Functional measurement approach to self-estimation in multiattribute evaluation

Multiattribute analysis depends on measurement of values and weights. Unless these measures reflect the decision maker's true values and weights, the multiattribute formula may put a less-preferred alternative in first place. To avoid such disordinality requires stringent measurement conditions: First, the values and weights must be on linear (equal interval) or ratio (known zero) scales. Second, these scales must satisfy a condition of common unit across disparate attribute dimensions. Most methods of range adjustment beg both of these measurement questions. Functional measurement theory can solve both problems and so can be useful in multiattribute analysis. Past work has established the operation of a general cognitive algebra as an empirical reality. The averaging model, in particular, makes possible the definition and estimation of weights and values as distinct psychological parameters. It can also solve the problem of common unit. Cognitive algebra thus provides a grounded theoretical foundation on which to develop self-estimation methodology, in which decision makers provide direct estimates of their values and weights. The logic is straightforward. Functional measurement can analyze global judgments to obtain validated psychological scales. These scales may then be used as validational criteria for the self-estimates. Procedures to eliminate biases in the self-estimates can thus be tested and refined in well-learned multiattribute tasks, such as judgments of meals, in which global judgments are trustworthy. Once developed, such self-estimation procedures may be used with some confidence for general multiattribute analysis. A number of studies from 20-odd years of work on the theory of information integration are summarized to show good, although not unmixed promise for self-estimation.     

Biological Implications of Gene–Environment Interaction

Gene–environment interaction (G × E) has been treated as both a statistical phenomenon and a biological reality. It is argued that, although there are important statistical issues that need to be considered, the focus has to be on the biological implications of G × E. Four reports of G × E deriving from the Dunedin longitudinal study are used as exemplars of the biological considerations that should lead to an hypothesis-driven choice of the specific genetic polymorphisms and the specific environmental influence to be investigated. The same four studies are used to discuss how the assessment of internal and external validity can be undertaken and how experimental approaches in humans and with animal models may be informative in the elucidation of the relevant operative biological mechanisms.     

Dissimilarity cumulation theory in arc-connected spaces

This paper continues the development of the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling [Dzhafarov, E.N and Colonius, H. (2007). Dissimilarity Cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290-304]. In arc-connected spaces the notion of a chain length (the sum of the dissimilarities between the chain’s successive elements) can be used to define the notion of a path length, as the limit inferior of the lengths of chains converging to the path in some well-defined sense. The class of converging chains is broader than that of converging inscribed chains. Most of the fundamental results of the metric-based path length theory (additivity, lower semicontinuity, etc.) turn out to hold in the general dissimilarity-based path length theory. This shows that the triangle inequality and symmetry are not essential for these results, provided one goes beyond the traditional scheme of approximating paths by inscribed chains. We introduce the notion of a space with intermediate points which generalizes (and specializes to when the dissimilarity is a metric) the notion of a convex space in the sense of Menger. A space is with intermediate points if for any distinct there is a different point such that (where D is dissimilarity). In such spaces the metric G induced by D is intrinsic: coincides with the infimum of lengths of all arcs connecting to In Universal Fechnerian Scaling D stands for either of the two canonical psychometric increments and (ψ denoting discrimination probability). The choice between the two makes no difference for the notions of arc-connectedness, convergence of chains and paths, intermediate points, and other notions of the Dissimilarity Cumulation theory.     

Risk perception in Taiwan

In a questionnaire study, 51 Taiwanese college students were asked to judge 48 natural and human-made hazards on nine risk characteristics. Another group of 61 students were asked to rate the magnitude of 80 hazards and their attitudes toward these hazards. To evaluate the dimensionality of risk perception, participants' ratings for the nine risk characteristics were analyzed using Profile Analysis via Multidimensional Scaling approach. Two dimensions of risk perception were identified: (i) Involuntary versus Immediate Effect; and (ii) Delayed Effect versus Known to Science and Chronic. The relationships of risk perceptions and perceived public and private responsibilities in risk management were examined. Catastrophic, certain-to-be-fatal, dreaded, and uncontrollable risks were perceived as more deserving of public risk management, while controllable risks that were known to science, known to those exposed, and chronic were perceived as more deserving of private management. In particular, diseases are perceived as most deserving of private risk management and least deserving of public risk management; and technologies are perceived as most deserving of public risk management and least deserving of private risk management.     

