Measurement foundations for multiattribute psychophysical theories based on first order polynomials

Unique finite conjoint measurement

Conjoint measurement in utility theory with incomplete product sets

Additive conjoint measurement with ordered categories

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.

Assessment of pseudo-plastic and dilatant materials flow in channel driven cavity: application of metallurgical processes

A discussion of problems and methods in modern psychophysics is presented. A distinction is made between prothetic and metathetic continua, and between ratio scales, category scales and what are called confusion scales. The paper includes a survey of some scaling experiments and reports the exponents of a number of power functions describing the relation between stimulus magnitude and subjective magnitude.

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.

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.

The search for general laws governing our perceptual representation of the external world goes back at least to Fechner and is no less important now than it was then. Fechner used human discrimination performance to infer that the basic relationship between subjective intensity and the intensity of a physical stimulus was logarithmic. A hundred years later, Stevens demonstrated that direct subjective report frequently results in a power law rather than a logarithmic law. However, it was soon appreciated that power laws and logarithmic laws are indistinguishable without peering inside the mechanisms leading to a subject's responses. After doing so, Mountcastle and his colleagues proposed that the basic law is linearity between the neural representation of an intensive continuum and its subjective magnitude. We were drawn to the same conclusion in a study of the neural coding mechanisms of roughness perception that was designed to be independent of any assumptions about the basic laws of psychophysics. We adopted consistency as the test of neural coding hypotheses. The single, consistent neural coding hypothesis that survived all challenges resulted in a linear relationship between the neural coding measure and subjects' reports of intensity. That hypothesis was that roughness perception depends on spatial variation in the SAI afferent population response. This study and other similar studies support the idea that once the internal neural representation of intensity is established, the fundamental laws are linear, as Mountcastle proposed over thirty years ago.

Vibrotactile subjective magnitude as a function of hand preference

: 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.

Nontransitive Decomposable Conjoint Measurement

Current understandings of human craniofacial growth are based on multiple historic longitudinal growth studies. The extent to which regional variation in growth patterns is present among the various growth studies even within the United States, however, is not well understood. The aim of this study is to compare growth patterns across six of the nation's largest growth studies.Lateral cephalographs were examined from the historical archives of the Denver Growth Study, Iowa Growth Study, and Oregon Growth Study (available via the AAOF Legacy Collection) as well as the Fels Longitudinal Study, the Michigan Growth Study, and the Bolton‐Brush Growth Study. A set of 44 two‐dimensional landmarks were collected on longitudinal series from participants 6–22 years old. A total of 5,622 cephalographs from 726 males and 5,514 cephalographs from 723 females were assessed. Fifth order polynomials were used to evaluate growth of 11 linear craniofacial measures for each growth study and by sex. Rates of growth and associated growth milestones were calculated from polynomial models and compared across study and by sex. In addition, geometric morphometric analyses were used to assess ontogenetic shape differences among studies using a regression of the shape variables on log centroid size, pooled by study, with subsequent evaluation of residual variation.Growth curves for the separate studies roughly parallel each other yet show differences in the timing of growth milestones and adult morphology. In general, for each linear trait participants in the Denver study are smaller and participants in the Iowa and Michigan studies are larger than participants in other studies at the same chronological age. Timing of onset and peak growth is similar in all 11 craniofacial measures, although trait values at those growth milestones differ by study. Preliminary results from the geometric morphometric analysis identify a common ontogenetic pattern shared across studies but demonstrate that, for a given size, individuals from the Denver study are more advanced along the common shape trajectory relative to other studies. Although ontogenetic trajectories are roughly similar, overall shape differences are present between study populations.Variations in growth and overall morphology among these six longitudinal growth study populations demonstrate regional differences in the rate and timing of growth that may be attributable to the ancestry and environmental conditions of study participants. Further study of the mechanisms for these differences in growth will improve the accuracy of craniofacial growth predictions, thereby improving the efficacy of growth modification interventions in pediatric craniofacial treatment.Support or Funding InformationFunding: NIH/NIDCR R03‐DE021435; NIH/NIDCR R01 DE024732This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Many of the laws and empirical observations of fundamental psychophysics can be unified with a single equation, which has been called the complete form of Fechner's law. It can be shown that this law embraces both of the commonly used forms: Stevens's and Fechner's laws. It assumes one or the other form with appropriate values of the parameters. However, the complete equation confers an advantage beyond simply containing the classical laws. It offers greater flexibility in the representation of experimental data. It is shown that psychophysical phenomena may be represented by any number of triplets of quantities: subjective magnitude of stimulus, subjective just noticeable difference (jnd), and differential threshold. Each of the preceding quantities are functions of the physical magnitude of the stimulus. The investigator has the license to choose two of these quantities in the form he or she thinks is best; the third quantity is determined by the choice of the first two. Thus, for example, different forms of the law of sensation and different forms of the mathematical function for differential threshold may coexist with equal validity.

Security issues have always been one of the main points of interest of all states. Scientifically, this issue can be researched using a wide range of perspectives. Security studies use much from the general theory of international relations. The field uses theoretical paradigms and concrete methods of research. In this article, a wide approach to the issue of security and security policy is presented. In accordance with the theoretical-methodological foundation of realist and liberal theories, this article inquires in what way research concerning the issues of security and security policy of contemporary states can be conducted.