Department of Public Health and Preventive Medicine, Oregon Health and Science University, Portland, OR, USA.
Stat Med. 2011 Dec 20;30(29):3403-15. doi: 10.1002/sim.4366. Epub 2011 Oct 14.
In medical and social studies, it is often desirable to assess the correlation between characteristics of interest that are not directly observable. In such cases, repeated measures are often available, but the correlation between the repeated measures is not the same as that between the true characteristics that are confounded with the measurement errors. The latter is called the hidden correlation. Previously, the problem has been treated by assuming prior knowledge about the measurement errors or by using relatively complex statistical models, such as the mixed-effects models, with no closed-form expression for the estimated hidden correlation. We propose a simple estimator of the hidden correlation that is very much like the Pearson correlation coefficient, with a closed-form expression, under assumptions much weaker than the mixed-effects model. Simulation results show that the proposed simple estimator performs similarly as the restricted maximum likelihood (REML) estimator in mixed models but is computationally much more efficient than REML. We also made simulation comparison with the Pearson correlation. We considered a real data example.
在医学和社会研究中，通常需要评估那些不可直接观测的感兴趣特征之间的相关性。在这种情况下，通常可以获得重复测量数据，但重复测量之间的相关性与存在测量误差的真实特征之间的相关性并不相同。后者称为隐藏相关性。以前，这个问题是通过假设测量误差的先验知识或使用相对复杂的统计模型（如混合效应模型）来处理的，这些模型没有用于估计隐藏相关性的闭式表达式。我们提出了一种简单的隐藏相关性估计量，它与 Pearson 相关系数非常相似，在比混合效应模型弱得多的假设下具有闭式表达式。模拟结果表明，在混合模型中，所提出的简单估计量与受限最大似然（REML）估计量的性能相似，但计算效率比 REML 高得多。我们还与 Pearson 相关系数进行了模拟比较。我们考虑了一个真实的数据示例。
