V2EX random intercept

Random Intercept

定义 / Definition

随机截距:统计建模(尤其是混合效应模型/多层模型)中的一种设定,允许不同组/个体在基线水平(截距)上有各自的偏移量,这些偏移被视为来自某个概率分布(常假设为正态分布)的随机效应。常用于处理组内相关个体差异

发音 / Pronunciation (IPA)

/rndm ntrspt/

例句 / Examples

A random intercept lets each student have a different baseline score.
随机截距让每个学生都有不同的基线分数。

We fit a mixed-effects model with a random intercept for each hospital to account for differences in baseline patient risk.
我们拟合了一个混合效应模型,为每家医院设置随机截距,以反映患者基础风险的差异。

词源 / Etymology

random 源自中古法语 random(“迅速、冲力”相关含义),在现代统计语境中发展为“以概率方式变化、不可用固定常数完全描述”。intercept 来自拉丁语 intercipere(“截住、拦截”),在解析几何与回归中指“与坐标轴相交处”,进而指回归方程中的常数项/基线。合在一起,random intercept 就是“基线项在不同组之间随机变化”的建模概念。

相关词 / Related Words

文献与著作中的用例 / Notable Works

  • Gelman & Hill, Data Analysis Using Regression and Multilevel/Hierarchical Models(多层/层级模型中系统讨论随机截距)
  • Pinheiro & Bates, Mixed-Effects Models in S and S-PLUS(混合效应模型的经典参考)
  • Snijders & Bosker, Multilevel Analysis(多层模型教材,常用随机截距示例)
  • Fitzmaurice, Laird & Ware, Applied Longitudinal Analysis(纵向数据分析中广泛使用随机截距)
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