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題名 平均邊際效果中處理連續自變數相關之方法
Addressing the Correlation between Continuous Covariates in Average Marginal Effects作者 蔡岳倫
Tsai, Yueh-Lun貢獻者 蔡宗漢
Tsai, Tsung-Han
蔡岳倫
Tsai, Yueh-Lun關鍵詞 廣義線性模型
平均邊際效果
異質性效果
次群體比較
經濟投票
GLM model
Average marginal effect
Heterogeneous effect
Subgroup comparison
Economic voting日期 2024 上傳時間 5-八月-2024 14:34:02 (UTC+8) 摘要 在政治學研究的討論中，經常涉及不同自變數對同一個依變數的影響，而這些自變數之間時常是彼此相關的。舉例來說，在選舉研究的文獻中發現，選民對政府經濟表現的評估與其政黨認同都會對投票選擇產生影響。然而亦有許多研究發現，選民的經濟表現評估和政黨認同存在相關性，當認同的政黨執政時，選民傾向給予較好的經濟表現評估。若要在這樣的架構下分析自變數的影響效果，必然需要將彼此的相關性納入估計，並於解釋效果時排除相關性的影響，使比較可以在控制變數相同的情況下進行。近年來，許多研究者在對模型結果進行詮釋時，不是直接觀察迴歸係數估計值，而是計算「平均邊際效果」（average marginal effect），特別是採用非線性模型時更是如此，認為這樣的詮釋更為直觀，也可以避免研究者設定變數時必然面臨的代表性問題。然而，前述所提及自變數間的相關性，卻可能對於平均邊際效果的計算產生影響，進而導致錯誤推論的可能性。由於在計算平均邊際效果時將代入資料中的實際觀察值，則產生該筆資料背後的變數間相關性便會同時透過估計係數與個別觀察值的變數分布對平均邊際效果產生影響，這使得平均邊際效果的解釋並不能如同係數解釋般排除變數間的相關性。若未辨明兩者的差異，可能不經意地在解釋上強加了變數間相互獨立的假定。從自變數聯合分布的觀點，本文認為邊際效果作為預測結果解釋途徑，選擇如何於計算過程中設定變數是檢驗理論與推論母體上的取捨。檢驗理論要求符合控制其他因素相同的條件，而推論母體則要求變數設定符合真實情形，於是如何選擇設定變數將視研究目的而定。本文透過效果平均，將既有文獻提到的幾種邊際效果解釋囊括於設定自變數於特定水準與否的架構中，一方面釐清平均邊際效果的意義，另一方面也檢視變數相關性所帶來的影響，並嘗試提出消彌變數相關性在平均邊際效果影響的方法。本文透過模擬分析證實相關性的影響，並分別檢視其影響在不同的變數分布、平均預測機率、以及效果規模中有何不同。最後，本文以經濟投票為例，說明文中提出的效果平均如何應用於不同研究目的。
Political science research always aims to explore the influence of multiple correlated variables. For example, both voters' evaluations of government on economic performance and their party identification significantly impact voting choices, and these variables often exhibit correlations: voters tend to assess the economy more positively when their preferred party holds power. To estimate the effect of variable, it is crucial to account for these correlations. When interpreting the effects, the influence of these correlations must be excluded to ensure that comparisons are made under all-else-equal conditions. While many researchers advocate for using "average marginal effect" (AME) as an alternative to interpreting model instead of coefficients in complex model settings such as nonlinear model, I argue that the role of correlations differs between these approaches. Failure to distinguish between them can lead to unintended assumptions of independence. From the perspective of the joint distribution of variables, this paper argues that using marginal effects as a method of interpreting predictive values involves trade-offs in how variables are set. On the one hand, testing theory requires controlling for other variables, while inferring population requires setting variables as they would be in real situations. The choice of how to set variables depends on the research purpose. I incorporate different marginal effect interpretations into the framework of setting variables at specific levels through average of effects, and I use this to clarify the meaning of AMEs, examine the impact of variable correlations, and propose methods to mitigate these effects. I demonstrate these effects by simulation and illustrate how they vary across different variable distributions, average predicted probabilities, and effect sizes. Using an example of economic voting, I show how the proposed methods can be applied to various research purposes.參考文獻 一、中文 吳親恩、林奕孜，2012，〈經濟投票與總統選舉：效度與內生問題的分析〉，《台灣政治學刊》，16 卷2 期，頁175–232。 黃紀，2020， 《2016 年至2020 年「選舉與民主化調查」四年期研究規劃(4/4)：2020 年總統與立法委員選舉面訪案》， 計畫編號：MOST 105-2420-H-004-015-SS4，台北：行政院科技部補助專題研究計畫（成果報告）。 