Some counterexamples in multidimensional scaling

Given a set X with elements x, y,… which has a partial order < on the pairs of the Cartesian product X², one may seek a distance function ? on such pairs (x, y) which satisfies ?(x₁, y₁) < ?(x₂, y₂) precisely when (x₁, y₁) < (x₂, y₂), and even demand a metric space (X, ?) with some such compatible ? which has an isometric imbedding into a finite-dimensional Euclidean space or a separable Hilbert space. We exhibit here systems (X, <) which cannot meet the latter demand. The space of real m-tuples (ξ₁,…,ξ_m) with either the “city-block” norm Σ_i ∥ξ_i∥ or the “dominance” norm max_i, ∥ξ_i∥ cannot possibly become a subset of any finite-dimensional Euclidean space. The set of real sequences (ξ₁, ξ₂,…) with finitely many nonzero elements and the supremum norm sup_i, ∥ξ_i∥ cannot even become a subset of any separable Hilbert space.     

Some statistical considerations in multidimensional scaling

Some shortcomings of current methods of estimating the magnitude of perceived difference are considered. A statistical model for perceived difference is derived which avoids these difficulties and employs judgments of ratios of differences as data. Three estimators of squared difference are developed.This study was conducted while the author was a Psychometric Fellow at Princeton University and Educational Testing Service and is part of a dissertation presented in candidacy for the degree of doctor of philosophy. This research was supported by Office of Naval Research Contract Nonr 1858 and by National Science Foundation Grant GB3402. Extensive use was made of the computing facilities of Princeton University supported in part by National Science Foundation Grant NSF-GP579. The author wishes to express his appreciation to Prof. H. Gulliksen, Prof. F. Geldard, Dr. C. Helm, and Dr. F. Lord for their comments and encouragement.     

Some small sample results for maximum likelihood estimation in multidimensional scaling

Some aspects of the small sample behavior of maximum likelihood estimates in multidimensional scaling are investigated by Monte Carlo. An investigation of Model M2 in the MULTISCALE program package shows that the chi-square test of dimensionality requires a correction of tabled chi-square values to be unbiased. A formula for this correction in the case of two dimensions is estimated. The power of the test of dimensionality is acceptable with as few as two replications for 15 stimuli and as few as five replications for 10 stimuli. The biases in the exponent and standard error estimates in this model are also investigated.The research reported here was supported by grant number APA 320 to the author by the National Science and Engineering Research Council of Canada.     

Asymmetric population axiology: deliberative neutrality delivered

Two related asymmetries have been discussed in relation to the ethics of creating new lives: First, we seem to have strong moral reason to avoid creating lives that are not worth living, but no moral reason to create lives that are worth living. Second, we seem to have strong moral reason to improve the wellbeing of existing lives, but, again, no moral reason to create lives that are worth living. Both asymmetries have proven very difficult to account for in any coherent moral framework. I propose an impersonal population axiology to underpin the asymmetries, which sidesteps the problematic issue of whether or not people can be harmed or benefited by creation or non-creation. This axiology yields perfect asymmetry from a deliberative perspective, in terms of expected value. The axiology also yields substantial asymmetry for large and realistic populations in terms of their actual value, beyond deliberative relevance.     

Cardiovascular medicine at face value: a qualitative pilot study on clinical axiology

Introduction

Cardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they have to make them. Therefore, there is an urgent need to reconsider clinical ethics and Value-Based Medicine. This study proposes a qualitative analysis of the values and the virtues of healthcare professionals in a cardiology hospital in order to establish how the former impact upon the medical and ethical decisions made by the latter.

Results

We point out the need for strengthening the roles of healthcare personnel as educators and guidance counselors in order to meet the ends of medicine, as well as the need for an ethical discernment that is compatible with our results, namely, that the ethical values developed by healthcare professionals stem from their life history as well as their professional education.

Conclusion

We establish the kind of actions, communication skills and empathy that are required to build a stronger patient-healthcare professional relationship, which at the same time improves prognosis, treatment efficiency and therapeutic adhesion.

     

The impossibility of a satisfactory population prospect axiology (independently of Finite Fine-Grainedness)

Philosophical Studies - Arrhenius’s impossibility theorems purport to demonstrate that no population axiology can satisfy each of a small number of intuitively compelling adequacy conditions....     

