Constrained Estimators and Age-Period-Cohort Models
Constrained Estimators and Age-Period-Cohort Models
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DOI：
10.1177/0049124111415367
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发表时间：
2011-08-01
影响因子：
6.3
通讯作者：
O'Brien, Robert M.
中科院分区：
文献类型：
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作者：
O'Brien, Robert M.
如果研究者想在年龄-时期-队列（age-period-cohort， APC）模型中估计个体的年龄、时期和队列系数，选择的方法是约束回归，其中包括Yang等人最近引入的内在估计器（intrinsic estimator， IE）。为了更好地理解这些约束模型，作者从代数上展示了每个约束是如何与一个特定的广义逆相关联的，该逆与一个特定的解向量相关联（当模型在约束下被识别时），该解向量产生APC模型的最小二乘解。然后，作者从解与约束正交、各种约束的解都位于多维空间中的一条直线上、各种解之间在那条直线上的距离以及零向量的关键作用等方面讨论了约束估计的几何。这提供了对所有约束估计器共有的特征以及IE的独特之处的洞察。本文的第一部分着重于一般的约束估计器（包括IE），后一部分比较和对比了传统约束APC估计器和IE的性质。最后，作者对研究人员使用和解释约束估计量提出了一些注意事项和建议。
If a researcher wants to estimate the individual age, period, and cohort coefficients in an age-period-cohort (APC) model, the method of choice is constrained regression, which includes the intrinsic estimator (IE) recently introduced by Yang and colleagues. To better understand these constrained models, the author shows algebraically how each constraint is associated with a specific generalized inverse that is associated with a particular solution vector that (when the model is just identified under the constraint) produces the least square solution to the APC model. The author then discusses the geometry of constrained estimators in terms of solutions being orthogonal to constraints, solutions to various constraints all lying on a line single line in multidimensional space, the distance on that line between various solutions, and the crucial role of the null vector. This provides insight into what characteristics all constrained estimators share and what is unique about the IE. The first part of the article focuses on constrained estimators in general (including the IE), and the latter part compares and contrasts the properties of traditionally constrained APC estimators and the IE. The author concludes with some cautions and suggestions for researchers using and interpreting constrained estimators.