多變量分類依變數之潛在類別迴歸分析：模型之建立及其於「多合一選舉」之應用

Abstract

政治學的經驗研究中，常遇到學理上有兩個或兩個以上的依變數必須同時分析，而且這 幾個依變數均為質的無序多分類變數，構成「多變量之分類依變數」（multivariate multinomial responses），不適用一般常見之多變量連續依變數的迴歸模型。例如在分析三項公職同日併 選（即「三合一選舉」）時，研究者想同時分析選民在這三張選票的投票模式（例如一致或 分裂投票），而假設每張選票上有三個政黨／候選人，便一次處理三個三分類的依變數。若 以傳統的交叉分類法界定依變數，則有33 = 27 類，故一般之多項勝算對數（multinomial logit） 或多項機率單元（multinomial probit）等模型均難適用。 有鑑於往後「多合一選舉」將成選舉常態，本兩年期研究計畫的目的有二： 一、 在方法方面：以廣義線性迴歸模型（generalized linear models,GLM）為基礎，發展適 用於「多變量分類依變數」的模型（multivariate multinomial models），並將之整合潛在 類別迴歸（latent class regression）的學理，以利同時分析兩個以上的無序多分類依變 數，且能區辨選民異質性（voter heterogeneity）的潛在類別。 二、 在應用研究方面：將「多變量分類依變數模型」應用至2014 年「七合一選舉」的一致 與分裂投票研究，既可克服傳統上將依變數交叉分類後，造成類別過多、有些重要類 別樣本不足、無法納入交叉選項特徵等的問題，又可檢證學理上選民對若干張選票的 投票抉擇因素。

In empirical political studies, it is not uncommon to encounter the need to simultaneously analyze severalnominal dependent variables, i.e., multivariate multinomial responses. The classical textbook multivariate regression models for continuous responses no longer apply in these cases. For example, in a concurrent election of three public offices with each ballot listing three parties/candidates as options, a three-way cross-table typology reveals 33 = 27 possible patterns of straight- and split-ticket voting. Trying to analyze a 27-category response is cumbersome, if possible at all, even with statistical models developed for multinomial responses such as multinomial logit or multinomial probit. Given the fact that concurrent elections will become regular in Taiwan, this two-year research project proposal aims to reach two goals: 1. To develop a multivariate multinomial latentclass choice model. This model will start from the popular generalized linear models (GLM), then extend to multivariate GLM and further incorporate latent class regression model into it. The latent class component will allow us not only to take account voter heterogeneity but uncover unobserved classes of voters. 2. To apply our newly developed multivariate multinomial latent-class choice model to the study of straight- and split-ticketing in the so-called “seven-in-one” local concurrent elections to be held in 2014 in Taiwan. We will demonstrate how this new model can overcome the traditional typology problems with spare category and test hypotheses concerning voter’s simultaneous choices among several ballots.