A semiparametric Bayesian approach for structural equation models
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摘要In the development of structural equation models (SEMs), observed variables are usually assumed to be normally distributed. However, this assumption is likely to be violated in many practical researches. As the non-normality of observed variables in an SEM can be obtained from either nonnormal latent variables or non-normal residuals or both, semiparametric modeling with unknown distribution of latent variables or unknown distribution of residuals is needed. In this article, we find that an SEM becomes nonidentifiable when both the latent variable distribution and the residual distribution are unknown. Hence, it is impossible to estimate reliably both the latent variable distribution and the residual distribution without parametric assumptions on one or the other. We also find that the residuals in the measurement equation are more sensitive to the normality assumption than the latent variables, and the negative impact on the estimation of parameters and distributions due to the non-normality of residuals is more serious. Therefore, when there is no prior knowledge about parametric distributions for either the latent variables or the residuals, we recommend making parametric assumption on latent variables, and modeling residuals nonparametrically. We propose a semiparametric Bayesian approach using the truncated Dirichlet process with a stick breaking prior to tackle the non-normality of residuals in the measurement equation. Simulation studies and a real data analysis demonstrate our findings, and reveal the empirical performance of the proposed methodology. A free WinBUGS code to perform the analysis is available in Supporting Information.
著者Song XY, Pan JH, Kwok T, Vandenput L, Ohlsson C, Leung PC
期刊名稱Biometrical Journal
出版年份2010
月份6
日期1
卷號52
期次3
出版社Wiley-VCH Verlag
頁次314 - 332
國際標準期刊號0323-3847
電子國際標準期刊號1521-4036
語言英式英語
關鍵詞Dirichlet process; Non-normal data; Stick-breaking prior; Structural equation models
Web of Science 學科類別Mathematical & Computational Biology; MATHEMATICAL & COMPUTATIONAL BIOLOGY; Mathematics; Statistics & Probability; STATISTICS & PROBABILITY

上次更新時間 2021-15-04 於 23:43