雙底冊電話抽樣調查之事後校正：聯立方程式法之理論與實務

Post-Calibration of Dual-Frame Telephone Surveys: Theory and Practice of the System-of-Equations Method

10.6683/TPSR.202206_26(1).0001

蔡奇霖(Chi-Lin Tsai)

抽樣調查 ； 電話調查 ； 雙底冊調查 ； 聯立方程式法 ； 加權 ； Sample Survey ； Telephone Survey ； Dual-Frame Survey ； System-of-Equations Method ； Weighting

台灣政治學刊

26卷1期（2022 / 06 / 01）

1 - 55

繁體中文;英文

因應近年來市內住宅電話用戶減少以及只用手機通話的人口增加，電話抽樣調查開始在市話訪問之外加入手機訪問以維持調查的涵蓋範圍。但由於缺乏一份同時涵蓋市話使用者與手機使用者的抽樣底冊，調查前僅能分別從市話與手機各自的底冊抽樣，訪問後再合併資料，從而形成所謂的「雙底冊調查」。然而市話底冊與手機底冊部份重疊（亦即市話與手機都有使用的民眾），而且兩份底冊的取樣率不見得相同，因此受訪者的中選率不完全一致，必須在訪問後加以校正。以此為研究焦點，本文首先簡介歐美文獻中常見的校正方法，並且說明為何這些方法無法用於臺灣當前的雙底冊電話調查。接著，本文聚焦於一項適用於臺灣的校正法：聯立方程式法（或稱組合估計法）。此方法雖已逐漸為臺灣民意調查業界所採用，但學界對它的研究仍有不足。為此，本文嘗試從三個面向來補足這段空缺：第一、檢驗聯立方程式法的統計性質；第二、改良該校正法的操作程序；第三、探討其適用前提及違反前提的後果。這些研究充實了聯立方程式法的理論內涵，並為其實務應用提供具體指引，也為未來雙底冊調查研究指出方向。

In response to the decline of landline households and the growth of cellphone-only users, more and more telephone surveys conduct interviews by cellphone as well as by landline. However, in the absence of a sampling frame that covers both landline households and cellphone users, a dual-frame sampling design is inevitable, that is, sampling from a landline frame and a cellphone frame separately, and then combining the two samples for the analysis. These two frames overlap in the subpopulation that uses both a landline and cellphone, and the sampling rates of them are usually different. Consequently, respondents in a dual-frame survey have unequal chances of being sampled. Several methods for correcting this problem have been proposed in the Western literature, but most of them are not suitable for Taiwan. A viable alternative referred to as the "System-of-Equations Method" is increasingly being adopted in the Taiwanese polling industry, but academic research has not considered it in much detail. To fill this gap, this paper examines this method in three respects: 1) by elaborating its underlying assumptions and evaluating the consequences of assumption violation; 2) by examining the statistical properties of the method; and 3) by improving the procedure for applying the method. The results of this study establish the theoretical basis of the System-of-Equations Method, provide a practical guide for its proper use, and suggest directions for future research on dual-frame surveys.

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