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Constraints in Random Effects Age-Period-Cohort Models
Sociological Methodology ( IF 6.118 ) Pub Date : 2020-02-11 , DOI: 10.1177/0081175020903348
Liying Luo 1 , James S Hodges 2
Affiliation  

Random effects (RE) models have been widely used to study the contextual effects of structures such as neighborhoods or schools. The RE approach has recently been applied to age-period-cohort (APC) models that are unidentified because the predictors are exactly linearly dependent. However, research has not fully explained how the RE specification identifies these otherwise unidentified APC models. We address this challenge by first making explicit that RE-APC models have greater—not less—rank deficiency than the traditional fixed-effects model, followed by two empirical examples. We then provide intuition and a mathematical proof to explain that for APC models with one RE, treating one effect as an RE is equivalent to constraining the estimates of that effect’s linear component and the random intercept to be zero. For APC models with two REs, the effective constraints implied by the model depend on the true (i.e., in the data-generating mechanism) nonlinear components of the effects that are modeled as REs, so that the estimated linear components of the REs are determined by the true nonlinear components of those effects. In conclusion, RE-APC models impose arbitrary although highly obscure constraints and thus do not differ qualitatively from other constrained APC estimators.

中文翻译:

随机效应年龄-周期-队列模型中的约束

随机效应 (RE) 模型已广泛用于研究社区或学校等结构的背景效应。RE 方法最近已应用于未识别的年龄-周期-队列 (APC) 模型,因为预测变量完全线性相关。但是,研究尚未完全解释 RE 规范如何识别这些未识别的 APC 模型。我们通过首先明确表明 RE-APC 模型比传统的固定效应模型具有更大(而不是更少)的等级缺陷来应对这一挑战,然后是两个实证示例。然后我们提供直觉和数学证明来解释对于具有一个 RE 的 APC 模型,将一种效应视为 RE 等同于将该效应的线性分量和随机截距的估计值限制为零。对于具有两个 RE 的 APC 模型,模型隐含的有效约束取决于模拟为 RE 的效果的真实(即在数据生成机制中)非线性分量,因此 RE 的估计线性分量由那些真实非线性分量确定效果。总之,RE-APC 模型施加了任意但非常模糊的约束,因此与其他受约束的 APC 估计量没有定性差异。
更新日期:2020-02-11
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