A defense of an entropy based index of multigroup segregation
This paper defends the use of the entropy based Mutual Information index of multigroup segregation for the following five reasons. (1) It satisfies 14 basic axioms discussed in the literature when segregation takes place along a single dimension. (2) It is additively decomposable into between- and within-group terms for any partition of the set of occupations (or schools) and the set of demographic groups in the multigroup case. (3) The underlying segregation ordering has been recently characterized in terms of 8 properties. (4) It is a monotonic transformation of log-likelihood tests for the existence of segregation in a general model. (5) It can be decomposed so that a term independent of changes in either of the two marginal distributions can be isolated in pair wise segregation comparisons. Other existing measures of segregation have not been characterized, fail to satisfy one or more of the basic axioms, do not admit a between- within-group decomposition, have not been motivated from a statistical approach, or are based on more restricted econometric models.
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