Parameters for cluster analysis of library overlap

Abstract

The relationship between two common approaches to library overlap is discussed : I) the practice of tabulating frequencies of 0,1,2 ..., n copies of titles in a network, and 2) reporting of the number of co-occurring titles in a symmetric resemblance matrix. It is contended that an understanding of the first approach is important in the practice of the second approach-- e.g., in constructing a resemblance coefficient between any two libraries and in establishing sample size when the matrix is used as input for cluster analysis. The Poisson and negative binomial distributions were tested for fit with several samples of data. The negative binomial ditribution provides a much better fit t h a n the Poisson and generates frequencies of 2, the essential ingredient in symmetric overlap matrices, which are very close to frequencies of 2 in the sam~les. Since the Poisson assumes equal propabilities of success, while' the negative binomial assumes variable probability, the better fit may be explained by assuming that each book has its own probability of being acquired.