Abstract
Classical statistical inference procedures usually assume the independence of sample units. However, the assumption of independence is often unrealistic in cross‐cultural research because societies in neighboring or historically related regions tend to be duplicates of one another across a wide variety of traits that are spread by historical fission, diffusion, or migration of peoples. A recent generalization of the usual regression model explicitly allows for networks of interdependencies among sample units as part of the model specification. Here, two new estimation procedures for this network autocorrelation model are compared to previously employed maximum likelihood procedures, and to the usual regression procedures which ignore interdependence. The results of comparisons based on simulated autocorrelation data and the reanalyses of two previously published empirical studies indicate that both of the procedures proposed here compare very favorably with the maximum likelihood approach, and both are vastly superior to the usual regression procedures when there is moderate to high autocorrelation (i.e., interdependence). [Galton's Problem, cultural diffusion, networks, cultural evolution, statistical methodology]
Highlights
The assumption of independence is often unrealistic in cross-cultural research because societies in neighboring or historically related regions tend to be duplicates of one another across a wide variety of traits that are spread by historical fission, diffusion, or migration of peoples
The results of comparisons based on simulated autocorelation data and the reanalyses of two previously published empirical studies indicate that both of the proceduresproposed here compare very favorably with the maximum likelihoodapproach, and both are vastly superior to the usual regression procedures when there is moderate to high autocorrelation. [Galton’s Problem, cultural diffusion, networks, cultural evolution, statistical methodology]
Mathematical, empirical, and Galton’s Problem as network autocorrelation 755 simulation work (Dow, Burton, and White 1982) have all shown that these maximum likelihood (ML) autocorrelation procedures yield markedly different and more accurate results, in the presence of autocorrelation, than ordinary least squares (OLS) regression, which assumes the absence of autocorrelation
Summary
Mathematical, empirical, and Galton’s Problem as network autocorrelation 755 simulation work (Dow, Burton, and White 1982) have all shown that these ML autocorrelation procedures yield markedly different and more accurate results, in the presence of autocorrelation, than ordinary least squares (OLS) regression, which assumes the absence of autocorrelation. The results of this simulation indicate that both methods compare very favorably with the ML procedure in terms of bias and efficiency of the regression coefficient estimates Both methods offer major improvements over the usual OLS regressionwhen moderate to high autocorrelation is present. Before presenting the network autocorrelated disturbances model in equational form, we first examine the representation of cultural diffusion as a matrix of relationships among the sample units. This model is a generalization of the usual OLS (ordinary least squares) multiple regression model, which can be compactly stated in matrix form’ as
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