Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

Correlated Factors Modeling (CFM) is proposed as an alternative to LISREL and similar methods of estimating structural equations. CFM employs weak mathematics and is appropriate for a rapid, preliminary look at a model. The factors produced by CFM are exact linear components of their indicator variates. (Author/GDC)

Explains the phenomenon of Brownian motion, which serves as a mathematical model for random processes. Topics addressed include kinetic theory, Einstein's theory, particle displacement, and others. Points out that observations of the random course of a particle suspended in fluid led to the first accurate measurement of atomic mass. (DH)

A new approach to time series analysis was developed. It employs a generalized transformation of the observed data to meet the assumptions of the general linear model, thus eliminating the need to identify a specific model. This approach permits alternative computational procedures, based on a generalized least squares algorithm. (Author/BW)

This paper describes a simulation that determines the adequacy of various indices as decision criteria for assessing unidimensionality. Using the sum of absolute residuals from the two-parameter latent trait model, indices were obtained that could discriminate between one latent trait and more than one latent trait. (Author/BW)

After introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data, an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed. The possibility of testing various hypotheses is discussed and the algorithm is applied to some existing data…

The present study compares the performance of phi coefficients and tetrachorics along two dimensions of factor recovery in binary data. These dimensions are (1) accuracy of nontrivial factor identifications; and (2) factor structure recovery given a priori knowledge of the correct number of factors to rotate. (Author/LMO)

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. (Author/LMO)

The Generalized Inverse Gaussian-Poisson Distribution is suggested as an all-embracing mathematical model for bibliometric frequency distributions. Twelve examples are given which show that the new model cannot be rejected by virtue of an objective chi-squared test. A mathematical appendix and 20 references are included. (Author/EJS)

An example shows how a group of professionals and citizens can select a feasible site for a facility by rank ordering criteria of availability, population, accessibility, and cost. (MLF)

Investigates the properties of a global model consisting of "n" local information retrieval systems based on thesaurus. Definitions of a distributed information retrieval system (thesaurus, documents set, set of queries) and proofs of theorems denoting further properties of the systems are highlighted. Five references are included. (EJS)

Latent trait and latent class analyses of Likert-type data are compared. Key similarities and differences between these methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of "life satisfaction" data. (Author/NSF)

Describes the instructional strategies and activities used to illustrate the essential features of mathematical modeling to a group of infant and junior high school teachers. The intent was to involve the group with some number work, elementary algebra, and some simple work on arrangements by way of tree-diagrams. (JN)