Application of model-selection criteria to some problems in multivariate analysis

A review of model-selection criteria is presented, with a view toward showing their similarities. It is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model-selection criteria. Consideration is given to application of model-selection criteria to some problems of multivariate analysis, especially the clustering of variables, factor analysis and, more generally, describing a complex of variables.     

Application of a large sampling criterion to some sampling problems in factor analysis

A technique is presented to test the completeness of factor solutions and also to test the significance of common-component loadings. The chisquare test involved is based upon the asymptotic normal properties of the residuals.The research work on which the results presented are based was conducted under the supervision of Prof. P. S. Dwyer, Mathematics Department, University of Michigan. The complete results of this research were presented in a Ph. D. thesis, June, 1951.     

Solutions to the problems of incremental validity testing in relationship science

Incremental validity testing (i.e., testing whether a focal predictor is associated with an outcome above and beyond a covariate) is common (e.g., 57% of Personal Relationships articles in 2017), yet it is fraught with conceptual and statistical problems. First, researchers often use it to overemphasize the novelty or counterintuitiveness of findings, which hinders cumulative understanding. Second, incremental validity testing requires that the focal predictor and the covariate represent separate constructs; researchers risk committing the “jangle fallacy” without such evidence. Third, the most common approach to incremental validity testing (i.e., standard multiple regression, 88% of articles) inflates Type I error and can produce invalid conclusions. This article also discusses the relevance of these issues to dyadic/longitudinal designs and offers concrete solutions.     

Solutions to some nonlinear equations from nonmetric data

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.This work was begun while the author was on sabbatical leave during 1970–71 at the Department of Mathematical Psychology, University of Nijmegen, the Netherlands, where discussions with E. E. Roskam on the problem were very helpful. Support was provided by Grant A0151 from the Natural Sciences and Engineering Council, Canada.     

Theory and tests of the conjoint commutativity axiom for additive conjoint measurement

The empirical study of the axioms underlying additive conjoint measurement initially focused mostly on the double cancellation axiom. That axiom was shown to exhibit redundant features that made its statistical evaluation a major challenge. The special case of double cancellation where inequalities are replaced by indifferences–the Thomsen condition–turned out in the full axiomatic context to be equivalent to the double cancellation property but without exhibiting the redundancies of double cancellation. However, it too has some undesirable features when it comes to its empirical evaluation, the chief among them being a certain statistical asymmetry in estimates used to evaluate it, namely two interlocked hypotheses and a single conclusion. Nevertheless, thinking we had no choice, we evaluated the Thomsen condition for both loudness and brightness and, in agreement with other lines of research, we found more support for conjoint additivity than not. However, we commented on the difficulties we had encountered in evaluating it. Thus we sought a more symmetric replacement, which as Gigerenzer and Strube (1983) first noted, is found in the conjoint commutativity axiom proposed by Falmagne (1976, who called it the “commutative rule”). It turns out that, in the presence of the usual structural and other necessary assumptions of additive conjoint measurement, we can show that conjoint commutativity is equivalent to the Thomsen condition, a result that seems to have been overlooked in the literature. We subjected this property to empirical evaluation for both loudness and brightness. In contrast to Gigerenzer and Strube (1983), our data show support for the conjoint commutativity in both domains and thus for conjoint additivity.     

The integration of motivational information: A conjoint measurement analysis

Within Anderson's (1974a, b, c, 1978b) information integration theory, the integration of motivational information was investigated by means of conjoint measurement techniques. Eighteen university students were asked to judge hypothetical co-students characterized by three features (intelligence, motivation and the extent to which they study) according to their chances to pass. Both rank order data and ratings were obtained. The orderings of most subjects could be represented very well by an additive model. A polynomial regression procedure was applied to determine the shape of the response function for the ratings. As this function was quite linear for all subjects, the ratings could be said to form an interval scale.     

Expectancy-value models of health behaviour: An analysis by conjoint measurement

Various studies in the health area consistently rejected the multiplicative combination between severity and probability of threat which is predicted by expectancy-value (EV) theories. It is hypothesized here, that this negative evidence may be due to an overly demanding assumption underlying the multiplicative combination, namely, the assumption that people are able to performs trade-offs between expectancies and valences. This hypothesis is tested in two studies in which subjects judged hypothetical health threats. Results from a nonparametric analysis (conjoint measurement) of individual data (Study 1) and an experimental study of trade-off judgments (Study 2) are mostly consistent with the prediction. Unexpectedly, however, an ANOVA of the aggregate data of Study 1 yielded a small, but significant effect consistent with the multiplicative assumption. Whereas this latter result can be interpreted as evidencing an attempt to perform trade-offs, the overall results show as predicted that trade-off judgments are associated with a systematic error component due to the inherent difficulty of this type of judgment.     

An empirical comparison of three variants of the AHP and two variants of conjoint analysis

This paper provides an empirical comparison of two methods of attribute valuation: the analytic hierarchy process (AHP) and conjoint analysis. Variants within each approach are also examined. The results of two empirical studies indicate that the methods differ in their predictive and convergent validity. Within the AHP methods no significant difference in predictive validity was found. Within the conjoint methods, the ranking method significantly outperformed the rating method. The difference in predictive validity between the AHP and conjoint methods was significant in the second study but not in the first study, suggesting superior performance of the AHP over conjoint analysis in complex problems. Copyright© 1998 John Wiley & Sons, Ltd.     

Methods of solving some personnel-classification problems

The personnel-classification problems considered in this paper are related to those studied by Brogden (2), Lord (6), and Thorndike (8). Section 1 gives an approach to personnel classification. A basic problem and variations of it are treated in section 2; and the computation of a solution is illustrated in section 3. Two extensions of the basic problem are presented in section 4. Most of the methods indicated for computing solutions are applications of the simplex method used in linear programming (see 1, Chs. XXII, XXIII). The capabilities of a high speed computer in regard to the simplex method are discussed briefly (see section 1).This work was supported in part by the United States Air Force under Contract AF 33(038)-25192, monitored by the Personnel Research Laboratory of the Air Training Command Human Resources Research Center. Permission is granted for reproduction, translation, publication, use, and disposal in whole or in part by or for the United States Government.     

Some problems and issues in the implementation of mental health programs in the public schools

New roles are possible for school psychologists because of mental health needs engendered by today's problems in educational settings. There is a great urgency for school psychologists to seek larger scale kinds of solutions than have typified the more frequently practiced therapeutic efforts of school psychologists in the past. Mental health programs that are more suitably adapted to the life styles of low-income and minority groups is a high priority requisite for such work to be successful in today's schools.     

On some structural aspects of physical problems

Bachelard's concept of the problématique is used in order to classify physical problems and their interrelations. This classification is effectuated along two dimensions. Along the horizontal dimension, physical problems are divided into the kinds that the different modes of physics' development define. These modes are themselves determined by the interplay among the conceptual system, the object and the experimentation transactions specific to physics. Along the vertical dimension, physical problems are classified according to the different stages of maturation they have to undergo before the process of their solution is effectively undertaken. To determine these maturation stages, the Althusserian conception of ideology is used. The interrelations between physical problems are examined through the introduction and elaboration of the notion interdependence network.It is a pleasure to thank Marcello Pera and Kostas Gavroglou for their very helpful comments and criticisms.