Additive conjoint measurement with ordered categories

Unique finite conjoint measurement

This article surveys recent investigations of real sequences (d 1,..., d n ) which arise in the theory of measurement from considerations of uniqueness for numerical representations of qualitative relations on finite sets. The sequences we discuss arise from measurement problems which include measurement of subjective probability, extensive measurement, difference measurement, and additive conjoint measurement. The measurement problems lead to sequences with fascinating combinatorial and number-theoretic properties.The unifying mathematical framework under which we analyze uniqueness of measurement in these diverse areas involves the analysis of the sequences (d 1,...,d n)as the solutions of finite systems of linear equations. Different applications are translated into different restrictions on the types of linear equations that are admissible for each area.Two primary concerns of measurement theory are involved in the work being surveyed: (1) axioms for the qualitative relation that are necessary and sufficient, or at least sufficient, for unique represent ability; (2) the structure of sets of unique solutions. The latter concern leads to combinatorial and number-theoretic problems involving characterizations of unique solutions, counts of numbers of unique solutions, and extreme-value questions. Definitive results and presently open problems are described for the areas covered by the basic theory.KeywordsSubjective ProbabilityIndependent EquationRegular SequenceExtensive MeasurementFibonacci SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The counselor in a children's health camp is the central figure in the system of interaction with children. He has a significant impact on the psychological and physical development of his charges. This circumstance requires attention to the psychological aspects of his work. These aspects include both theoretical and practical levels, which are inextricably linked. The theoretical level is represented by professional knowledge in the fields of pedagogy and psychology. The practical level is expressed in psychological attitudes and the possession of a professional pedagogical perspective on the educational and upbringing process in a children's health camp. In turn, the practical level has an external and internal side that requires psychological support in order to improve the quality of the counselor's work.

Conjoint measurement in utility theory with incomplete product sets

The axioms of additive conjoint measurement provide a means of testing the hypothesis that testing data can be placed onto a scale with equal-interval properties. However, the axioms are difficult to verify given that item responses may be subject to measurement error. A Bayesian method exists for imposing order restrictions from additive conjoint measurement while estimating the probability of a correct response. In this study an improved version of that methodology is evaluated via simulation. The approach is then applied to data from a reading assessment intentionally designed to support an equal-interval scaling.

It is common to note that the English law of torts protects privacy interests in a less direct and more disjointed manner than such interests are protected in France, Germany and the United States.1 Those who regard this as a deficiency and consequently urge reform are met by counter-arguments at three levels: theoretical, practical and strategic. At the theoretical level, the dispute between ‘privacy sceptics’ and ‘privacy disciples’ is over the value of privacy, and how it is to be weighted relative to other values such as freedom of expression and freedom of the press. At the practical level, the dispute is over the translation of concern about privacy into workable law. At the strategic level, the dispute is over whether reform will be best managed by the judiciary or the legislature, or even whether privacy interests are likely to be better protected by extra-legal approaches. The three levels cannot be kept separate. Conclusions at the theoretical level are clearly relevant to discussion at the practical level, and the view taken on the degree of difficulty at the practical level may affect the choice of strategy.

Contemporary South Africa places the practice of sociology before unusual challenges on both theoretical and practical problem-solving levels. In order to meet these challenges we urgently need a paradigm in which the creational nature of reality is acknowledged. Accepting such a paradigm is in itself a challenge because of the foothold the existing paradigm has on western thought. Until sociologists accept this challenge they will continue to contend with existing paradigms which try to explain reality by approaching it in terms of its own existence. For this purpose one of the aspects of reality is absolutized time and again and made a principal of origin for the whole of reality. This means that the rest of reality is theoretically forced to function according to the mode of the absolutized aspect. This misconception leads to many problems on theoretical and practical levels. Scientists can be freed from this by accepting the creational nature of reality, which should lead to a better understanding of its problems. S. Afr. J. Sociol. 1986, 17(4): 143–147

Scientific findings involve description, and description requires measurements on the dimensions descriptive of the phenomena described. The richer a description the more multidimensional is the abstract space in which that description in effect locates what is described. Many of the dimensions of human psychological phenomena, including those of psychotherapy, are naturally gradated only ordinally. So descriptions of these phenomena locate them in merely ordinal hyperspaces, which imposes severe constraints on data analysis for inducing or testing explanatory theory involving them. Therefore, it is important to be clear about what these constraints are and so what properly can be concluded on the basis of ordinal-scale multivariate data, which also provides a test for methods that are proposed to transform ordinal-scale data into ratio-scale data (e.g., classical test theory, item response theory, additive conjoint measurement), because such transformations must not violate these constraints and so distort descriptions of studied phenomena.