Bayesian multidimensional scaling for the estimation of a Minkowski exponent

The Minkowski property of psychological space has long been of interest to researchers. A common strategy has been calculating the stress in multidimensional scaling for many Minkowski exponent values and choosing the one that results in the lowest stress. However, this strategy has an arbitrariness problem—that is, a loss function. Although a recently proposed Bayesian approach could solve this problem, the method was intended for individual subject data. It is unknown whether this method is directly applicable to averaged or single data, which are common in psychology and behavioral science. Therefore, we first conducted a simulation study to evaluate the applicability of the method to the averaged data problem and found that it failed to recover the true Minkowski exponent. Therefore, a new method is proposed that is a simple extension of the existing Euclidean Bayesian multidimensional scaling to the Minkowski metric. Another simulation study revealed that the proposed method could successfully recover the true Minkowski exponent. BUGS codes used in this study are given in the Appendix.     

Design considerations for multidimensional scaling

This paper begins with a short tutorial on multidimensional scaling. The focus of the remainder of the paper is on the proper designing of research that will use multidimensional scaling analysis techniques and includes suggestions for the interpretation of results.     

The axiology of Robert S. Hartman: A critical study

Formal axiology is based on the logical nature of meaning, namely intension, and on the structure of intension as a set of predicates. It applies set theory to this set of predicates. Set theory is a certain kind of mathematics that deals with subsets in general, and of finite and infinite sets in particular. Since mathematics is objective and a priori, formal axiology is an objective and a priori science; and a test based on it is an objective test based on an objective standard.

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Memory for multidimensional source information

Source memory may comprise recollection of multiple features of the encoding episode. To analyze the simultaneous representation and retrieval of those multiple features, a multinomial memory model is presented that measures memory for crossed dimensions of source information. The first experiment investigated the validity of the new model. The model showed an excellent statistical fit to empirical data, and the parameters of multidimensional source memory were sensitive to manipulations of source similarity on distinct dimensions. The second experiment used the model to test the hypothesis that source memory for individual context attributes is stochastically related in the case of conscious recollection but independent in the case of familiarity-based recognition judgments. The prediction was supported by the introduction of a "remember"-"know" distinction in a multidimensional source memory test.     

Toward a multidimensional definition of sportsmanship

Abstract

One major problem with research conducted on sportsmanship is the absence of an accepted definition. The purpose of this study was to attempt to derive a definition of sportsmanship by applying premises from social psychological theories and research. A major assumption of this perspective is that sportsmanship meanings and labels attached to given behaviors are learned through interpersonal interactions with various sport participants and that eventually a consensual agreement develops regarding the nature of sportsmanship. It thus follows that a meaningful definition of sportsmanship should be obtained through the athletes themselves. In this study, 1056 male and female athletes completed a questionnaire which contained various items pertaining to sportsmanship. Results from a factor analysis revealed the presence of 5 factors corresponding to the respect and concern for: a) one's full commitment toward sport participation, b) the rules and officials. c) social conventions, d) the opponent, as well as e) a negative approach toward sport participation. Implications of this multidimensional definition for future sportsmanship research are drawn.     

Confidence regions for multidimensional scaling analysis

Techniques are developed for surrounding each of the points in a multidimensional scaling solution with a region which will contain the population point with some level of confidence. Bayesian credibility regions are also discussed. A general theorem is proven which describes the asymptotic distribution of maximum likelihood estimates subject to identifiability constraints. This theorem is applied to a number of models to display asymptotic variance-covariance matrices for coordinate estimates under different rotational constraints. A technique is described for displaying Bayesian conditional credibility regions for any sample size.The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada.     

Measuring change for a multidimensional test using a generalized explanatory longitudinal item response model

Even though many educational and psychological tests are known to be multidimensional, little research has been done to address how to measure individual differences in change within an item response theory framework. In this paper, we suggest a generalized explanatory longitudinal item response model to measure individual differences in change. New longitudinal models for multidimensional tests and existing models for unidimensional tests are presented within this framework and implemented with software developed for generalized linear models. In addition to the measurement of change, the longitudinal models we present can also be used to explain individual differences in change scores for person groups (e.g., learning disabled students versus non‐learning disabled students) and to model differences in item difficulties across item groups (e.g., number operation, measurement, and representation item groups in a mathematics test). An empirical example illustrates the use of the various models for measuring individual differences in change when there are person groups and multiple skill domains which lead to multidimensionality at a time point.