Stakhovych Stanislav, Bijmolt Tammo H A, Wedel Michel
a Monash University.
b University of Groningen.
Multivariate Behav Res. 2012 Nov;47(6):803-39. doi: 10.1080/00273171.2012.731927.
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.
在本文中，我们提出了一种贝叶斯空间因子分析模型。我们通过纳入地理分布的潜在变量并考虑异质性和空间自相关性，扩展了先前关于验证性因子分析的工作。模拟研究表明模型参数的恢复效果极佳，并证明了忽略空间依赖性的后果。具体而言，我们发现因子得分均值估计存在低效性，以及相应协方差矩阵估计存在偏差和低效性。我们将该模型应用于从5个欧洲国家获得的施瓦茨价值观优先级数据。我们表明，施瓦茨动机类型的价值观，如遵从、传统、仁爱和享乐主义，具有高度的空间自相关性。我们识别出几种空间模式——具体来说，遵从和享乐主义具有特定国家的结构，传统具有跨越国界的南北梯度，而仁爱具有南北跨国梯度。最后，我们表明，与所提出的方法相比，传统因子分析可能会导致失去有价值的见解。