Measurement foundations for multiattribute psychophysical theories based on first order polynomials

In almost all current approaches to decision making under uncertainty, it is assumed that a decision problem is described by a set of states and set of outcomes, and the decision maker (DM) has a preference relation on a rather rich set of acts, which are functions from states to outcomes. The standard representation theorems of decision theory give conditions under which the preference relation can be represented by a utility function on outcomes and numerical representation of beliefs on states. For example, Savage [4] shows that if a DM’s preference order satisfies certain axioms, then the DM’s preference relation can be represented by a probability Pr on the state space and a utility function mapping outcomes to the reals such that she prefers act a to act b iff the expected utility of a (with respect to Pr) is greater than that of b. Moreover, the probability measure is unique and the utility function is unique up to affine transformations. Similar representations of preference can be given with respect to other representations of uncertainty (see, for example, [2,5]).

Nontransitive Decomposable Conjoint Measurement

Decision maker usually should consider multi-attribute alternatives and choose one or some of them which seems to be best or better than others. Especially in the developed information society, there is a plenty of information for each alternative, and it is not quite easy to find out some of most proper alternatives in view of important attributes. In this paper, we propose a ranking method with uncertainty for multi-attribute alternatives which would help decision maker to decide what alternatives should be proper for a problem he/she is confronting. Since our method is systematically completed with some numerical computations and with fuzzy outranking method, it makes the decision maker possible to concentrate to each attribute and to retain the uncertainty of their priorities up until the final stage.

In 2004, the American Academy of Pediatrics (AAP) Board of Directors formed the Task Force on Mental Health and charged it with developing strategies to improve the quality of child and adolescent mental health* services in primary care. The task force acknowledged early in its deliberations that enhancing the mental health care that pediatricians and other primary care clinicians† provide to children and adolescents will require systemic interventions at the national, state, and community levels to improve the financing of mental health care and access to mental health specialty resources. Systemic strategies toward achieving these improvements are the subject of other publications of the task force: “ Strategies for System Change in Children's Mental Health: A Chapter Action Kit ” (chapter action kit),1 “Improving Mental Health Services in Primary Care: Reducing Administrative and Financial Barriers to Access and Collaboration,”2 and “Enhancing Pediatric Mental Health Care: Strategies for Preparing a Community.”3 The task force also recognized that enhanced mental health practice will require competencies not currently achieved by many primary care clinicians; in the policy statement “The Future of Pediatrics: Mental Health Competencies for Pediatric Primary Care,”4 the task force collaborated with the AAP Committee on Psychosocial Aspects of Child and Family Health to outline these competencies and propose strategies for achieving them. This report offers strategies for preparing the primary care practice itself for provision of enhanced mental health care services. The task force proposes incrementally applying chronic care principles to the care of children with mental health and substance abuse problems as primary care clinicians apply them to the care of children with chronic medical conditions such as asthma. Most primary care clinicians will find that significant gaps exist between their current practice and the proposed ideal. The task force offers guidance in … Address correspondence to Jane Meschan Foy, MD, Department of Pediatrics, Wake Forest University School of Medicine, Medical Center Blvd, Winston-Salem, NC 27157. E-mail: jmfoy{at}wfubmc.edu

Utility representation of lower separable preferences

: This report presents the results of an attempt to propose a basis for an error theory of conjoint measurement methodology. Conjoint measurement methodology offers a new and potentially useful approach for obtaining psychological scale values for components of multidimensional attributes. This report describes the mathematical foundations of this methodology as well as a means of evaluating the fit of an additive conjoint measurement model to a three factor design. For each of the critical axioms of conjoint measurement, proportions of errors that would be expected by chance for different conditions of simple independence are examined. In addition, a computer-based algorithm that can be used to perform specific kinds of conjoint analysis has been generalized and documented as a technique for assessing the fit of an additive model to a set of data. The program is called SWAT and its current state of development is described in this report. Finally, the appendices provide a step-by-step explanation of data deck arrangements for SWAT as well as some actual printouts from the program.