Equality of endogamy: Statistical approaches

Abstract In research on assimilation through marriage or defining racial groups as castes or classes, it is important to be able to test the equality of endogamy of groups of differing sizes and sex ratios. A variety of proposed solutions all have major difficulties. Log-linear models constitute an improvement but still retain some undesirable properties, including an inability to deal with both the linear and quadratic dimensions of the relationship between group size and endogamy levels by focusing on one to the exclusion of the other. Moreover, in the context of studies of comparative analysis of racial groups it is handicapped by providing inconsistent results for uncollapsed categories when other groups are combined. We recommend instead the weighted least-squares methodology both to test for statistical significance of differences in endogamy and to rank racial or ethnic groups according to their degree of endogamy. This method incorporates both the linear and quadratic components influencing the diagonal frequencies in marriage studies. Linear effects (see Table 2) are stronger when endogamy is high, and quadratic effects (see Table 3) are stronger when endogamy is low, although in general both are present together. Furthermore, this approach permits separate calculation of endogamy levels by sex and provides a test to ascertain when separate statistics should be computed. It is relatively free from biases in terms of the amount of “extra credit” given smaller groups, and is invariant when categories are combined. Conditional kappa values can be utilized to judge whether a racial group was relatively closed or open (compared to other groups) and to analyze the impact of the structural characteristics of group size and sex ratio on endogamy. In one area log-linear models retain an advantage over GSK-based analyses. The former have been employed to examine patterns of intermarriage via the quasi-symmetry, quasi-independence, and other tests based on off-diagonal elements. So far no comparable method has appeared for analyzing the intermarriage or exogamy behavior using GSK. Applications of log-linear models have been less successful in dealing with endogamy or inmarriage patterns. The comparison of degrees of endogamy by the GSK approach is based on direct measurement of endogamy by racial groups, allowing for calculation of standard error figures for each group's endogamy value. The ability of the GSK method to accomplish the above—as well as provide kappas which are invariant under group collapsing, tests of equal endogamy (by sex if necessary), and a test of marginal homogeneity—may be unique. Our recommendation is that in future discussions, involving comparisons of endogamy among several populations, conditional kappas and their standard errors at the very least should be presented. The distinction between male-oriented, female-oriented, and balanced conditional kappas, as well as the use of formal tests of endogamy, homogeneity, and marginal homogeneity permits examination of important population issues. The broad applicability of these techniques derives from their provision of a basis for comparing endogamy levels, since they produce consistent results for unaggregated data regardless of how minor or intermediate groups are combined. Such analyses are fundamental for gaining a more basic insight as to whether social and cultural factors, legal discrimination, or the basic structural elements of group size and sex ratio have greater influence on assimilation or the degree of closure in racial groups in the Americas.