Todem David, Hsu Wei-Wen, Kim KyungMann
Department of Epidemiology and Biostatistics, Michigan State University, B601 West Fee Hall, East Lansing, Michigan 48824, USA.
Biometrics. 2012 Sep;68(3):975-82. doi: 10.1111/j.1541-0420.2011.01737.x. Epub 2012 Feb 20.
In many applications of two-component mixture models for discrete data such as zero-inflated models, it is often of interest to conduct inferences for the mixing weights. Score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose. But the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model. In this article, we develop a score test of homogeneity that overcomes the limitations of existing procedures. The technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation. We exploit this decomposition to lay the foundation of the test. Simulation results show that the proposed covariate-adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights. A real-life example in dental caries research is used to illustrate the methodology.
在许多用于离散数据的双组分混合模型应用中，如零膨胀模型，对混合权重进行推断通常很有意义。从允许负混合权重的边际模型导出的得分检验在此目的上特别有用。但现有的检验程序往往依赖于诸如混合权重恒定等限制性假设，并且通常忽略边际模型的结构约束。在本文中，我们开发了一种同质性得分检验，克服了现有程序的局限性。该技术基于将混合权重分解为具有明显统计解释的项。我们利用这种分解来奠定检验的基础。模拟结果表明，所提出的协变量调整检验统计量相比基于恒定混合权重的检验统计量可大大提高效率。一个龋齿研究中的实际例子用于说明该方法。
