再探全國性民調推估地方民意的可行性:應用改良式多層次貝氏定理估計模型及事後分層加權預測立法委員選舉結果

Abstract

本研究利用2016年大選前的民意調查資料，並採用多層次貝氏定理估計模型搭配分層加權的方式（multilevel regression and poststratification：MRP），預測73個區域立委選舉結果。具體來說，本文所採用的預測模式包含三個步驟：首先，透過基本人口特徵變數（性別、年齡、及教育程度）輔以選區層級的特徵，估計不同類型選民分別支持國民黨立委參選人及民進黨立委參選人的機率。其次，我們使用內政部2015年全國人口調查資料，求得每一個選區當中，不同類型選民的聯合機率分佈。最後，將各個選區內不同類型選民當中，支持國民黨立委參選人（及民進黨立委參選人）的成年人口數加總（每個選區皆含50種類型），並分別除以各選區的總成年人口數，以推估每一選區當中，國民黨立委參選人及民進黨立委參選人的得票率。在選區樣本數有限（平均約55個）的情況下，本研究仍能透過多層次統計模型及人口調查資料輔助，得出各選\n區政黨候選人得票率預測值與實際得票率之間的平均誤差值之絕對值僅約5個百分點。此外，本研究成功預測61個立委選區的選舉輸贏，與「未來事件交易所」的選舉預測結果相比較，僅落後一個選區。

This study uses pre-election national survey data and a method combining the Bayesian multilevel modeling approach with the population information for post-stratification(i.e., multilevel regression and post-stratification: MRP) to predict Legislative Yuan elections in the 73 singlemember districts. Specifically, our method is consisted of three steps: first, we construct a multilevel logistic regression model to estimate the vote choice variables for the Kuomintang (KMT) and Democratic Progressive Party (DPP) candidates, respectively, given demographics and districts of residence. Second, we post-stratify on all the variables in the model by using the joint population distribution of the demographic variables within each district. Third, we then combine the above two steps and estimate the mean of support for the KMT and DPP candidates in the district level. Given that each district only has about 55 samples on average, this study shows that MRP method can be regarded as an effective tool for election prediction, as the average absolute measurement error between the estimates and actual vote shares is just about 5 percentage\npoints. In a comparison with the pre-election districtlevel predictions issued by the prediction market“xFuture”, our estimates are almost as good as the results of “xFuture”.