雙向交叉或摺疊隨機模式之變方成分函數的統計推論及在遺傳率與檢測方法再現性的應用

Abstract

在雙向交叉或摺疊隨機模式中，變方成分函數之信賴區間的各種建構方法已見於文獻討論，然而利用這些近似法求得之信賴區間，其涵蓋機率(coverage probability)難免有嚴格或寬鬆等不確定性現象存在，對於不平衡模式的整體狀況並未全面調查研究，因此仍保有許多未知空間。 本論文應用Weerahandi所提出的廣義基準量(Generalized Pivotal Quantities, GPQs)統計方法的概念，在雙向交叉或摺疊隨機模式之變方成分函數，求得精確的信賴區間及進行統計推論，進一步檢定我們所感興趣的變方成分函數測度是否滿足預設的門檻值。這些統計檢定可應用於農工醫各領域中，如動植物育種上遺傳率之研究，量測工具重複性及再現性之管控研究，以及設備儀器檢測可靠性之評估研究等。本文透過電腦模擬(simulation)，驗證此法信賴區間之涵蓋機率、平均區間長度及檢定力(power)之整體表現，並以實例數據來說明廣義基準量方法的應用。

Various different approaches for constructing confidence interval for functions of variance components proposed under cross-classification or nested random-effects models. However, these approaches are approximate and their probability coverage is either conservative or liberal. Their performances under the imbalanced situations are not fully investigated and hence remain unknown. Therefore, we apply the concept of Generalized Pivotal Quantities (GPQs) to obtain the exact confidence intervals under the two-way cross-classification with interaction random-effects model and the two-stage nested random-effects model . The exact confidence interval can be used to test the hypothesis whether the interested measure of variance components exceeds a pre-specified threshold. This hypothesis can be applied to the heritability study of animal and plant breeding and the gauge repeatability and reproducibility (R&R) study and to the reliability in validation studies during the development of instruments. A large simulation study was conducted to empirically investigate the coverage probability and expected length of the proposed exact confidence intervals, and size and power of the proposed testing procedures based on the exact confidence intervals. Numeric data from public domains illustrate the applications of the proposed methods.