DC 欄位 值 語言 DC.contributor 統計研究所 zh_TW DC.creator 陳玟潔 zh_TW DC.creator Wen-Chieh Chen en_US dc.date.accessioned 2020-7-9T07:39:07Z dc.date.available 2020-7-9T07:39:07Z dc.date.issued 2020 dc.identifier.uri http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=107225008 dc.contributor.department 統計研究所 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract 生活中不難發現網路的存在，例如社交網路、代謝網路、生物網絡和引文網路等，而相關的議題在各領域中也被廣泛地討論。在實驗設計領域中，實驗單位被視為網路中的節點，有關聯的實驗單位被稱為彼此的鄰居。當一個處理被應用於一個實驗單位上時，它會同時影響自身及其鄰居，因此產生了兩種對反應變數的影響：處理效應和網路效應。Parker et al. (2017) 提出一線性模型來處理具備網路結構的實驗，並且假設處理效應和網路效應都是固定效應。Chang et al. (2020) 採用了類似的模型，但他們將網路效應假設為隨機效應。本文將此模型擴展至有方向與加權之網路結構，並且尋找特定網路結構下的最佳設計。最後我們歸納出相關的理論結果，並提供對應的最佳設計。 關鍵字: 處理效應、網路效應、非結構化處理、二分圖/路徑圖/循環圖、D最佳化準則、(M.S)最佳化準則 zh_TW dc.description.abstract Connected experimental units can be characterized by a network structure, where related examples are abundant in the world. If there exists a connection between two units, then they are neighbors of each other. In this case, a treatment affects both the unit to which it applies and the neighbors of that unit, simultaneously causing a treatment effect and a network effect. Parker, Gilmour, and Schormans (2017) launched a numerical study for designing experiments on general network structures. They proposed a linear model with unstructured treatments and assumed both treatment effects and network effects were fixed effects. A relevant work is Chang, Phoa, and Huang (2020), which argued using random network effects. In this work, we adopt the model in Chang, Phoa, and Huang (2020) and extend the network structure to directed/weighted graphs. We study optimal designs on specific graphs, devote to obtaining theoretical results, and provide templates of the corresponding optimal designs. Keywords: Treatment Effect, Network Effect, Unstructured Treatment, Bipartite/Path/Cycle Graph, D-optimality, (M.S)-optimality. en_US DC.subject 處理效應 zh_TW DC.subject 網路效應 zh_TW DC.subject 非結構化處理 zh_TW DC.subject 二分圖/路徑圖/循環圖 zh_TW DC.subject D-最佳化準 則 zh_TW DC.subject (M.S)最佳化準則 zh_TW DC.subject Treatment E ffect en_US DC.subject Network E ffect en_US DC.subject Unstructured Treatment en_US DC.subject Bipartite/Path/Cycle Graph en_US DC.subject D-optimality en_US DC.subject (M.S)- optimality en_US DC.title Optimal Designs for Simple Directed/Weighted Network Structures en_US dc.language.iso en_US en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US