黃紀、王德育，2012，《質變數與受限依變數的迴歸分析》，台北：五南。 二、英文 Ai, Chunrong and Edward C Norton. 2003. “Interaction Terms in Logit and Probit Models.” Economics Letters 80(1):123–129. Allison, Paul D. 1999. “Comparing Logit and Probit Coefficients Across Groups.” Sociological Methods & Research 28(2):186–208. Anderson, Christopher J. 2000. “Economic Voting and Political Context: A Comparative Perspective.” Electoral Studies 19(2-3):151–170. Anderson, Christopher J, Silvia M Mendes and Yuliya V Tverdova. 2004. “Endogenous Economic Voting: Evidence from the 1997 British election.” Electoral Studies 23(4):683–708. Ashworth, Scott, Christopher R Berry and Ethan Bueno de Mesquita. 2021. Theory and Credibility: Integrating Theoretical and Empirical Social Science. Princeton University Press. Berk, Richard, Andreas Buja, Lawrence Brown, Edward George, Arun Kumar Kuchibhotla, Weijie Su and Linda Zhao. 2021. “Assumption Lean Regression.” The American Statistician 75(1):76–84. Berry, William D, Jacqueline HR DeMeritt and Justin Esarey. 2010. “Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?” American Journal of Political Science 54(1):248–266. Berry, William D, Matt Golder and Daniel Milton. 2012. “Improving Tests of Theories Positing Interaction.” The Journal of Politics 74(3):653–671. Brambor, Thomas, William Roberts Clark and Matt Golder. 2006. “Understanding Interaction Models: Improving Empirical Analyses.” Political Analysis 14(1):63–82. Breen, Richard, Kristian Bernt Karlson and Anders Holm. 2018. “Interpreting and Understanding Logits, Probits, and Other Nonlinear Probability Models.” Annual Review of Sociology 44:39–54. Buja, Andreas, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang and Linda Zhao. 2019. “Models as Approximations I: Consequences Illustrated with Linear Regression.” Statistical Science 34(4):523–544. Campbell, Angus., Philip E. Converse, Warren E. Miller and Donald E. Stokes. 1960. The American Voter. University of Chicago Press. Downs, Anthony. 1957. “An Economic Theory of Political Action in a Democracy.” Journal of Political Economy 65(2):135–150. Evans, Geoffrey and Robert Andersen. 2006. “The Political Conditioning of Economic Perceptions.” The Journal of Politics 68(1):194–207. Fiorina, Morris P. 1978. “Economic Retrospective Voting in American National Elections: A Micro-Analysis.” American Journal of Political Science pp. 426–443. Fiorina, Morris P. 1983. “Who is Held Responsible? Further Evidence on the Hibbing-Alford thesis.” American Journal of Political Science pp. 158–164. Frisch, Ragnar and Frederick V Waugh. 1933. “Partial Time Regressions as Compared with Individual Trends.” Econometrica: Journal of the Econometric Society pp. 387–401. Gelman, Andrew and Iain Pardoe. 2007. “Average Predictive Comparisons for Models with Nonlinearity, Interactions, and Variance Components.” Sociological Methodology 37(1):23–51. Ghosn, Faten, Tiffany S Chu, Miranda Simon, Alex Braithwaite, Michael Frith and Joanna Jandali. 2021. “The Journey Home: Violence, Anchoring, and Refugee Decisions to Return.” American Political Science Review 115(3):982–998. Gujarati, Damodar. 1970. “Use of Dummy Variables in Testing for Equality between Sets of Coefficients in Two Linear Regressions: A Note.” The American Statistician 24(1):50–52. Hainmueller, Jens, Jonathan Mummolo and Yiqing Xu. 2019. “How Much Should We Trust Estimates from Multiplicative Interaction Models? Simple Tools to Improve Empirical Practice.” Political Analysis 27(2):163–192. Hanmer, Michael J and Kerem Ozan Kalkan. 2013. “Behind the Curve: Clarifying the Best Approach to Calculating Predicted Probabilities and Marginal Effects from Limited Dependent Variable Models.” American Journal of Political Science 57(1):263–277. Hanretty, Chris, Jonathan Mellon and Patrick English. 2021. “Members of Parliament are Minimally Accountable for their Issue Stances (and They Know It).” American Political Science Review 115(4):1275–1291. Hansen, Bruce. 2022. Econometrics. Princeton University Press. Huang, Chi. 2018. “Testing Partisan Effects on Economic Perceptions: A Panel Design Approach.” Journal of Electoral Studies 25(2). Huang, Chi and Todd G Shields. 2000. “Interpretation of Interaction Effects in Logit and Probit Analyses: Reconsidering the Relationship between Registration Laws, Education, and Voter Turnout.” American Politics Quarterly 28(1):80–95. Huddy, Leonie, Lilliana Mason and Lene Aarøe. 2015. “Expressive Partisanship: Campaign Involvement, Political Emotion, and Partisan Identity.” American Political Science Review 109(1):1–17. Kinder, Donald R and D Roderick Kiewiet. 1981. “Sociotropic Politics: the American Case.” British Journal of Political Science 11(2):129–161. King, Gary. 1989. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. Cambridge University Press. King, Gary and Langche Zeng. 2006. “The Dangers of Extreme Counterfactuals.” Political Analysis 14(2):131–159. King, Gary, Michael Tomz and Jason Wittenberg. 2000. “Making the Most of Statistical Analyses: Improving Interpretation and Presentation.” American Journal of Political Science pp. 347–361. Kramer, Gerald H. 1971. “Short-Term Fluctuations in US Voting Behavior, 1896–1964.” American Political Science Review 65(1):131–143. Kuha, Jouni and Colin Mills. 2020. “On Group Comparisons with Logistic Regression Models.” Sociological Methods & Research 49(2):498–525. Kuklinski, James H and Darrell M West. 1981. “Economic Expectations and Voting Behavior in United States House and Senate Elections.” American Political Science Review 75(2):436–447. Leighley, Jan E. 2010. The Oxford Handbook of American Elections and Political Behavior. OUP Oxford. Lewis-Beck, Colin and Nicholas F Martini. 2020. “Economic Perceptions and Voting Behavior in US Presidential Elections.” Research & Politics 7(4):2053168020972811. Little, Roderick JA and Donald B Rubin. 2019. Statistical Analysis with Missing Data. Vol. 793 John Wiley & Sons. Long, J Scott and Jeremy Freese. 2006. Regression Models for Categorical Dependent Variables Using Stata. Vol. 7 Stata press. Long, J Scott and Sarah A Mustillo. 2021. “Using Predictions and Marginal Effects to Compare Groups in Regression Models for Binary Outcomes.” Sociological Methods & Research 50(3):1284–1320. Lovell, Michael C. 1963. “Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis.” Journal of the American Statistical Association 58(304):993–1010. Lundberg, Ian, Rebecca Johnson and Brandon M Stewart. 2021. “What is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory.” American Sociological Review 86(3):532–565. MacKuen, Michael B, Robert S Erikson and James A Stimson. 1992. “Peasants or Bankers? The American Electorate and the US Economy.” American Political Science Review 86(3):597–611. Mize, Trenton D. 2019. “Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effects.” Sociological Science 6:81–117. Mood, Carina. 2010. “Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do about It.” European Sociological Review 26(1):67–82. Morisi, Davide, John T Jost and Vishal Singh. 2019. “An Asymmetrical “President-in-Power＂Effect.” American Political Science Review 113(2):614–620. Mustillo, Sarah A, Omar A Lizardo and Rory M McVeigh. 2018. “Editors＇Comment: A Few Guidelines for Quantitative Submissions.” American Sociological Review 83(6):1281–1283. Nagler, Jonathan. 1991. “The Effect of Registration Laws and Education on US Voter Turnout.” The American Political Science Review pp. 1393–1405. Nagler, Jonathan. 1994. “Scobit: An Alternative Estimator to Logit and Probit.” American Journal of Political Science pp. 230–255. Nelder, John Ashworth and P. McCullagh. 1989. Generalized Linear Models. 2 ed. Chapman and Hall, London. Nelder, John Ashworth and Robert WM Wedderburn. 1972. “Generalized Linear Models.” Journal of the Royal Statistical Society: Series A (General) 135(3):370–384. Osmundsen, Mathias, Alexander Bor, Peter Bjerregaard Vahlstrup, Anja Bechmann and Michael Bang Petersen. 2021. “Partisan Polarization is the Primary Psychological Motivation Behind Political Fake News Sharing on Twitter.” American Political Science Review 115(3):999–1015. Powell Jr, G Bingham and Guy D Whitten. 1993. “A Cross-National Analysis of Economic Voting: Taking Account of the Political Context.” American Journal of Political Science pp. 391–414. Sydsæter, Knut, Peter Hammond, Atle Seierstad and Arne Strom. 2008. Further Mathematics for Economic Analysis. Pearson education. Tilley, James and Sara B Hobolt. 2011. “Is the Government to Blame? An Experimental Test of How Partisanship Shapes Perceptions of Performance and Responsibility.” The Journal of Politics 73(2):316–330. Williams, Richard. 2012. “Using the Margins Command to Estimate and Interpret Adjusted Predictions and Marginal Effects.” The Stata Journal 12(2):308–331. Wlezien, Christopher, Mark Franklin and Daniel Twiggs. 1997. “Economic Perceptions and Vote Ehoice: Disentangling the Endogeneity.” Political Behavior 19(1):7–17. Woldense, Josef and Alex Kroeger. 2023. “Elite Change without Regime Change: Authoritarian Persistence in Africa and the End of the Cold War.” American Political Science Review pp. 1–17. Wooldridge, Jeffrey M. 2005. “Unobserved Heterogeneity and Estimation of Average Partial Effects.” Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg pp. 27–55. Wooldridge, Jeffrey M. 2010. Econometric Analysis of Cross Section and Panel Data. MIT press. 描述 碩士
國立政治大學
政治學系
110252019資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110252019 資料類型 thesis dc.contributor.advisor 蔡宗漢 zh_TW dc.contributor.advisor Tsai, Tsung-Han en_US dc.contributor.author (作者) 蔡岳倫 zh_TW dc.contributor.author (作者) Tsai, Yueh-Lun en_US dc.creator (作者) 蔡岳倫 zh_TW dc.creator (作者) Tsai, Yueh-Lun en_US dc.date (日期) 2024 en_US dc.date.accessioned 5-八月-2024 14:34:02 (UTC+8) - dc.date.available 5-八月-2024 14:34:02 (UTC+8) - dc.date.issued (上傳時間) 5-八月-2024 14:34:02 (UTC+8) - dc.identifier (其他 識別碼) G0110252019 en_US dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152880 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 政治學系 zh_TW dc.description (描述) 110252019 zh_TW dc.description.abstract (摘要) 在政治學研究的討論中，經常涉及不同自變數對同一個依變數的影響，而這些自變數之間時常是彼此相關的。舉例來說，在選舉研究的文獻中發現，選民對政府經濟表現的評估與其政黨認同都會對投票選擇產生影響。然而亦有許多研究發現，選民的經濟表現評估和政黨認同存在相關性，當認同的政黨執政時，選民傾向給予較好的經濟表現評估。若要在這樣的架構下分析自變數的影響效果，必然需要將彼此的相關性納入估計，並於解釋效果時排除相關性的影響，使比較可以在控制變數相同的情況下進行。近年來，許多研究者在對模型結果進行詮釋時，不是直接觀察迴歸係數估計值，而是計算「平均邊際效果」（average marginal effect），特別是採用非線性模型時更是如此，認為這樣的詮釋更為直觀，也可以避免研究者設定變數時必然面臨的代表性問題。然而，前述所提及自變數間的相關性，卻可能對於平均邊際效果的計算產生影響，進而導致錯誤推論的可能性。由於在計算平均邊際效果時將代入資料中的實際觀察值，則產生該筆資料背後的變數間相關性便會同時透過估計係數與個別觀察值的變數分布對平均邊際效果產生影響，這使得平均邊際效果的解釋並不能如同係數解釋般排除變數間的相關性。若未辨明兩者的差異，可能不經意地在解釋上強加了變數間相互獨立的假定。從自變數聯合分布的觀點，本文認為邊際效果作為預測結果解釋途徑，選擇如何於計算過程中設定變數是檢驗理論與推論母體上的取捨。檢驗理論要求符合控制其他因素相同的條件，而推論母體則要求變數設定符合真實情形，於是如何選擇設定變數將視研究目的而定。本文透過效果平均，將既有文獻提到的幾種邊際效果解釋囊括於設定自變數於特定水準與否的架構中，一方面釐清平均邊際效果的意義，另一方面也檢視變數相關性所帶來的影響，並嘗試提出消彌變數相關性在平均邊際效果影響的方法。本文透過模擬分析證實相關性的影響，並分別檢視其影響在不同的變數分布、平均預測機率、以及效果規模中有何不同。最後，本文以經濟投票為例，說明文中提出的效果平均如何應用於不同研究目的。 zh_TW dc.description.abstract (摘要) Political science research always aims to explore the influence of multiple correlated variables. For example, both voters' evaluations of government on economic performance and their party identification significantly impact voting choices, and these variables often exhibit correlations: voters tend to assess the economy more positively when their preferred party holds power. To estimate the effect of variable, it is crucial to account for these correlations. When interpreting the effects, the influence of these correlations must be excluded to ensure that comparisons are made under all-else-equal conditions. While many researchers advocate for using "average marginal effect" (AME) as an alternative to interpreting model instead of coefficients in complex model settings such as nonlinear model, I argue that the role of correlations differs between these approaches. Failure to distinguish between them can lead to unintended assumptions of independence. From the perspective of the joint distribution of variables, this paper argues that using marginal effects as a method of interpreting predictive values involves trade-offs in how variables are set. On the one hand, testing theory requires controlling for other variables, while inferring population requires setting variables as they would be in real situations. The choice of how to set variables depends on the research purpose. I incorporate different marginal effect interpretations into the framework of setting variables at specific levels through average of effects, and I use this to clarify the meaning of AMEs, examine the impact of variable correlations, and propose methods to mitigate these effects. I demonstrate these effects by simulation and illustrate how they vary across different variable distributions, average predicted probabilities, and effect sizes. Using an example of economic voting, I show how the proposed methods can be applied to various research purposes. en_US dc.description.tableofcontents 第一章 緒論 1 第一節 研究動機及背景 1 第二節 研究目的 4 第三節 章節安排 5 第四節 英漢詞彙對照表 5 第二章 文獻回顧 7 第一節 模型解釋途徑：係數解釋與預測結果解釋 7 第二節 相關性在兩種解釋途徑的影響 10 第三節 平均邊際效果的詮釋 13 第三章 理論建構 18 第一節 二分勝算對數模型 18 第二節 自變數聯合分布與預測結果解釋的關係 21 第三節 相關性在模型的影響：係數與效果平均 28 第四節 排除自變數相關性的平均邊際效果 30 第四章 模擬實驗 35 第一節 模擬實驗架構 35 第二節 自變數分布與相關性的影響 38 第三節 平均發生機率的影響 40 第四節 變數相對影響強度的影響 42 第五節 排除自變數相關性的效果平均 46 第五章 實例分析：政黨認同與經濟投票 48 第一節 經濟表現評估與政黨認同的相關性 49 第二節 比較經濟表現評估的效果 50 第六章 結論 56 第一節 計算效果平均的建議 56 第二節 研究限制與未來研究之建議 57 參考文獻 61 附錄A 相關性在OLS 的影響 68 附錄B 次資料分析與類別變數交互作用項模型的相等性 70 附錄C 模擬實驗的步驟 73 附錄D 政黨認同與經濟投票的變數測量與處理方式 74 附錄E 經濟投票與投票選擇的二分勝算對數模型：完整分析結果 76 zh_TW dc.format.extent 2331345 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110252019 en_US dc.subject (關鍵詞) 廣義線性模型 zh_TW dc.subject (關鍵詞) 平均邊際效果 zh_TW dc.subject (關鍵詞) 異質性效果 zh_TW dc.subject (關鍵詞) 次群體比較 zh_TW dc.subject (關鍵詞) 經濟投票 zh_TW dc.subject (關鍵詞) GLM model en_US dc.subject (關鍵詞) Average marginal effect en_US dc.subject (關鍵詞) Heterogeneous effect en_US dc.subject (關鍵詞) Subgroup comparison en_US dc.subject (關鍵詞) Economic voting en_US dc.title (題名) 平均邊際效果中處理連續自變數相關之方法 zh_TW dc.title (題名) Addressing the Correlation between Continuous Covariates in Average Marginal Effects en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 一、中文 吳親恩、林奕孜，2012，〈經濟投票與總統選舉：效度與內生問題的分析〉，《台灣政治學刊》，16 卷2 期，頁175–232。 黃紀，2020， 《2016 年至2020 年「選舉與民主化調查」四年期研究規劃(4/4)：2020 年總統與立法委員選舉面訪案》， 計畫編號：MOST 105-2420-H-004-015-SS4，台北：行政院科技部補助專題研究計畫（成果報告）。 黃紀、王德育，2012，《質變數與受限依變數的迴歸分析》，台北：五南。 二、英文 Ai, Chunrong and Edward C Norton. 2003. “Interaction Terms in Logit and Probit Models.” Economics Letters 80(1):123–129. Allison, Paul D. 1999. “Comparing Logit and Probit Coefficients Across Groups.” Sociological Methods & Research 28(2):186–208. Anderson, Christopher J. 2000. “Economic Voting and Political Context: A Comparative Perspective.” Electoral Studies 19(2-3):151–170. Anderson, Christopher J, Silvia M Mendes and Yuliya V Tverdova. 2004. “Endogenous Economic Voting: Evidence from the 1997 British election.” Electoral Studies 23(4):683–708. Ashworth, Scott, Christopher R Berry and Ethan Bueno de Mesquita. 2021. Theory and Credibility: Integrating Theoretical and Empirical Social Science. Princeton University Press. Berk, Richard, Andreas Buja, Lawrence Brown, Edward George, Arun Kumar Kuchibhotla, Weijie Su and Linda Zhao. 2021. “Assumption Lean Regression.” The American Statistician 75(1):76–84. Berry, William D, Jacqueline HR DeMeritt and Justin Esarey. 2010. “Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?” American Journal of Political Science 54(1):248–266. Berry, William D, Matt Golder and Daniel Milton. 2012. “Improving Tests of Theories Positing Interaction.” The Journal of Politics 74(3):653–671. Brambor, Thomas, William Roberts Clark and Matt Golder. 2006. “Understanding Interaction Models: Improving Empirical Analyses.” Political Analysis 14(1):63–82. Breen, Richard, Kristian Bernt Karlson and Anders Holm. 2018. “Interpreting and Understanding Logits, Probits, and Other Nonlinear Probability Models.” Annual Review of Sociology 44:39–54. Buja, Andreas, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang and Linda Zhao. 2019. “Models as Approximations I: Consequences Illustrated with Linear Regression.” Statistical Science 34(4):523–544. Campbell, Angus., Philip E. Converse, Warren E. Miller and Donald E. Stokes. 1960. The American Voter. University of Chicago Press. Downs, Anthony. 1957. “An Economic Theory of Political Action in a Democracy.” Journal of Political Economy 65(2):135–150. Evans, Geoffrey and Robert Andersen. 2006. “The Political Conditioning of Economic Perceptions.” The Journal of Politics 68(1):194–207. Fiorina, Morris P. 1978. “Economic Retrospective Voting in American National Elections: A Micro-Analysis.” American Journal of Political Science pp. 426–443. Fiorina, Morris P. 1983. “Who is Held Responsible? Further Evidence on the Hibbing-Alford thesis.” American Journal of Political Science pp. 158–164. Frisch, Ragnar and Frederick V Waugh. 1933. “Partial Time Regressions as Compared with Individual Trends.” Econometrica: Journal of the Econometric Society pp. 387–401. Gelman, Andrew and Iain Pardoe. 2007. “Average Predictive Comparisons for Models with Nonlinearity, Interactions, and Variance Components.” Sociological Methodology 37(1):23–51. Ghosn, Faten, Tiffany S Chu, Miranda Simon, Alex Braithwaite, Michael Frith and Joanna Jandali. 2021. “The Journey Home: Violence, Anchoring, and Refugee Decisions to Return.” American Political Science Review 115(3):982–998. Gujarati, Damodar. 1970. “Use of Dummy Variables in Testing for Equality between Sets of Coefficients in Two Linear Regressions: A Note.” The American Statistician 24(1):50–52. Hainmueller, Jens, Jonathan Mummolo and Yiqing Xu. 2019. “How Much Should We Trust Estimates from Multiplicative Interaction Models? Simple Tools to Improve Empirical Practice.” Political Analysis 27(2):163–192. Hanmer, Michael J and Kerem Ozan Kalkan. 2013. “Behind the Curve: Clarifying the Best Approach to Calculating Predicted Probabilities and Marginal Effects from Limited Dependent Variable Models.” American Journal of Political Science 57(1):263–277. Hanretty, Chris, Jonathan Mellon and Patrick English. 2021. “Members of Parliament are Minimally Accountable for their Issue Stances (and They Know It).” American Political Science Review 115(4):1275–1291. Hansen, Bruce. 2022. Econometrics. Princeton University Press. Huang, Chi. 2018. “Testing Partisan Effects on Economic Perceptions: A Panel Design Approach.” Journal of Electoral Studies 25(2). Huang, Chi and Todd G Shields. 2000. “Interpretation of Interaction Effects in Logit and Probit Analyses: Reconsidering the Relationship between Registration Laws, Education, and Voter Turnout.” American Politics Quarterly 28(1):80–95. Huddy, Leonie, Lilliana Mason and Lene Aarøe. 2015. “Expressive Partisanship: Campaign Involvement, Political Emotion, and Partisan Identity.” American Political Science Review 109(1):1–17. Kinder, Donald R and D Roderick Kiewiet. 1981. “Sociotropic Politics: the American Case.” British Journal of Political Science 11(2):129–161. King, Gary. 1989. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. Cambridge University Press. King, Gary and Langche Zeng. 2006. “The Dangers of Extreme Counterfactuals.” Political Analysis 14(2):131–159. King, Gary, Michael Tomz and Jason Wittenberg. 2000. “Making the Most of Statistical Analyses: Improving Interpretation and Presentation.” American Journal of Political Science pp. 347–361. Kramer, Gerald H. 1971. “Short-Term Fluctuations in US Voting Behavior, 1896–1964.” American Political Science Review 65(1):131–143. Kuha, Jouni and Colin Mills. 2020. “On Group Comparisons with Logistic Regression Models.” Sociological Methods & Research 49(2):498–525. Kuklinski, James H and Darrell M West. 1981. “Economic Expectations and Voting Behavior in United States House and Senate Elections.” American Political Science Review 75(2):436–447. Leighley, Jan E. 2010. The Oxford Handbook of American Elections and Political Behavior. OUP Oxford. Lewis-Beck, Colin and Nicholas F Martini. 2020. “Economic Perceptions and Voting Behavior in US Presidential Elections.” Research & Politics 7(4):2053168020972811. Little, Roderick JA and Donald B Rubin. 2019. Statistical Analysis with Missing Data. Vol. 793 John Wiley & Sons. Long, J Scott and Jeremy Freese. 