blau.index: Diversity as variety: Blau's Index

In DLEIVA/diversity: Diversity indexes for organizational research

Description

This function computes Blau's index for quantifying diversity as variety.

Usage

blau.index(X, categories)

Arguments

X	A string vector with categorical data.
categories	The number of posible categories for the random variable.

Details

Blau's index (1977) is computed by means of the well-known formula: 1 - ∑\limits_{i = 1}^k {p_i^2 }, where p_i corresponds to the proportion of group members in ith category and k denotes the number of categories for an attribute of interest. This index quantifies the probability that two members randomly selected from a group would be in different categories. This index reaches its minimum value (0) when there is no variety, that is to say, when all individuals are classified in the same category. The maximum value depends on the number of categories and on the fact that individuals can be evenly distributed in all categories. blau.index also computes proper theoretical upper bound for Blau's index as well as a normalized measure that allows researchers to get a measure that ranges from 0 to 1.

Value

The function returns a list of class blau with following components:

call	Function call.
categories	Levels of categorical variable.
blau.index	Blau's Index.
blau.max	Maximum value of Blau's Index.
blau.norm	Normalized value of Blau's Index.

Author(s)

Antonio Solanas, Rejina M. Selvam, Jose Navarro and David Leiva.

References

Blau, P. M. (1977). Inequality and heterogeneity. New York: Free Press.

Solanas, A., Selvam, R. M., Navarro, J., & Leiva, D. (2010). On the measurement of diversity in organizations. Unpublished manuscript.

Examples

g.3 <- c('F','A','P')
blau.index(g.3,3)

g.4 <- c(rep('F',2),'A','P')
blau.index(g.4,3)

g.5 <- c(rep('F',2),rep('A',2),'P')
blau.index(g.5,3)

g.10 <- c(rep('F',6),rep('A',3),'P')
blau.index(g.10,3)

DLEIVA/diversity documentation built on May 10, 2019, 1:14 a.m.