應用混合模型於資料效果異質性之辨識： 以肥料處理篩選場景為例

Abstract

全球人口持續增長與氣候變遷是當前農業發展所面臨的兩大挑戰。農業生物製劑因具有促進作物產量與維護環境永續的潛力，逐漸受到重視。此類產品多以天然來源為基礎，如微生物、植物萃取物或其他有機物質。然而，新型微生物製劑的開發需仰賴大量溫室與田間試驗，且作物、微生物與環境三者間的複雜交互作用，使得預測最終作物表現具高度不確定性。此外，開發階段早期的微生物製劑穩定性不足，常導致產量或其他性狀出現雙峰或多峰分布，進而降低統計檢定力與篩選具有潛力的處理之效能。本研究提出一套結合混合模型與最大概似估計法（MLE）的統計分析架構，用以處理具反應異質性的資料。模型中具有兩個成分，其一成分為對植物的生長具正向效果，另一成分則對植物的生長不具效果或具負向效果。本研究同時進行模擬實驗與實際資料驗證。模擬結果顯示，在參數 估計上，除誤差劇烈波動區外，平均絕對誤差（MAE）均低於 0.5，均方根誤差（rMSE）最低可達 0.434，相對誤差（MRE）最低為 0.087，顯示本方法具備良好預測效能。本方法能識別出在效果上略優於對照組的處理，並進一步設計雙標準決策機制，透過設定有正向效果之成分比例（0.3 至 0.6）及增長幅度是否排除 0，篩選具潛力之處理組。此機制可依使用者需求進行調整，條件可更嚴格或更寬鬆，以達到使用者的成本考量。與傳統統計方法如變異數分析（ANOVA）相比，本模型可額外發掘超過 20% 的潛在處理組，並提供更具使用者導向的選擇依據。此研究亦進行溫室試驗以驗證本模型在實際資料上的應用潛力，結果顯示本方法相較於 ANOVA 能偵測出更多具異質性反應的處理組。綜合而言，本研究並非意圖取代 ANOVA，而是提供一套可因應資料不一致性、並兼顧使用者偏好的替代性方法，協助研究者在面對生物產品表現不穩定時，有更好的決策依據。

The escalating global population and climate change are two major challenges facing humanity. Agricultural biologicals are regarded as potential solutions to increase crop yields while maintaining a sustainable environment. They are products created from natural materials, such as microorganisms, plant extracts, or other organic matter. The development of new microbial products requires extensive testing in greenhouse experiments and field trials. However, the complex three-way interactions between crops, living microorganisms, and environments make it difficult to predict the final responses. In addition, in the early stages of the development process, microbial treatments are often unstable, resulting in bimodal or multimodal distributions in the responses of interest. Hence, this reduces statistical power for discovering potential products. We developed a statistical framework using a mixture model and maximum likelihood estimator (MLE) to analyze data with heterogeneous responses. The model takes into account the fact that not all microbial treatments are equally effective; some are active microbes with a positive effect, while others are inactive microbes with no or deleterious effects. In this study, we conducted both in silico simulations and real-world validation. Results show that our model's performance among parameters in mean absolute error (MAE) does not exceed 0.5, except in the fluctuating error area. Results from the root mean square error (RMSE) and mean relative error (MRE) show that the lowest values reach 0.434 and 0.087, respectively. These results prove the effectiveness of our model. This new methodology enables us to identify microbial treatments that slightly outperform the control. We also provide a dual-criteria decision-making method to select favorable treatments by setting thresholds for component probability from 0.3 to 0.6 and determining whether the shifting parameter excludes 0 or not. The advantage of our model is that these criteria can be customized to be more strict or more lenient to meet users' cost restrictions. Compared to traditional statistical methods such as ANOVA, the new method can identify an additional 20% of potential treatments and allows users to customize their own preferences. In the real greenhouse experiment, we validated that our approach extends beyond simulated data to include real-world applications. Results show that our model provides more heterogeneous response treatment candidates than ANOVA. In conclusion, we are not claiming to provide a better method than ANOVA, but rather offering an alternative method that allows users to decide their own preferences and helps them make decisions when faced with inconsistent results from biological products.