Idealization and modeling

This paper examines the role of mathematical idealization in describing and explaining various features of the world. It examines two cases: first, briefly, the modeling of shock formation using the idealization of the continuum. Second, and in more detail, the breaking of droplets from the points of view of both analytic fluid mechanics and molecular dynamical simulations at the nano-level. It argues that the continuum idealizations are explanatorily ineliminable and that a full understanding of certain physical phenomena cannot be obtained through completely detailed, nonidealized representations.     

On scaling models applied to data from several groups

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estimated item reliabilities (or item response error rates) for the different groups, and (c) test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints (i.e., constraints that describe which parameters in the model are the same for the several groups). Various kinds of scaling models are considered here in the multiple-group context.Support for this research was provided in part by the National Science Foundation, to Clogg by Grant No. SES-7823759 and to Goodman by Grant No. SES-8303838. Clogg and Goodman were Fellows at the Center for Advanced Study in the Behavioral Sciences when part of the research was done, with financial support provided in part by National Science Foundation grant BNS-8011494 to the Center. The authors are indebted to Mark P. Becker and James W. Shockey for helpful comments.     

Dissimilarity cumulation theory and subjective metrics

We present a new mathematical notion, dissimilarity function, and based on it, a radical extension of Fechnerian Scaling, a theory dealing with the computation of subjective distances from pairwise discrimination probabilities. The new theory is applicable to all possible stimulus spaces subject to the following two assumptions: (A) that discrimination probabilities satisfy the Regular Minimality law and (B) that the canonical psychometric increments of the first and second kind are dissimilarity functions. A dissimilarity function Dab for pairs of stimuli in a canonical representation is defined by the following properties: (1) a≠b?Dab>0; (2) Daa=0; (3) If and , then ; and (4) for any sequence {a_nX_nb_n}_n∈N, where X_n is a chain of stimuli, Da_nX_nb_n→0?Da_nb_n→0. The expression DaXb refers to the dissimilarity value cumulated along successive links of the chain aXb. The subjective (Fechnerian) distance between a and b is defined as the infimum of DaXb+DbYa across all possible chains X and Y inserted between a and b.     

An Intervention to Help Community-Based Organizations Implement an Evidence-Based HIV Prevention Intervention: The Mpowerment Project Technology Exchange System

Considerable resources have been spent developing and rigorously testing HIV prevention intervention models, but such models do not impact the AIDS pandemic unless they are implemented effectively by community-based organizations (CBOs) and health departments. The Mpowerment Project (MP) is being implemented by CBOs around the US. It is a multilevel, evidence-based HIV prevention program for young gay/bisexual men that targets individual, interpersonal, social, and structural issues by using empowerment and community mobilization methods. This paper discusses the development of an intervention to help CBOs implement the MP called the Mpowerment Project Technology Exchange System (MPTES); CBOs’ uptake, utilization and perceptions of the MPTES components; and issues that arose during technical assistance. The seven-component MPTES was provided to 49 CBOs implementing the MP that were followed longitudinally for up to two years. Except for the widely used program manual, other program materials were used early in implementing the MP and then their use declined. In contrast, once technical assistance was proactively provided, its usage remained constant over time, as did requests for technical assistance. CBOs expressed substantial positive feedback about the MPTES, but felt that it needs more focus on diversity issues, describing real world implementation approaches, and providing guidance on how to adapt the MP to diverse populations.     

Sequential estimation in multidimensional scaling

The concept of sequential estimation is introduced in multidimensional scaling (MDS). The sequential estimation method developed in this paper refers to continually updating estimates of a configuration as new observations are added. This method has a number of advantages, such as a locally optimal design of the experiment can be easily constructed, and dynamic experimentation is made possible. Using artificial data, the performance of our sequential method is illustrated.We are indebted to anonymous reviewers for their suggestions. In addition, we thank Dr. Frank Critchley for his helpful comments on our Q/S algorithm.     

Asymmetry and performance: toward a neurodevelopmental theory

Hemispheric asymmetry implies the existence of developmental influences that affect one hemisphere more than the other. However, those influences are poorly understood. One simple view is that asymmetry may exist because of a relationship between a mental process' degree of lateralization and how well it functions. Data scaling issues have largely prevented such investigations, but it is shown that scaling effects are minimized after correction for ceiling and floor effects. After correction, lateralization-performance correlations are pervasive. However, while some correlations are positive, others are negative, with the direction depending on the underlying lateralized process. Two hypotheses are proposed that can account for these relationships by pointing either to individual differences in maturation of the corpus callosum or to developmental limits encountered at different ages of childhood. Their investigation should contribute toward a neurodevelopmental theory of hemispheric asymmetry.