# 鲁宾因果框架

## 一个扩展案例

130 135 −5

130 135 −5

### 稳定单元处理值假设 (SUTVA)

SUTVA 违规使因果推断更加困难。我们可以通过考虑更多的处理来解释相关的观察结果。我们通过考虑 Mary 是否接受处理来创建 4 个处理。

140 130 125 120

130 135 −5

### 因果推理的基本问题

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130 ? ?

$\displaystyle{ Y_{t}(u)=T+Y_{c}(u) }$$\displaystyle{ Y_{t}(u)-T=Y_{c}(u) }$

130 140 −10

130 115 15

130 ? ?

130 ? ?

130 ? ?

130 115 15

? 115 ?

## 结论

Rubin 因果模型还与工具变量（Angrist、Imbens 和 Rubin，1996 年）[6]和其他因果推断技术相关联。有关 Rubin 因果模型、结构方程建模和其他因果推断统计方法之间联系的更多信息，请参见 Morgan 和 Winship (2007)。[7]

## 参考文献

1. Sekhon, Jasjeet (2007). "The Neyman–Rubin Model of Causal Inference and Estimation via Matching Methods". The Oxford Handbook of Political Methodology.
2. Holland, Paul W. (1986). "Statistics and Causal Inference". J. Amer. Statist. Assoc. 81 (396): 945–960. doi:10.1080/01621459.1986.10478354. JSTOR 2289064.
3. Neyman, Jerzy. Sur les applications de la theorie des probabilites aux experiences agricoles: Essai des principes. Master's Thesis (1923). Excerpts reprinted in English, Statistical Science, Vol. 5, pp. 463–472. (D. M. Dabrowska, and T. P. Speed, Translators.)
4. Rubin, Donald (2005). "Causal Inference Using Potential Outcomes". J. Amer. Statist. Assoc. 100 (469): 322–331. doi:10.1198/016214504000001880.
5. Rubin, Donald (1974). "Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies". J. Educ. Psychol. 66 (5): 688–701 [p. 689]. doi:10.1037/h0037350.
6. Angrist J.,Imbens G.,Rubin D. (1996) Identification of Causal effects Using Instrumental Variables.J. Amer. Statist. Assoc.91.434:(444–455)
7. Morgan S.,Winship C. (2007) Counterfactuals and Causal Inference: Methods and Principles for Social Research.