Zhang Daowen, Lin Xihong
Department of Statistics, North Carolina State University, USA.
Biostatistics. 2003 Jan;4(1):57-74. doi: 10.1093/biostatistics/4.1.57.
We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the variance component score test by treating the inverse of the smoothing parameter as an extra variance component. We also consider testing the equivalence of two nonparametric functions in semiparametric additive mixed models for two groups, such as treatment and placebo groups. The proposed tests are applied to data from an epidemiological study and a clinical trial and their performance is evaluated through simulations.
我们考虑检验半参数加法混合模型中的非参数函数是否为简单的固定次数多项式，例如简单线性函数。该检验提供了一种拟合优度检验，用于检验参数模型与非参数模型。它基于非参数函数的平滑样条估计器的混合模型表示以及通过将平滑参数的倒数视为额外方差分量的方差分量得分检验。我们还考虑检验两组半参数加法混合模型中两个非参数函数的等价性，比如治疗组和安慰剂组。所提出的检验应用于一项流行病学研究和一项临床试验的数据，并通过模拟评估其性能。
