AI 中文总结
本文针对非正偏态非负观测值违背传统双因子ANOVA假设的问题，提出含2因子的Gamma模型（ANOGaM-2）及参数自助似然比检验（PBLRT），模拟与真实数据验证了PBLRT的有效性及与传统ANOVA推断的差异。
AI 中文摘要
双因子方差分析（ANOVA）广泛应用于实验研究，但依赖可加性、正态性、独立性和同方差性假设，这些假设常被非负、正偏态的观测值违背。尽管Box-Cox类变换被广泛使用，但会降低可解释性且需主观选择变换方式。本文提出替代框架，将受两个因子影响的非负观测值建模为Gamma分布，其未知形状和尺度参数可依赖因子水平。我们开发主效应和交互效应的似然比检验（LRT）：渐近似然比检验（ALRT）采用渐近卡方分布，对小到中等样本可能不准确，因此提出参数自助似然比检验（PBLRT），通过模拟确定临界值。大量模拟显示PBLRT能很好地保持名义显著性水平，真实数据示例验证了其适用性，且其推断结果与传统ANOVA存在差异。
英文摘要
Two-factor ANOVA is widely used in experimental studies but relies on additivity, normality, independence, and homoscedasticity. These assumptions are often violated for nonnegative, positively skewed observations. Although Box--Cox-type transformations are commonly used, they may reduce interpretability and require a subjective choice of transformation. We propose an alternative framework in which nonnegative observations affected by two factors are modeled by gamma distributions with unknown shape and scale parameters that may depend on factor levels. We develop likelihood ratio tests (LRTs) for main and interaction effects. The asymptotic LRT (ALRT) uses the asymptotic chi-square distribution, which may be inaccurate for small to moderate samples. We therefore propose a parametric bootstrap LRT (PBLRT) that determines critical values by simulation. Extensive simulations show that the PBLRT maintains the nominal significance level well. Real-data examples demonstrate its applicability and show that its inferences can differ from those of traditional ANOVA.
Comments58 pages
