A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.     

Restricted multidimensional scaling models for asymmetric proximities

Restricted multidimensional scaling models [Bentler & Weeks, 1978] allowing constraints on parameters, are extended to the case of asymmetric data. Separate functions are used to model the symmetric and antisymmetric parts of the data. The approach is also extended to the case in which data are presumed to be linearly related to squared distances. Examples of several models are provided, using journal citation data. Possible extensions of the models are considered. This research was supported in part by USPHS Grant 0A01070, P. M. Bentler, principal investigator, and NIMH Grant MH-24819, E. J. Anthony and J. Worland, principal investigators. The authors wish to thank E. W. Holman and several anonymous reviewers for their valuable suggestions concerning this research.     

Canonical analysis of longitudinal and repeated measures data with stationary weights

When measuring the same variables on different occasions, two procedures for canonical analysis with stationary compositing weights are developed. The first, SUMCOV, maximizes the sum of the covariances of the canonical variates subject to norming constraints. The second, COLLIN, maximizes the largest root of the covariances of the canonical variates subject to norming constraints. A characterization theorem establishes a model building approach. Both methods are extended to allow for Cohort Sequential Designs. Finally a numerical illustration utilizing Nesselroade and Baltes data is presented.The authors wish to thank John Nesselroade for permitting us to use the data whose analysis we present.     

Vocational maturity in adulthood: Toward turning a model into a measure

It is postulated that adult vocational maturity needs to be assessed because of the changing developmental tasks encountered during the course of a career. Vocational maturity having been found to be multidimensional, existing undimensional inventories of adult vocational maturity are considered of limited although demonstrated validity. Relevant theories of adult vocational development and adjustment are reviewed. Super's proposed adult vocational maturity model is examined for the promise that it offers and for the problems that arise in developing a multidimensional measure of vocational maturity. A way of surmounting these problems is proposed as a basis for work now being undertaken.     

Back to basics: Percentage agreement measures are adequate, but there are easier ways

Percentage agreement measures of interobserver agreement or "reliability" have traditionally been used to summarize observer agreement from studies using interval recording, time-sampling, and trial-scoring data collection procedures. Recent articles disagree on whether to continue using these percentage agreement measures, and on which ones to use, and what to do about chance agreements if their use is continued. Much of the disagreement derives from the need to be reasonably certain we do not accept as evidence of true interobserver agreement those agreement levels which are substantially probable as a result of chance observer agreement. The various percentage agreement measures are shown to be adequate to this task, but easier ways are discussed. Tables are given to permit checking to see if obtained disagreements are unlikely due to chance. Particularly important is the discovery of a simple rule that, when met, makes the tables unnecessary. If reliability checks using 50 or more observation occasions produce 10% or fewer disagreements, for behavior rates from 10% through 90%, the agreement achieved is quite improbably the result of chance agreement.     

Axiomatic and numerical conjoint measurement: An evaluation of diagnostic efficacy

Synthetic data are used to examine how well axiomatic and numerical conjoint measurement methods, individually and comparatively, recover simple polynomial generators in three dimensions. The study illustrates extensions of numerical conjoint measurement (NCM) to identify and model distributive and dual-distributive, in addition to the usual additive, data structures. It was found that while minimum STRESS was the criterion of fit, another statistic, predictive capability, provided a better diagnosis of the known generating model. That NCM methods were able to better identify generating models conflicts with Krantz and Tversky's assertion that, in general, the direct axiom tests provide a more powerful diagnostic test between alternative composition rules than does evaluation of numerical correspondence. For all methods, dual-distributive models are most difficult to recover, while consistent with past studies, the additive model is the most robust of the fitted models.Douglas Emery is now at the Krannert Graduate School of Management, Purdue University, West Lafayette, IN, on leave from the University of Calgary.     

Text comprehension in aphasia

The semantic and pragmatic strategies in the comprehension of spoken texts are investigated in four subgroups of aphasic patients and in normal and brain-damaged controls. Short texts of similar linguistic structure were read to the subjects, who were required to choose the picture, from a multiple choice set of five, that was appropriate to the story. Besides a picture showing the main event of the story, one picture depicted the literal sense of a metaphorical comment, and the others misrepresented semantic functions expressed in the text. With respect to these types of responses, both aphasics and controls exhibited the same pattern of reaction. It is concluded that the redundancy of texts makes up for the difficulties aphasics have in comprehending isolated words and sentences.     

Two-step weighted least squares factor analysis of dichotomized variables

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure.