引用
Analyzing Group Inequality: The Problem of Unobserved Outcomes
群體差異的分析：隱性變項之難題
作者：譚康榮（Tony Tam） | 首次發表於 2020-07-05 | 第 28 期 September 2002
DOI：https://dx.doi.org/10.6786/TJS.200209.0231
研究紀要（Research Notes）
DOI：https://dx.doi.org/10.6786/TJS.200209.0231
研究紀要（Research Notes）
論文資訊 | Article information
摘要 Abstract
本文呼籲學界注意長久存在於群體不平等研究中的一個困境：群體不平等的研究問題往往需要做不同模型間參數的比較。然而，當研究的依變項不能直接測量，能觀察到的是二元的指標，此時模型間的參數是不能直接比較的。原因是，傳統二元迴歸模型的參數是不能識別的（under-identified），能估計的是參數的相對值，而非絕對值。針對前述問題，本文的重點有五：（1）指出傳統上用以解決識別不定性問題的方法，實導致了模型間量度的任意變換；（2）指出一般統計軟體所提供的二元迴歸估計值，呈現有系統偏差；（3）提出簡化的程序以執行Winship-Mare所提出的解決方法；（4）當分析群體不平等的來源時，無論依變項是可觀察與否，只要依變項是連續變項，詮釋標準迴歸模型和二元迴歸模型參數的邏輯應該都是一樣的；和（5）利用1998美國General Social Survey和1993台灣社會變遷的資料，以職業取得（是否聲望高的職業）和學校分流（高中和高職）相關研究的數據做爲例子，具體呈現當實質的研究課題的確需要做模型間的結構參數的比較時，如果忽略了識別不定性問題，對研究結果所造成的嚴重偏誤。
關鍵字：隱性變項、邏輯迴歸、波比迴歸、社群差異
關鍵字：隱性變項、邏輯迴歸、波比迴歸、社群差異
This paper addresses a longstanding problem of analyzing group inequality: when the outcome is continuous but only observed with a binary indicator, the parameters of conventional binary regression models are under-identified. The objectives of this paper are to (1) nontechnically expose the fact that the conventional solution to the identification problem actually results in arbitrary rescaling across models, (2) point out a systematic bias in the estimates of conventional binary regression programs, (3) propose a simple way to implement the Winship-Mare solution, (4) emphasize the parallels between standard and binary regression modeling when analyzing group inequality in a continuous outcome, and (5) present concrete examples of the analysis of group inequality in which a direct comparison of parameters across models is necessary and ignoring under-identification would have serious consequences. Using data from the 1998 General Social Survey of the United States and the 1993 Taiwan Social Change Survey, this paper presents numerical examples from the study of group differentials in occupational achievement (whether a job has high prestige) and school tracks (academic versus vocational schools). The substantive conclusions can be drastically different depending critically on the identifying assumption used.
Keywords: Latent variable, logit, probit, group inequality
Keywords: Latent variable, logit, probit, group inequality
