Similarity coefficients for binary data : properties of coefficients, coefficient matrices, multi-way metrics and multivariate coefficients

Warrens, M.J. (2008)

Doctoral Thesis

In data analysis, an important role is played by similarity coefficients. A similarity coefficient is a measure of resemblance or association of two entities or variables. Similarity coefficients for binary data are used, for example, in biological ecology for measuring the degree of coexistence between two species type over different locations, or in psychology for a 2×2 reliability study where two observers classify a sample of subjects using a dichotomous response. In choosing a coefficient, a measure has to be considered in the context of the data-analytic study of which it is a part. Because there are so many similarity coefficients for binary data to choose from, it is important that the different coefficients and their properties are better understood. The dissertation contains a mathematical approach to the analysis of similarity coefficients for binary data. A variety of data-analytic properties are considered for various coefficients it is established whether they possess the property or not. Part I contains results on correction for chance and maximum value. In part II sufficient conditions for Robinson matrices and some mathematical properties of multiple correspondence analysis are presented. In part III various two-way notions are generalized to the multi-way case. Part IV contains formulations of multi-way coefficients.

• Measures for 2×2 tables
• Correction for chance
• Robinson matrices
• Multi-way metricity

• All authors: Warrens, M.J.
• Supervisor: Heiser, W.J.
• Co-supervisor: Gruijter, D.N.M. de
• Committee: -
• Qualification: Doctor (dr.)
• Awarding Institution: Psychometrics and Research Methodology Group, Leiden University Institute for Psychological Research, Faculty of Social and Behavioural Sciences, Leiden University
• Date: 2008-06-25
• ISBN (print): 9789088910524
• Court: LEI Universiteit Leiden