區位推論方法在政治學應用上之限制─區位迴歸、EI模型與BNH模型之比較研究

Abstract

政治行為研究中，在個體資料不可得的情況下，從總體層次資料推論或得知個體層次行為的區位推論方法便有其必要性與實用性，但由於區位推論問題沒有正確的解答，所以本文的目的在藉由比較目前政治學領域中被應用的區位迴歸、EI模型與BBH模型三者，以期瞭解不同區位推論方法的適用性。本文首先界定政治學領域欲處理的區位推論問題，再以最簡化的2×2交叉列表形成的區位推論問題為核心，從統計模型的設立探究區位迴歸、EI模型和BBH模型如何排除區位謬誤的困難，最後以調查資料比較三個模型在不同面向所設定資料中的估計誤差表現，在執行上本文以BNH模型取代BBH模型。 根據本文的研究結果所示，當解釋變數與參數的相關關係顯著時，區位迴歸、EI模型與BNH模型會有較大的估計誤差。同樣地，當參數標準差減少時，三模型也會有較大的誤差。而參數平均數若改變，三個模型的估計誤差不會隨之增減。至於總體層次樣本數的減少，也不會使得三個模型在估計誤差有太大的變化。整體而言，區位迴歸的估計誤差高於EI模型和BNH模型，而EI模型和BNH模型的估計誤差表現大致相等。最後，本文根據上述研究結果討論以區位推論方法分析國內一致與分裂投票議題時，其應用上的限制。

In political behavior study, it is necessary and practical to infer individual behavior from aggregate data, which is called “ecological inference”, when individual-level data is not available. There is no determinate solution to the ecological inference problem so far, and the purpose of this paper is to clarify the applications of different ecological inference methods by comparing Ecological Regression, EI Model and BBH model which are applied in political science recently. Firstly, this paper makes a definition of the ecological inference problem with which the researchers are concerned in political science. Then it explores how these three models solve the ecological fallacy from statistical setting of models, provided that the ecological inference problem is in terms of a 2×2 cross-table. Finally, it evaluates their performance, among which BBH model is replaced by BNH model, in different data which are set up based on different dimension from survey data. The results show that Ecological Regression, EI Model and BNH model are all biased in the situation when the variable in the margin is correlated with the parameter in the cell. In the situation when the standard deviation of parameter decreases, all of the three models are biased as well. The performance of the three models would not be affected with the changes in the mean of parameter. As for the sample size of the aggregate level, it seems not to affect the performance of any model. Overall, Ecological Regression is worse than EI Model and BNH model and the performance of EI Model and BNH model is in a tie. According to the results mentioned above, this paper discusses the limit of ecological inference methods when they are applied to analyze split-ticket voting.