thumbnail

Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships

Mathematical Geology

By:
and
DOI: 10.1007/BF00893319

Links

Abstract

Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships
Series title:
Mathematical Geology
DOI:
10.1007/BF00893319
Volume
21
Issue:
7
Year Published:
1989
Language:
English
Publisher location:
Kluwer Academic Publishers-Plenum Publishers
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Mathematical Geology
First page:
741
Last page:
753
Number of Pages:
13