a tactile object that the bee can scan with its antennae. In this paper we describe the quantitative relationships between gustatory antennal stimulation, gustatory proboscis stimulation, and tactile learning and memory. Bees are 10-fold more responsive to sucrose solutions when they are applied to the antenna compared to proboscis stimulation. During tactile conditioning, the sucrose solution applied to the proboscis determines the level of acquisition, whereas antennal input is of minor importance. Bees differing in their gustatory responsiveness measured at the antenna differ strongly in their tactile acquisition and memory. We demonstrate how these differences in tactile acquisition and memory can be greatly reduced by calculating equal subjective rewards, based on individual gustatory responsiveness.     

Oblique rotation in correspondence analysis: A step forward in the search for the simplest interpretation

Correspondence analysis (CA) is a popular method that can be used to analyse relationships between categorical variables. It is closely related to several popular multivariate analysis methods such as canonical correlation analysis and principal component analysis. Like principal component analysis, CA solutions can be rotated orthogonally as well as obliquely into a simple structure without affecting the total amount of explained inertia. However, some specific aspects of CA prevent standard rotation procedures from being applied in a straightforward fashion. In particular, the role played by weights assigned to points and dimensions and the duality of CA solutions are unique to CA. For orthogonal simple structure rotation, procedures recently have been proposed. In this paper, we construct oblique rotation methods for CA that take into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.     

The solution of simultaneous equations

This paper is an attempt to integrate the various methods which have been developed for the numerical solution of simultaneous linear equations. It is demonstrated that many of the common methods, including the Doolittle Method, are variations of the method of single division. The most useful variation of this method, in case symmetry is present, appears to be the Abbreviated Doolittle method. The method of multiplication and subtraction likewise can be abbreviated in various ways of which the most satisfactory form appears to be the new Compact method. These methods are then applied to such problems as the solution of related equations, the solution of groups of equations, and the evaluation of the inverse of a matrix.     

Multi-objective combinatorial optimization problems: A survey

In the last 20 years many multi-objective linear programming (MOLP) methods with continuous variables have been developed. However, in many real-world applications discrete variables must be introduced. It is well known that MOLP problems with discrete variables can have special difficulties and so cannot be solved by simply combining discrete programming methods and multi-objective programming methods. The present paper is intended to review the existing literature on multi-objective combinatorial optimization (MOCO) problems. Various classical combinatorial problems are examined in a multi-criteria framework. Some conclusions are drawn and directions for future research are suggested.     

Approximate methods in calculating discriminant functions

Approximate methods of solving for discriminant functions have been tried on three sets of data. The principal illustration is the problem of finding a weighted sum of scores, on four psychological tests, so that men and women may be distinguished most clearly. The work starts from the complete solution, due to R. A. Fisher, where it is necessary to solve as many simultaneous equations, dependent on the standard deviations of the tests and their mutual correlations, as there are tests. It is proposed, by way of numerical simplification, that a set of equations be substituted where some one quantity replaces all the correlations. A solution is obtained where the weights to be assigned the tests are very simply expressed in terms of differences between the mean values of tests, the standard deviations of tests, and the said quantity. The difficulty remains of finding an estimate of the arbitrary constant that will give good discrimination. If an optimal solution is made a result is obtained which, in the three sets of data considered, is almost indistinguishable from that yielded by the complete solution. The calculation of this optimal common quantity is, however, itself so considerable that another estimate, previously suggested by R. W. B. Jackson, appears more profitable. This estimate is derived simply from the variability between the total scores for each subject and the variability of each test. Using this estimate, the discriminant functions can be rapidly calculated; the results compare very favorably, in the case of the data considered, with those from the complete solution.The present work was done while the writer was employed by the Ontario Department of Health.     

Toward a Model-Based Approach to the Clinical Assessment of Personality Psychopathology

Recent years have witnessed tremendous growth in the scope and sophistication of statistical methods available to explore the latent structure of psychopathology, involving continuous, discrete, and hybrid latent variables. The availability of such methods has fostered optimism that they can facilitate movement from classification primarily crafted through expert consensus to classification derived from empirically based models of psychopathological variation. The explication of diagnostic constructs with empirically supported structures can then facilitate the development of assessment tools that appropriately characterize these constructs. Our goal in this article is to illustrate how new statistical methods can inform conceptualization of personality psychopathology and therefore its assessment. We use magical thinking as an example, because both theory and earlier empirical work suggested the possibility of discrete aspects to the latent structure of personality psychopathology, particularly forms of psychopathology involving distortions of reality testing, yet other data suggest that personality psychopathology is generally continuous in nature. We directly compared the fit of a variety of latent variable models to magical thinking data from a sample enriched with clinically significant variation in psychotic symptomatology for explanatory purposes. Findings generally suggested a continuous latent variable model best represented magical thinking, but results varied somewhat depending on different indexes of model fit. We discuss the implications of the findings for classification and applied personality assessment. We also highlight some limitations of this type of approach that are illustrated by these data, including the importance of substantive interpretation, in addition to use of model fit indexes, when evaluating competing structural models.     

Psychological distress: A hierarchical factor model of the Multiple Affect Adjective Check List (MAACL)

Recent investigations of the structure of psychological distress have indicated that hierarchical models can accommodate both unitary and multifaceted conceptions of distress. The present study tested the hierarchical framework suggested by Zuckerman, Lubin, and Rinck (1983) for the Multiple Affect Adjective Check List (MAACL), a commonly used measure of psychological distress. One- and two-factor models were estimated using maximum-likelihood methods. Results indicated that the two-factor solution, with correlated positive and negative affect factors, provided a significantly better fit to the data than did the omnibus one-factor solution. These results provide further support for hierarchical models of distress.