Todem David, Hsu Wei-Wen, Fine Jason P
Michigan State University, East Lansing, USA.
Kansas State University, Manhattan, USA.
Scand Stat Theory Appl. 2018 Sep;45(3):465-481. doi: 10.1111/sjos.12308. Epub 2017 Dec 14.
In statistical modeling, it is often of interest to evaluate non-negative quantities that capture heterogeneity in the population such as variances, mixing proportions and dispersion parameters. In instances of covariate-dependent heterogeneity, the implied homogeneity hypotheses are nonstandard and existing inferential techniques are not applicable. In this paper, we develop a quasi-score test statistic to evaluate homogeneity against heterogeneity that varies with a covariate profile through a regression model. We establish the limiting null distribution of the proposed test as a functional of mixtures of chi-square processes. The methodology does not require the full distribution of the data to be entirely specified. Instead, a general estimating function for a finite dimensional component of the model that is of interest is assumed but other characteristics of the population are left completely unspecified. We apply the methodology to evaluate the excess zero proportion in zero-inflated models for count data. Our numerical simulations show that the proposed test can greatly improve efficiency over tests of homogeneity that neglect covariate information under the alternative hypothesis. An empirical application to dental caries indices demonstrates the importance and practical utility of the methodology in detecting excess zeros in the data.
在统计建模中，评估捕获总体异质性的非负量（如方差、混合比例和离散参数）通常很有意义。在协变量依赖异质性的情况下，隐含的同质性假设是非标准的，现有的推断技术不适用。在本文中，我们开发了一种准得分检验统计量，以评估针对通过回归模型随协变量概况变化的异质性的同质性。我们将所提出检验的极限零分布确定为卡方过程混合的函数。该方法不需要完全指定数据的完整分布。相反，假设对感兴趣的模型有限维分量有一个通用估计函数，但总体的其他特征完全未指定。我们将该方法应用于评估计数数据零膨胀模型中的超额零比例。我们的数值模拟表明，在备择假设下，所提出的检验相对于忽略协变量信息的同质性检验可以大大提高效率。对龋齿指数的实证应用证明了该方法在检测数据中超额零方面的重要性和实际效用。
