Consistent, asymptotically efficient and asymptotically normal stepwise estimators are given for a subclass of the uniparametric and multiparametric exponential families. Estimators are derived from the Robbins-Monro stochastic approximation procedure with certain families of random variables arising from the normalized log-likehood. Three…

An experimental paradigm is proposed for investigating interpersonal conflicts under conditions of intergroup competition. Two alternative models are proposed and their testable implications are derived and discussed. The effects of predecisional communication are examined and several extensions of the basic paradigm are outlined. (Author/LMO)

Exploratory factor analysis derives its key ideas from many sources, including Aristotle, Francis Bacon, Descartes, Pearson and Yule, and Kant. The conclusions of exploratory factor analysis are never complete without subsequent confirmatory factor analysis. (Author/GDC)

This analysis of Zipf's law uses an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified, shapes of Zipf-type curves are described, and parameters of the Mandelbrot-Zipf law are discussed. (Author/LRW)

A unidimensional latent trait model for continuous ratings extends Andrich's rating formulation which assumes the response process at latent thresholds is based on the dichotomous Rasch model. The separability of the structural and incidental parameters is demonstrated and a procedure for estimating the parameters is outlined. (Author/GDC)

Multivariate models for the triangular and duo-trio methods are described, and theoretical methods are compared to a Monte Carlo simulation. Implications are discussed for a new theory of multidimensional scaling which challenges the traditional assumption that proximity measures and perceptual distances are monotonically related. (Author/GDC)

Description of management games continues a previous article's discussion of how mathematical modeling and microeconomic concepts can be used by players. Highlights include an initial condition simulating a profit-maximizing monopoly; simulating the transition from monopoly to oligopoly; and how mathematical properties of the model affect final…

Compares and expands upon two approaches to dealing with fuzzy relational databases. The proposed similarity measure is based on a fuzzy Hausdorff distance and estimates the mismatch between two possibility distributions using a reduction process. The consequences of the reduction process on query evaluation are studied. (Author/EM)

Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative hypothesis is provided. (Author/LMO)

The application of the theory of fuzzy sets to the description of information retrieval systems makes it possible (1) to take into account the fact that the degree of importance of the particular terms is of a continuous character, (2) to formalize the relations between terms describing documents and information requests (fuzzy thesaurus).…

This paper describes a model that integrates an item response theory (IRT) Rasch model and a hierarchical linear model and presents a method of estimating model parameter values that does not rely on large-sample theory and normal approximations. The model resulting from the integration of a hierarchical linear model and the Rasch model allows one…

The feature that makes item response theory (IRT) models the models of choice for many psychometric data analysts is parameter invariance, the equality of item and examinee parameters from different populations. Using the well-known fact that item and examinee parameters are identical only up to a set of linear transformations specific to the…

This paper describes the graded response model. The graded response model represents a family of mathematical models that deal with ordered polytomous categories, such as: (1) letter grading; (2) an attitude survey with "strongly disagree, disagree, agree, and strongly agree" choices; (3) partial credit given in accord with an…

Using abstract models of thesaurus-based and multi-attribute retrieval systems a correspondence between the two systems is established so that equivalent transformation of problem statements expressed by notions developed for one system into problem statements expressed by notions pretaining to the other one may be effectively constructed. (5…