Clustering and tree models are being widely used in the social and biological sciences to analyze similarity relations. This volume describes how matrices of similarities or associations among entities can be modelled using trees, and explains some of the issues that arise in performing such analyses and interpreting the results correctly. James E Corter distinguishes ultrametric trees from additive trees and discusses how specific aspects of each type of tree can be interpreted through the use of applications as examples. He concludes with a discussion of when tree models might be preferable to spatial geometric models.
While many readers may be unfamiliar with the full complexity of the covariance structure model, many may have mastered at least one of its two components, each of which is a powerful and well-known statistical technique in its own right. The first is the confirmatory factor model frequently used in psychometrics; the second, the structural equation model, is familiar to econometricians. The discussion in this volume will be particularly useful for estimating models with equality constraints and correlated errors across some but not all equations. The final chapter includes a guide to appropriate software packages.
Goal programming is one of the most widely used methodologies in operations research and management science, and encompasses most classes of multiple objective programming models. Ignizio provides a concise and lucid overview of (a) the linear goal programming model, (b) a computationally efficient algorithm for solution, (c) duality and sensitivity analysis and (d) extensions of the methodology to integer as well as non-linear models.
This short monograph lays out the theory behind, and techniques for, using dynamic modelling, taking the reader through a series of increasingly complex models. At each step, examples are used to explain the process, and also to clarify specific applications of difference equation models in the social sciences. 'It is a good example of classical mathematical model building and I may well use it as a text for the course on that subject in our MSc on Quantitative Methods in the Behavioural Sciences...in general it is to be recommended.' -- Bethlem and Maudsley Gazette, Vol 31 No 2, 1983
Feiring provides a well-written introduction to the techniques and applications of linear programming. He shows readers how to model, solve, and interpret appropriate linear programming problems. His carefully-chosen examples provide a foundation for mathematical modelling and demonstrate the wide scope of the techniques.
A Guide to Multidimensional Scaling and Clustering
Three Way Scaling assumes a working knowledge of multidimensional scaling and Matrix Algebra, which are both introduced in earlier volumes of this series. Arabie, Carroll and DeSarbo begin their discussion with an example of the use of the INDSCAL model, they explain the model and give a second extended example. The authors then present a detailed analysis of SINDSCAL and provide an introduction to three-way scaling models as well as individual differences clustering models.
Multiple Comparisons demonstrates the most important methods of investigating differences between levels of an independent variable within an experimental design. The authors review the analysis of variance and hypothesis testing and describe the dimensions on which multiple comparisons vary. A feature is the use made of a famous experiment by Solomon Asch on group conformity. The authors demonstrate the statistical power of each method against this one experimental question.
An introduction to a variety of techniques that may be used in the analysis of data from a panel study -- information obtained from a large number of entities at two or more points in time. The focus of this volume is on analysis rather than problems of sampling or design, and its emphasis is on application rather than theory.
Ordinal data can be rank ordered but not assumed to have equal distances between categories. Using support by judges for civil rights measures and bussing as the primary example, this paper indicates how such data can best be analyzed.