2006. Regression Models for Categorical Dependent Variables Using Stata. Vol. 7 Stata press. Long, J Scott and Sarah A Mustillo. 2021. “Using Predictions and Marginal Effects to Compare Groups in Regression Models for Binary Outcomes.” Sociological Methods & Research 50(3):1284–1320. Lovell, Michael C. 1963. “Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis.” Journal of the American Statistical Association 58(304):993–1010. Lundberg, Ian, Rebecca Johnson and Brandon M Stewart. 2021. “What is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory.” American Sociological Review 86(3):532–565. MacKuen, Michael B, Robert S Erikson and James A Stimson. 1992. “Peasants or Bankers? The American Electorate and the US Economy.” American Political Science Review 86(3):597–611. Mize, Trenton D. 2019. “Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effects.” Sociological Science 6:81–117. Mood, Carina. 2010. “Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do about It.” European Sociological Review 26(1):67–82. Morisi, Davide, John T Jost and Vishal Singh. 2019. “An Asymmetrical “President-in-Power＂Effect.” American Political Science Review 113(2):614–620. Mustillo, Sarah A, Omar A Lizardo and Rory M McVeigh. 2018. “Editors＇Comment: A Few Guidelines for Quantitative Submissions.” American Sociological Review 83(6):1281–1283. Nagler, Jonathan. 1991. “The Effect of Registration Laws and Education on US Voter Turnout.” The American Political Science Review pp. 1393–1405. Nagler, Jonathan. 1994. “Scobit: An Alternative Estimator to Logit and Probit.” American Journal of Political Science pp. 230–255. Nelder, John Ashworth and P. McCullagh. 1989. Generalized Linear Models. 2 ed. Chapman and Hall, London. Nelder, John Ashworth and Robert WM Wedderburn. 1972. “Generalized Linear Models.” Journal of the Royal Statistical Society: Series A (General) 135(3):370–384. Osmundsen, Mathias, Alexander Bor, Peter Bjerregaard Vahlstrup, Anja Bechmann and Michael Bang Petersen. 2021. “Partisan Polarization is the Primary Psychological Motivation Behind Political Fake News Sharing on Twitter.” American Political Science Review 115(3):999–1015. Powell Jr, G Bingham and Guy D Whitten. 1993. “A Cross-National Analysis of Economic Voting: Taking Account of the Political Context.” American Journal of Political Science pp. 391–414. Sydsæter, Knut, Peter Hammond, Atle Seierstad and Arne Strom. 2008. Further Mathematics for Economic Analysis. Pearson education. Tilley, James and Sara B Hobolt. 2011. “Is the Government to Blame? An Experimental Test of How Partisanship Shapes Perceptions of Performance and Responsibility.” The Journal of Politics 73(2):316–330. Williams, Richard. 2012. “Using the Margins Command to Estimate and Interpret Adjusted Predictions and Marginal Effects.” The Stata Journal 12(2):308–331. Wlezien, Christopher, Mark Franklin and Daniel Twiggs. 1997. “Economic Perceptions and Vote Ehoice: Disentangling the Endogeneity.” Political Behavior 19(1):7–17. Woldense, Josef and Alex Kroeger. 2023. “Elite Change without Regime Change: Authoritarian Persistence in Africa and the End of the Cold War.” American Political Science Review pp. 1–17. Wooldridge, Jeffrey M. 2005. “Unobserved Heterogeneity and Estimation of Average Partial Effects.” Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg pp. 27–55. Wooldridge, Jeffrey M. 2010. Econometric Analysis of Cross Section and Panel Data. MIT press. zh_TW
