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Duncan & Duncan dissimilarity index

duncandepvargroupvar[weight] [ifexp] [inrange] [,frequenciesmissingnolabelformat(%fmt)]

duncan2depvargroupvar[weight] [ifexp] [inrange] [,missingformat(%fmt)d(newvar)ncat(newvar)nobs(newvar)dj(newvar)]

by...:may be used withduncanandduncan2; see help by.

fweights andaweights are allowed; see help weights.

Description

duncancomputes the segregation statistic known as dissimilarity index D (Duncan and Duncan 1955).depvaris the categorical characteristic of interest (e.g. occupations) andgroupvardefines the groups (e.g. sex). D will be displayed for all pairwise comparisons of groups. The maximum number of distinct categories indepvaris limited to 300 in Intercooled Stata and 1200 in Stata/SE.

duncan2also computes D, but has no limitation concerning the number of categories indepvar. However, note that thegroupvarmust be 0/1 withduncan2.Furthermore,

duncanandduncan2differ in the treatment of thebyprefix.duncancomputes and displays D one after another for each by-group, whereasduncan2does all computations in one call and displays all results in one table.

duncanandduncan2compute D from individual level data. To calculate D from aggregate data, see thedissimpackage by Nicholas J. Cox. Also consider thesegpackage by Sean F. Reardon, which may be used to compute a variety of segregation indices.

Options

frequenciesspecifies that a two-way table of frequency counts be displayed (duncanonly).

missingrequests that missing values be treated like other values.

nolabelcauses the numeric codes of the groups to be displayed rather than the value labels (duncanonly).

format(%fmt)specifies the format to be used to display the results. The default isformat(%10.0g).

d(newvar),ncat(newvar),nobs(newvar)may be used to save the results (D, the number of categories, the number of observations) as variables (duncan2only).

dj(newvar)may be used to save the dissimilarity values of the individual categories as a variable (the sum over these values results in D) (duncan2only).

ExamplesOccupational sex segregation:

. duncan isco88 sex

Sex segregation in schools by country:

. sort country . by country: duncan2 schoolid sex

Saved Results

duncansaves inr():Scalars:

r(c)number of distinct categories indepvarr(N)number of observationsMatrices:

r(D)pairwise dissimilarity indices

Methods and FormulasLet N(A_j) be the frequency of category j in group A (e.g. the frequency of male janitors) and N(B_j) be the frequency of category j in group B (e.g. the frequency of female janitors). The dissimilarity index D is defined as

D = 0.5 * sum_j | N(A_j)/N(A) - N(B_j)/N(B) | j = 1,...,J

where N(A) and N(B) are the overall group sizes. D may be interpreted as the proportion of subjects in group B that would have to change category in order to get the same relative distribution as in group A (or vice versa).

ReferencesDuncan, O.D., Duncan, B., 1955: A Methodological Analysis of Segregation Indexes. American Sociological Review 20: 210-217.

AuthorBen Jann, ETH Zurich, jann@soz.gess.ethz.ch

Also see