Spatial Dependence and Heterogeneity in Bayesian Factor Analysis: A Cross-National Investigation of Schwartz Values.

In this article, we present a Bayesian spatial factor analysis model. We extend previous work on confirmatory factor analysis by including geographically distributed latent variables and accounting for heterogeneity and spatial autocorrelation. The simulation study shows excellent recovery of the model parameters and demonstrates the consequences of ignoring spatial dependence. Specifically, we find inefficiency in the estimates of the factor score means and bias and inefficiency in the estimates of the corresponding covariance matrix. We apply the model to Schwartz value priority data obtained from 5 European countries. We show that the Schwartz motivational types of values, such as Conformity, Tradition, Benevolence, and Hedonism, possess high spatial autocorrelation. We identify several spatial patterns-specifically, Conformity and Hedonism have a country-specific structure, Tradition has a North-South gradient that cuts across national borders, and Benevolence has South-North cross-national gradient. Finally, we show that conventional factor analysis may lead to a loss of valuable insights compared with the proposed approach.