在生活中，具有網路結構的例子無所不在，例如在農業實驗、生物信息學、醫學實驗、機器學習、物理學、社會科學和許多其他科學領域，再加上社交網路的快速發展， 網路相關的議題已經成為一個新興的研究領域。為一個實驗單位指派處理會影響該實驗單位及其鄰居，並同時產生了處理效應和網路效應。在實驗設計的文獻中，Parker, Gilmour, and Schormans (2017) 和 Chang, Phoa, and Huang (2021) 都採用了線性網路效應模型來處理網路實驗。然而，這種模型並未得到廣泛應用。Kolaczyk and Cs?rdi (2014) 回顧了網路的統計模型，例如指數隨機圖模型和網路區塊模型。Zhang et al. (2019) 考慮了一種基於網路的邏輯斯迴歸模型來描述網路效應。本文擴展 Kolaczyk and Cs?rdi (2014) 以及 Zhang et al. (2019) 的想法提出了一種新的網路統計模型，並尋找最佳設計的條件。最後，我們通過模擬和真實例子來說明我們的理論且提供相對應的最佳設計。;With the rapid growth of social network services, network-related studies have become a burgeoning research area. Allocating a treatment to a unit affects the unit as well as its neighbors, simultaneously resulting in a treatment effect and a network effect. In the literature of experimental designs, Parker, Gilmour, and Schormans (2017) and Chang, Phoa, and Huang (2021) both adopted a linear network effect model to design experiments on general networks. However, this model has not been heavily recognized. Kolaczyk and Cs?rdi (2014) reviewed statistical models for network graphs such as exponential random graph models and network block models. Zhang et al. (2019) considered a network-based logistic regression model to describe the network effect. In this thesis, we propose a new statistical model for networks in the same spirit as Kolaczyk and Cs?rdi (2014) and Zhang et al. (2019). Moreover, we derive conditions for selecting optimal designs. Finally, we illustrate our theory through simulations and real examples.
