Issues in the detection and interpretation of interaction effects between quantitative variables in multiple regression analysis are discussed. Recent discussions associated with problems of multicollinearity are reviewed in the context of the conditional nature of multiple regression with product terms. (TJH)

In matrix comparison, the performance of four vector matching indices (the coefficient of congruence, the Pearson product moment correlation, the "s"-statistic, and kappa) was evaluated. Advantages and disadvantages of each index are discussed, and the performance of each was assessed within the framework of principal components…

Application of equality constraints on the categories of a variable is a simple and useful extension of multiple correspondence analysis. Equality is an easy way to incorporate prior knowledge. A procedure to deal with unequal category numbers and with subsets of variables is outlined and illustrated. (SLD)

PARAFAC is a generalization of principal components analysis in a factor score matrix and in a factor loadings matrix. How PARAFAC behaves when applied to positive manifold data is examined, and a constrained PARAFAC method is offered for use when PARAFAC does not produce a positive manifold solution. (SLD)

Studies the evolution of information production processes and their relation to the Lorenz dominance order as a theoretical framework for bibliometrics. The relation between the total number of sources, the total number of items, the average production, and the maximum production are examined. Geometric illustrations are provided. (Contains 14…

A simplified version of successive intervals scaling is described. Scale values for various datasets obtained with simplified successive intervals scaling are approximately linearly related to those obtained with traditional successive intervals scaling and the method of pair comparisons. The ease of use and some cautions in method use are…

The accuracy of Kendall's chi square approximation (M. Kendall, 1962) to circular triad distributions was assessed by comparing estimated indices to enumerated values across upper and lower tails of cumulative proportions of circular triad distributions. In general, the approximation was found to be quite good, and its use is discussed. (SLD)

As examples of models that are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale. (SLD)

Discusses two forms of separability of item and person parameters in the context of response time models. The first is "separate sufficiency," and the second is "ranking independence." For each form a theorem stating sufficient conditions is proved. The two forms are shown to include several cases of models from psychometric…

For trinary partial credit items, the shape of the item information and item discrimination functions is examined in relation to the item parameters. Conditions under which these functions are unimodal and bimodal are discussed, and the locations and values of maxima are derived. Practical relevance of the results is discussed. (SLD)

Traditional and innovative uses of the Rasch model in the development and validation of both small- and large-scale psychological instruments are illustrated and discussed. Advantages of the model in maximizing scale interpretability and validity are presented. Both mathematical and conceptual explanations are provided using counseling psychology…

Provides a general mathematical framework is provided that can be specialized to four different reliability coefficients. Consideration of this general framework makes it easier to convey to students the individual character of the formulations of reliability and the extent of their underlying similarity. (SLD)

Hazard rate models are described, and selected techniques are used to analyze paired hazard rates when event times are right censored. The techniques are illustrated by looking at mortality patterns in husbands and wives. Recently developed measures and models are introduced. The advantages and disadvantages of the measures are discussed.…

Describes the Rasch measurement partial credit model, what it is, how it differs from other Rasch models, and when and how to use it. Also describes the calibration of instruments with increasingly complex items. Explains pivot anchoring and illustrates its use and describes the effect of pivot anchoring on step calibrations, item hierarchy, and…

This book is a compendium of recent item response theory (IRT) research that reviews 27 IRT models. The book contains a historical overview of IRT followed by six sections that deal with the application of a particular IRT model or set of models. (SLD)