利用額外訊息之降維度分析方法

Abstract

在許多迴歸或是建立診斷準則的研究上，經常有一些自變項具有較 高的預測或分類能力，但同時也需要較高的成本。受限於現實的取樣， 研究者往往沒有足夠的經費或時間為每一位受試者量測這些資訊，因 此在許多實務研究上經常會使用較低廉的變項做初步的篩選，而對於 通過篩選的樣本再進一步取得高成本但更精確的資料。而在現今大型 資料的出現，預測或分類準則建立經常會面臨高維度的資料處理，針 對降維度的問題，充分維度縮減已發展多年，對於各種資料結構也有 不同應對的分析方法，然而當研究者直接對預先篩選用的自變項進行 降維度分析時，並沒有使用到高成本資料的訊息。在本研究中，我們 提出新的兩階段降維度方法來利用高成本資料的訊息，希望藉此增進 預先篩選模型的精準度。在模擬的結果跟實際資料的分析中，兩階段 降維度方法都有優於直接降維度分析的表現。

In practical applications, some independent variables usually require more cost but with better ability to predict the behaviors of outcome. In this situation, we may interested in constructing a prediction model or classification rule based on those cheaper covariates for pre-screening. For those identified subjects, we can obtain more detailed information for further treatment. To model the relationship between outcome and predictors, a commonly encountered problem is the large dimension of covariates. Sufficient dimension reduction has been proposed to solve this problem. When we focus on the relation between response and cheaper covariates, we can consider covariates with higher cost as additional information. In this article, we provide a twostage dimension reduction method to incorporate additional information into the estimation. The main idea is to confine the searching space of target by constructing an envelope subspace. Simulation and real data analysis support the improvement of the procedure.